tag:blogger.com,1999:blog-352777652024-02-19T00:23:27.381-08:00Thoughts from a Bionic LimeTart and green musings on chess, ratings, data science, R, and life.Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.comBlogger180125tag:blogger.com,1999:blog-35277765.post-54635326797492367392020-03-09T07:26:00.000-07:002020-03-09T07:26:04.188-07:00Coronavirus and covid-19 chartsCoronavirus and covid-19 charts<br />
<br />
I have created an automated process, written in R, that takes data compiled for the <a href="https://www.arcgis.com/apps/opsdashboard/index.html#/bda7594740fd40299423467b48e9ecf6" target="_blank">Johns Hopkins covid-19 dashboard</a>, and publishes charts on <a href="https://twitter.com/bioniclime" target="_blank">my twitter feed</a> as the data is updated.<br />
<br />
There is a different chart for each country. The height of the bars on this chart show the number of confirmed cases, on a log-scaled Y axis. The colors within each bar are <b>linear </b>proportions of the number of active cases (yellow), deaths (red), and those that recovered (green). <br />
<br />
An example of the most recent chart for the USA is below.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtKnWdry5XE6jKOIve806HCgacI5ivA0UwT79Vnm6XbtVun96x_8ulXOCzmVQsdx7oVkxj41rjVaFuBGnVIM2SfnuZAWRZCPVcEC8dWZU6J4kxlx6860-L_c3zfiWvcQNkmuaJ/s1600/US+8+Mar+2020.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="1080" height="355" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtKnWdry5XE6jKOIve806HCgacI5ivA0UwT79Vnm6XbtVun96x_8ulXOCzmVQsdx7oVkxj41rjVaFuBGnVIM2SfnuZAWRZCPVcEC8dWZU6J4kxlx6860-L_c3zfiWvcQNkmuaJ/s640/US+8+Mar+2020.png" width="640" /></a></div>
<br />Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com0tag:blogger.com,1999:blog-35277765.post-26687348190244422842016-12-01T09:50:00.004-08:002017-01-31T06:35:23.865-08:00RTextTools demo error<br />
There is a nifty little "one-stop-shopping" text analytics package in R called "RTextTools" that was created by Timothy P. Jurka from UC-Davis. The package allows you to do a whole variety of text classification algorithms automatically, and with ease.<br />
<br />
However, it appears (and I cannot say this for sure, but that's what it seems like) that if you use it in R version 3.3.0 and later, there is a bug (at least in the demo). (It apparently does not occur in earlier versions of R.) The demo asks you to do the following:<br />
<br />
<span style="color: blue; font-family: "courier new" , "courier" , monospace; font-size: x-small;"><b>library(RTextTools)</b></span><br />
<span style="color: blue; font-family: "courier new" , "courier" , monospace; font-size: x-small;"><b>data(USCongress)</b></span><br />
<span style="color: blue; font-family: "courier new" , "courier" , monospace; font-size: x-small;"><b><br /></b></span>
<span style="color: blue; font-family: "courier new" , "courier" , monospace; font-size: x-small;"><b>doc_matrix &#60- create_matrix(USCongress$text,</b></span><br />
<span style="color: blue; font-family: "courier new" , "courier" , monospace; font-size: x-small;"><b> language = "english", </b></span><br />
<span style="color: blue; font-family: "courier new" , "courier" , monospace; font-size: x-small;"><b> removeNumbers = TRUE, </b></span><br />
<span style="color: blue; font-family: "courier new" , "courier" , monospace; font-size: x-small;"><b> stemWords = TRUE, </b></span><br />
<span style="color: blue; font-family: "courier new" , "courier" , monospace; font-size: x-small;"><b> removeSparseTerms = .998)</b></span><br />
<br />
The problem is that the following error occurs.<br />
<br />
<span style="color: #cc0000; font-family: "courier new" , "courier" , monospace; font-size: x-small;">Error in if (any(lens > lim)) stop("There is a limit of ", lim, "characters on the number of characters in a word being stemmed") : missing value where TRUE/FALSE needed</span><br />
<br />
One astute user (<a href="http://stackoverflow.com/users/1327739/lukea" target="_blank">lukeA</a>) on Stack Overflow discovered that the characters " NA " in the strings in your text fields are converted to an actual R object <span style="font-family: "courier new" , "courier" , monospace;">NA</span>. <br />
<a href="https://www.blogger.com/goog_730221740"><br /></a>
<a href="http://stackoverflow.com/questions/38199396/stemming-words-in-r-missing-value">http://stackoverflow.com/questions/38199396/stemming-words-in-r-missing-value</a><br />
<br />
Therefore, in order to fix this with the demo, you have to eliminate the two records in USCongress that have an NA lurking in the text. These are records 3674 and 3675. Therefore, prior to the create_matrix statement, you can fix this with:<br />
<br />
<span style="color: blue; font-family: "courier new" , "courier" , monospace; font-size: x-small;"><b>USCongress <- 3675="" b="" c="" uscongress=""></-></b></span><br />
<div>
<br /></div>
<div>
Once that line is there, the create_matrix field works, and you can continue with the demo.</div>
<div>
<br /></div>
Follow me on Twitter: @bioniclime<br />
<br />
<br />
<br />
<br />
<br />Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com0tag:blogger.com,1999:blog-35277765.post-23812253828593519582016-09-24T18:57:00.000-07:002016-09-24T18:57:03.609-07:00A Parent's Guide to Tournament Chess<i>I wrote this several years ago for a blog, but it has since been deleted, so I thought I would post it here.</i><br />
<b><br /></b>
<b>A Parent's Guide to Tournament Chess</b><br />
by Robert N. Bernard<br />
<br />
So your child has been playing chess for a while, and his or her chess teacher has suggested they play in a tournament. Your child begs you to play; "They even have trophies - big ones!", the child exclaims. You relent, and the chess teacher provides the time and place. How should you prepare? Once you get there, what should you expect?
<br />
<br />
Many kids' first tournaments are small, local get-togethers (of perhaps 10-20 participants), but some are noticeably larger. Most of what's written here applies to most of the tournaments in the USA and Canada, but there will always be some variation.<br />
<br />
Before the tournament - buy a tournament chess set, board, and scorebook. Plastic sets and vinyl boards work well, and, if your child is in elementary school, the spaces in which to write moves should be large enough to accommodate children's larger handwriting. Unless you have an older child who has played with a clock before, you will probably not need a clock at first, but if they play in more and more tournaments they will need one.<br />
<br />
On the morning of the tournament, there's Rule Number One - pack food. Chess tournaments on the weekend are held in elementary schools, roadside hotels, libraries, and multi-purpose rooms, and the dining options are usually limited to non-existent. You might think that you will have time between games to go out and get something, but don't count on it - the games are typically played in as short a time as possible.<br />
<br />
At the tournament, parents frequently are afraid that their child will lose their first game and then be sent home. In the vast majority of tournaments, this is not the case; each child will play one game for each round of the tournament - there are no eliminations. Also, larger tournaments are broken into sections by "ratings", a estimation of skill level of the player (more on ratings below), but in a child's first tournament, they will not have a rating and be called an "unrated" player. The tournament director determines the "pairings" (which child plays which other child) usually with help of a computer program. The pairings are usually posted on a wall or door on what's called the "pairing sheet", one for each section of the tournament. The pairing sheet is easy to find - it will be where the crowd gathers when the tournament director announces, "Pairings are up!". Each row of the pairing sheet first lists a "board number" that corresponds to a placard adjacent to a board on a table, the names of two players indicating who is to play what color (the player with the white pieces is listed first), and two columns which are blank, for the result (1 - 0 White wins; 0 - 1 Black wins; 0.5 - 0.5 draw).<br />
<br />
Pairings are determined using a method called the Swiss system. Essentially, the Swiss system (which is explained in more depth at the end of this article) dictates that kids should play other kids with the same score as themselves (where a win is worth 1 point, a draw 0.5 point, and a loss 0 points). For example, after three rounds of play, there may be a few kids who have won all their games and have 3 points - in the fourth round, they would play each other, while those kids with 1 total point (i.e., 1 win and 2 losses, or 2 draws and 1 loss) would play each other. In this way, kids with the same performance (and presumably similar skill levels) are more likely to play each other as the tournament progresses.<br />
<br />
After the pairings are posted, the child should go sit at the board they are assigned, and you should ensure they are sitting with the correct color of the pieces in front of them. At that point, you should stay with your child for a while until you are asked to leave the playing area. Unlike almost every other child sporting event (soccer, little league, swim meets), parents are (usually) not allowed to watch their child play. There are two reasons for this. First, it is to eliminate the possibility of having a parent signal a child. intentionally or unintentionally. Intentionally signaling is reprehensible, but unintentionally signaling (e.g., wincing or grimacing when your child is about to let go of a piece that will lose the game for the child, or smirking or chuckling when the child's opponent just made an obvious mistake) is far more common. Second, your child's opponent might very well be intimidated by you standing near the board, scowling.<br />
<br />
At the end of each game of kids' tournaments, tournament directors will usually have younger or more inexperienced kids raise their hands to summon a tournament director to verify the game is over, and help them record their results. Older or more experienced kids should simply clean up the pieces, and go to the pairing sheet and write the result. In either case, both players should record the result, and verify that it is correct. When mistakes happen in result recording, it is an ordeal that neither child, nor parent, nor especially tournament director wants to go through.<br />
<br />
While the game is going on, each parent has his or her own coping strategy; some read, some eat, some pace, some talk incessantly to anyone and everyone, but what all parents should realize is that - perhaps for the first time - your child is totally on their own, doing something by themselves, which is quite an accomplishment, especially if your child is on the young side.<br />
<br />
After each game, the child will come out of the room projecting some emotion between elation and bitter disappointment. Losses are hard on all chess players, children or adults - unlike most other games or sports, you cannot blame the loss on the luck of the dice or a bad bounce, only themselves. I do not recommend minimizing the loss, because it will have mattered to the child, but instead try to encourage and congratulate them on playing their first tournament game, and prepare them for the next one.<br />
<br />
Inevitably, your child will be asked "What's your rating?" and the child will then ask you about ratings. Ratings are a statistical measure of a player's approximate skill level, and in the USA, ratings range from a low of 100 to 2800 or more. (Note that it improper to use "chess ranking", when you mean a rating instead; when you rank something, a low number -- ranked number 1 -- indicates that it is the best, but a higher number is better in a rating scale.) A player receives a rating if they play in a rated tournament. For the first 25 games or so, ratings are determined by averaging each opponent's rating plus 400 if you beat that opponent, each opponent's rating if you drew that opponent, and each opponent's rating minus 400 if you lost to that opponent. For example, in your first tournament you beat opponents of ratings 800 and 900, draw an opponent rated 600, and lose to an opponent rated 700; your first rating would be (800+400) plus (900+400) plus (600+-0), plus (700-400), or 1200+1300+600+300 all divided by 4, which is 850. There are some complications if your opponent's ratings are very low, or if you win or lose all your games, but this is a rough estimate. Once your rating becomes established (i.e., you have played more than 25 games), the general guideline is that you will gain many rating points if you beat someone higher rated than you, lose many rating points if you lose to someone lower rated than you, gain only a few rating points if you beat someone lower rated than you, and lose only a few rating points if you lose to someone higher rated than you. If you are curious about the math behind all of this, the United States Chess Federation's rating system is explained <a href="http://www.glicko.net/ratings/rating.system.pdf">here</a>.<br />
<br />
Finally, after the tournament is over, be prepared for some sort of catharsis in the car, no matter the age of the child. Your child may talk excitedly for the next hour and not be able to sleep at night. Your child may weep inconsolably because every game was a loss. Both outpourings of emotion are healthy, and indicate that the tournament really meant something to the child. After the emotions are drained out of the child -- joy or despair -- keep your ears open, as you may very well hear, "When's the next tournament?"<br />
<br />
<b>Appendix: The Swiss System </b><br />
<br />
Here's an short description of the Swiss System of pairing opponents in chess tournaments. Refer also to the diagram below. Each step is marked with a circle around it.<br />
<br />
Step 1: At the beginning of the tournament, rank all the players from highest rating to lowest rating. Unrated players should be ranked lowest. The number given is called the "pairing number". In the example, Helen has pairing number 1 and David has pairing number 4.<br />
<br />
Step 2: Split the list of players into two equally sized groups, where the split occurs between the two middle pairing numbers. If there are an odd number of players, one player is given a "bye", which means that they get a full point for the round, but they do not have an opponent.<br />
<br />
Step 3: Pair the top half of the group with the bottom half of the group, but maintain the rankings in the top and bottom halves. You might expect that for 8 players, 1 would play 8, 2 would play 7, and so forth, but in a Swiss, 1 plays 5, 2 plays 6, etc. Alternate colors so that if 1 gets white, 2 gets black, and so on. Post these pairings on the pairing sheet.<br />
<br />
Step 4: Once the round is complete, record the results. 1-0 means white won, 0-1 means black won, and 0.5-0.5 is a draw. In the example, Helen beat Sadie, Mateo beat Dhiren, Julie beat Ming, and Chris beat David.<br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXlmiip3wE2stN5RoxJ9VUxpLLrRyBeRrogdMaVRGMPDVuYhLBfRGg-VOe0hzWBBAQtBjQkto4tVzlHXxon3SYRmsMBcQ4V1btQKmr5YlUeixraDwmHhp2OWfKKbOofMBfm6S0/s1600/swiss.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXlmiip3wE2stN5RoxJ9VUxpLLrRyBeRrogdMaVRGMPDVuYhLBfRGg-VOe0hzWBBAQtBjQkto4tVzlHXxon3SYRmsMBcQ4V1btQKmr5YlUeixraDwmHhp2OWfKKbOofMBfm6S0/s640/swiss.png" width="640" /></a>Step 5: In the next round (and all subsequent rounds), group players again, but this time by their total score. In the example, there are four players with 1 point, and four players with 0 points. Each of these is called a "score group". Within each score group, use the players' ranking numbers, and split them again.<br />
<br />
Step 6: For each score group, pair the top half of that score group with the bottom half of that score group. In this way, players with the same score will play each other. Try and maintain alternation of colors for each player (so they get white, black, white, black, etc., in each round).<br />
<br />
Step 7: Post the pairing sheet with the new pairings. In the example, Chris has white against Helen with black. Notice that both Chris and Helen have the same score (1 point) and that Helen was "due" black this
Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com0tag:blogger.com,1999:blog-35277765.post-12157801207827037112016-02-12T09:58:00.000-08:002017-01-31T06:35:33.840-08:00Counting objects in a vector in R<br />
There is an easy way to count the number of objects in a vector in R.... also known as getting your <span style="font-family: "courier new" , "courier" , monospace;">Freq</span><span style="font-family: "courier new" , "courier" , monospace; font-size: x-small;"> </span>on.<br />
<br />
Suppose you create a vector called <span style="font-family: "courier new" , "courier" , monospace;">myVec </span>with some elements in it, and you want to know the frequency (i.e., the count) of each object.<br />
<br />
Simply convert it into a <span style="font-family: "courier new" , "courier" , monospace;">table</span>, and then cast it <span style="font-family: "courier new" , "courier" , monospace;">as.data.frame</span>. The column names are the original vector name (<span style="font-family: "courier new" , "courier" , monospace;">myVec</span>) and <span style="font-family: "courier new" , "courier" , monospace;">Freq</span>.<br />
<br />
<pre style="background-color: #eeeeee; border: 1px dashed #999999; color: black; font-family: "andale mono" , "lucida console" , "monaco" , "fixed" , monospace; font-size: 12px; line-height: 14px; overflow: auto; padding: 5px; width: 100%;"> <code style="color: black; word-wrap: normal;">
> myVec <- c="" cat="" dog="" mouse=""> myDF <- as.data.frame="" myvec="" table=""> myDF
myVec Freq
1 cat 3
2 dog 1
3 mouse 2
</-></-></code>
</pre>
<br />
This also works if your vector is a column of a data frame as well.<br />
<br />
The mysteries of the R programming language revealed.<br />
<br />
Follow me on Twitter: @bioniclime<br />
<br />Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com0tag:blogger.com,1999:blog-35277765.post-16116851199107909062011-11-02T22:03:00.000-07:002011-11-02T22:06:50.977-07:00USCL Power Rankings Week 10 - Final<div><br /></div><div>The final regular season week of the United States Chess League has finished, and with that, I give to you the final week of the power rankings.</div><div><br /></div><div>The only big change was Miami dropping to 11th. Also notable is that Manhattan is ranked more powerful than Boston, even though Boston is a higher seed in the playoff structure.</div><div><br /></div><div>Here is how the final week looks.</div><div><br /><table cellpadding="2"><tbody><tr><td align="center"> Rank </td><td> Team </td><td> Score </td><td align="center"> Change </td></tr><tr><td align="center"> 1 - </td><td> Chicago </td><td> 1.000 </td><td align="center"> 0 </td></tr><tr><td align="center"> 2 - </td><td> Philadelphia </td><td> 0.955 </td><td align="center"> 0 </td></tr><tr><td align="center"> 3 - </td><td> Los Angeles </td><td> 0.859 </td><td align="center"> 0 </td></tr><tr><td align="center"> 4 - </td><td> New York </td><td> 0.838 </td><td align="center"> 0 </td></tr><tr><td align="center"> 5 - </td><td> Manhattan </td><td> 0.831 </td><td align="center"> 0 </td></tr><tr><td align="center"> 6 - </td><td> Boston </td><td> 0.815 </td><td align="center"> +1 </td></tr><tr><td align="center"> 7 - </td><td> San Francisco </td><td> 0.812 </td><td align="center"> +1 </td></tr><tr><td align="center"> 8 - </td><td> Dallas </td><td> 0.811 </td><td align="center"> +2 </td></tr><tr><td align="center"> 9 - </td><td> New England </td><td> 0.800 </td><td align="center"> 0 </td></tr><tr><td align="center"> 10 - </td><td> Arizona </td><td> 0.777 </td><td align="center"> +1 </td></tr><tr><td align="center"> 11 - </td><td> Miami </td><td> 0.771 </td><td align="center"> -5 </td></tr><tr><td align="center"> 12 - </td><td> Seattle </td><td> 0.685 </td><td align="center"> +1 </td></tr><tr><td align="center"> 13 - </td><td> Baltimore </td><td> 0.683 </td><td align="center"> -1 </td></tr><tr><td align="center"> 14 - </td><td> Carolina </td><td> 0.651 </td><td align="center"> 0 </td></tr><tr><td align="center"> 15 - </td><td> New Jersey </td><td> 0.645 </td><td align="center"> 0 </td></tr><tr><td align="center"> 16 - </td><td> St. Louis </td><td> 0.616 </td><td align="center"> 0 </td></tr></tbody></table><br /></div><div><br /></div><div>Good luck to all the teams in the playoffs!</div><div><br /></div>Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com0tag:blogger.com,1999:blog-35277765.post-68438844224339594302011-10-26T22:38:00.000-07:002011-10-26T22:45:10.119-07:00USCL Power Rankings Week 9<div><br /></div><div>The penultimate week of the power rankings are here. The top 5 stay the same, although New York and Los Angeles swapped 3rd and 4th.</div><div><br /></div><div>Miami moves up three spots at the expense of Dallas, which falls three spots. Indeed, Miami is in 6th place, only a hair behind Manhattan. </div><div><br /></div><div>Comparing to the actual USCL standings, the power rankings are very similar, except that Manhattan is ranked more powerful than Boston, even though Boston is ahead in the standings.</div><div><br /></div><div>As a side note, summing the power scores, the West is rated slightly more powerful than the East.<br /><br /><table cellpadding="2"><tbody><tr><td align="center"> Rank </td><td> Team </td><td> Score </td><td align="center"> Change </td></tr><tr><td align="center"> 1 - </td><td> Chicago </td><td> 1.000 </td><td align="center"> 0 </td></tr><tr><td align="center"> 2 - </td><td> Philadelphia </td><td> 0.914 </td><td align="center"> 0 </td></tr><tr><td align="center"> 3 - </td><td> Los Angeles </td><td> 0.850 </td><td align="center"> +1 </td></tr><tr><td align="center"> 4 - </td><td> New York </td><td> 0.837 </td><td align="center"> -1 </td></tr><tr><td align="center"> 5 - </td><td> Manhattan </td><td> 0.788 </td><td align="center"> 0 </td></tr><tr><td align="center"> 6 - </td><td> Miami </td><td> 0.788 </td><td align="center"> +3 </td></tr><tr><td align="center"> 7 - </td><td> Boston </td><td> 0.777 </td><td align="center"> +1 </td></tr><tr><td align="center"> 8 - </td><td> San Francisco </td><td> 0.773 </td><td align="center"> -2 </td></tr><tr><td align="center"> 9 - </td><td> New England </td><td> 0.763 </td><td align="center"> +1 </td></tr><tr><td align="center"> 10 - </td><td> Dallas </td><td> 0.754 </td><td align="center"> -3 </td></tr><tr><td align="center"> 11 - </td><td> Arizona </td><td> 0.741 </td><td align="center"> 0 </td></tr><tr><td align="center"> 12 - </td><td> Baltimore </td><td> 0.681 </td><td align="center"> 0 </td></tr><tr><td align="center"> 13 - </td><td> Seattle </td><td> 0.652 </td><td align="center"> +1 </td></tr><tr><td align="center"> 14 - </td><td> Carolina </td><td> 0.648 </td><td align="center"> -1 </td></tr><tr><td align="center"> 15 - </td><td> New Jersey </td><td> 0.644 </td><td align="center"> 0 </td></tr><tr><td align="center"> 16 - </td><td> St. Louis </td><td> 0.607 </td><td align="center"> 0 </td></tr></tbody></table><br /><br /></div>Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com0tag:blogger.com,1999:blog-35277765.post-29310201658990205962011-10-21T21:08:00.000-07:002011-10-21T21:21:39.125-07:00USCL Season Simulation 2011 (end of Week 8)Week 8 has ended, and another set of simulations has been completed. Unlike the midweek simulations, I only needed 100,000 runs for each division to get some interesting results.<div><div><br /></div><div>Once again, the chances that the team will make the playoffs, be in the top 2, and win the division.</div><div><br /><div>Here are the results (to three significant digits).</div><div><br /><span style="font-weight: bold; ">Western Division (based on 100,000 simulations)</span><br /><font="courier"><br /><table cellpadding="2"><tbody><tr><td align="left"><span class="Apple-style-span">Team</span></td><td align="right"><span class="Apple-style-span">Playoffs</span></td><td align="right"><span class="Apple-style-span"> Top 2</span></td><td align="right"><span class="Apple-style-span">Number 1</span></td></tr><tr><td align="left"><span class="Apple-style-span">Arizona</span></td><td align="right"><span class="Apple-style-span">35.0%</span></td><td align="right"><span class="Apple-style-span">2.20%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Chicago</span></td><td align="right"><span class="Apple-style-span">100%</span></td><td align="right"><span class="Apple-style-span">100%</span></td><td align="right"><span class="Apple-style-span">100%</span></td></tr><tr><td align="left"><span class="Apple-style-span">San Francisco</span></td><td align="right"><span class="Apple-style-span">71.0%</span></td><td align="right"><span class="Apple-style-span">6.23%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">St. Louis</span></td><td align="right">0%</td><td align="right"><span class="Apple-style-span">0%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Seattle</span></td><td align="right"><span class="Apple-style-span">0.339%</span></td><td align="right"><span class="Apple-style-span">0%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Miami</span></td><td align="right"><span class="Apple-style-span">44.2%</span></td><td align="right"><span class="Apple-style-span">1.45%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Los Angeles</span></td><td align="right"><span class="Apple-style-span">99.9%</span></td><td align="right"><span class="Apple-style-span">90.0%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Dallas</span></td><td align="right"><span class="Apple-style-span">55.9%</span></td><td align="right"><span class="Apple-style-span">2.78%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr></tbody></table><p><span class="Apple-style-span"><span style="font-weight: bold; ">Eastern Division (based on 100,000 simulations)</span></span></p><font="courier"><table cellpadding="2"><tbody><tr><td align="left"><span class="Apple-style-span">Team</span></td><td align="right"><span class="Apple-style-span">Playoffs</span></td><td align="right"><span class="Apple-style-span"> Top 2</span></td><td align="right"><span class="Apple-style-span">Number 1</span></td></tr><tr><td align="left"><span class="Apple-style-span">New England</span></td><td align="right"><span class="Apple-style-span">33.1%</span></td><td align="right"><span class="Apple-style-span">0%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Boston</span></td><td align="right"><span class="Apple-style-span">51.1%</span></td><td align="right"><span class="Apple-style-span">0.239%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">New York</span></td><td align="right"><span class="Apple-style-span">100%</span></td><td align="right"><span class="Apple-style-span">92.6%</span></td><td align="right"><span class="Apple-style-span">41.4%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Baltimore</span></td><td align="right"><span class="Apple-style-span">17.8%</span></td><td align="right"><span class="Apple-style-span">0%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Manhattan</span></td><td align="right"><span class="Apple-style-span">90.9%</span></td><td align="right"><span class="Apple-style-span">16.0%</span></td><td align="right"><span class="Apple-style-span">0.728%</span></td></tr><tr><td align="left"><span class="Apple-style-span">New Jersey</span></td><td align="right"><span class="Apple-style-span">0%</span></td><td align="right"><span class="Apple-style-span">0%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Philadelphia</span></td><td align="right"><span class="Apple-style-span">100%</span></td><td align="right"><span class="Apple-style-span">92.6%</span></td><td align="right"><span class="Apple-style-span">58.9%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Carolina</span></td><td align="right"><span class="Apple-style-span">9.95%</span></td><td align="right"><span class="Apple-style-span">0.792%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr></tbody></table><br /><p>Again, if you have suggested scenarios, please comment with your requests.<br /><br /><br /></p><p><br /></p></font="courier"></font="courier"></div></div></div>Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com0tag:blogger.com,1999:blog-35277765.post-66297161366207892092011-10-21T20:57:00.000-07:002011-10-21T21:01:51.144-07:00USCL Power Rankings Week 8<div><br /></div><div>Very little change at the top of the power rankings this week - the top four teams maintain their position. Manhattan vaults over Dallas and San Francisco to end up in fifth.</div><div><br /></div><div>Boston and Miami also both make big jumps, while Baltimore falls four places to twelfth. </div><div><br /></div><div>New Jersey drags itself out of the basement, and St. Louis takes New Jersey's place there.<br /><br /><br /><table cellpadding="2"><tbody><tr><td align="center"> Rank </td><td> Team </td><td> Score </td><td align="center"> Change </td></tr><tr><td align="center"> 1 - </td><td> Chicago </td><td> 1.000 </td><td align="center"> 0 </td></tr><tr><td align="center"> 2 - </td><td> Philadelphia </td><td> 0.847 </td><td align="center"> 0 </td></tr><tr><td align="center"> 3 - </td><td> New York </td><td> 0.835 </td><td align="center"> 0 </td></tr><tr><td align="center"> 4 - </td><td> Los Angeles </td><td> 0.811 </td><td align="center"> 0 </td></tr><tr><td align="center"> 5 - </td><td> Manhattan </td><td> 0.764 </td><td align="center"> +2 </td></tr><tr><td align="center"> 6 - </td><td> Dallas </td><td> 0.734 </td><td align="center"> -1 </td></tr><tr><td align="center"> 7 - </td><td> San Francisco </td><td> 0.715 </td><td align="center"> -1 </td></tr><tr><td align="center"> 8 - </td><td> Boston </td><td> 0.708 </td><td align="center"> +3 </td></tr><tr><td align="center"> 9 - </td><td> Miami </td><td> 0.697 </td><td align="center"> +3 </td></tr><tr><td align="center"> 10 - </td><td> New England </td><td> 0.693 </td><td align="center"> -1 </td></tr><tr><td align="center"> 11 - </td><td> Arizona </td><td> 0.685 </td><td align="center"> -1 </td></tr><tr><td align="center"> 12 - </td><td> Baltimore </td><td> 0.671 </td><td align="center"> -4 </td></tr><tr><td align="center"> 13 - </td><td> Carolina </td><td> 0.627 </td><td align="center"> 0 </td></tr><tr><td align="center"> 14 - </td><td> Seattle </td><td> 0.620 </td><td align="center"> 0 </td></tr><tr><td align="center"> 15 - </td><td> New Jersey </td><td> 0.565 </td><td align="center"> +1 </td></tr><tr><td align="center"> 16 - </td><td> St. Louis </td><td> 0.564 </td><td align="center"> -1 </td></tr></tbody></table><br /><br /></div>Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com0tag:blogger.com,1999:blog-35277765.post-20065315862166170532011-10-18T17:02:00.000-07:002011-10-18T17:43:41.254-07:00USCL Season Simulation Midweek 8It is middle of week 8 in the USCL, and half the teams have played their matches this week. Therefore I ran simulations again.<div><br /></div><div>The interesting thing was that when I ran 100,000 simulations for the Eastern Division, both Philadelphia and New York always made it into the playoffs. There's a chance, however unlikely, that one of those teams will not make it into the playoffs. Therefore, I ran it again, but this time with 2,500,000 simulations. In only one of those simulations, Philadelphia did not make it. So, Philly, don't coast now!<br /><br /><div>Here are the results.</div><div><br /><span style="font-weight: bold; ">Western Division (based on 100,000 simulations)</span><br /><font="courier"><br /><table cellpadding="2"><tbody><tr><td align="left"><span class="Apple-style-span">Team</span></td><td align="right"><span class="Apple-style-span">Playoffs</span></td><td align="right"><span class="Apple-style-span"> Top 2</span></td><td align="right"><span class="Apple-style-span">Number 1</span></td></tr><tr><td align="left"><span class="Apple-style-span">Arizona</span></td><td align="right"><span class="Apple-style-span">35.4%</span></td><td align="right"><span class="Apple-style-span">1.67%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Chicago</span></td><td align="right"><span class="Apple-style-span">100%</span></td><td align="right"><span class="Apple-style-span">99.981%</span></td><td align="right"><span class="Apple-style-span">99.0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">San Francisco</span></td><td align="right"><span class="Apple-style-span">71.1%</span></td><td align="right"><span class="Apple-style-span">5.67%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">St. Louis</span></td><td align="right"><span class="Apple-style-span">1.14%</span></td><td align="right"><span class="Apple-style-span">0%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Seattle</span></td><td align="right"><span class="Apple-style-span">0.584%</span></td><td align="right"><span class="Apple-style-span">0%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Miami</span></td><td align="right"><span class="Apple-style-span">20.6%</span></td><td align="right"><span class="Apple-style-span">0.366%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Los Angeles</span></td><td align="right"><span class="Apple-style-span">99.68%</span></td><td align="right"><span class="Apple-style-span">81.4%</span></td><td align="right"><span class="Apple-style-span">1.22%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Dallas</span></td><td align="right"><span class="Apple-style-span">79.3%</span></td><td align="right"><span class="Apple-style-span">14.9%</span></td><td align="right"><span class="Apple-style-span">0.122%</span></td></tr></tbody></table><p><span class="Apple-style-span"><span style="font-weight: bold; ">Eastern Division (based on 2,500,000 simulations)</span></span></p><font="courier"><table cellpadding="2"><tbody><tr><td align="left"><span class="Apple-style-span">Team</span></td><td align="right"><span class="Apple-style-span">Playoffs</span></td><td align="right"><span class="Apple-style-span"> Top 2</span></td><td align="right"><span class="Apple-style-span">Number 1</span></td></tr><tr><td align="left"><span class="Apple-style-span">New England</span></td><td align="right"><span class="Apple-style-span">37.7%</span></td><td align="right"><span class="Apple-style-span">0.763%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Boston</span></td><td align="right"><span class="Apple-style-span">51.0%</span></td><td align="right"><span class="Apple-style-span">0.274%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">New York</span></td><td align="right"><span class="Apple-style-span">99.989%</span></td><td align="right"><span class="Apple-style-span">96.0%</span></td><td align="right"><span class="Apple-style-span">41.6%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Baltimore</span></td><td align="right"><span class="Apple-style-span">38.3%</span></td><td align="right"><span class="Apple-style-span">0.654%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Manhattan</span></td><td align="right"><span class="Apple-style-span">66.4%</span></td><td align="right"><span class="Apple-style-span">7.06%</span></td><td align="right"><span class="Apple-style-span">0.252%</span></td></tr><tr><td align="left"><span class="Apple-style-span">New Jersey</span></td><td align="right"><span class="Apple-style-span">0.0568%</span></td><td align="right"><span class="Apple-style-span">0%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Philadelphia</span></td><td align="right"><span class="Apple-style-span">99.99996%</span></td><td align="right"><span class="Apple-style-span">96.6%</span></td><td align="right"><span class="Apple-style-span">58.9%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Carolina</span></td><td align="right"><span class="Apple-style-span">10.5%</span></td><td align="right"><span class="Apple-style-span">0.792%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr></tbody></table><br /><p>A scenario has been requested, and I will mention it in the comments.<br /><br /><br /></p><p><br /></p></font="courier"></font="courier"></div></div>Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com1tag:blogger.com,1999:blog-35277765.post-496163674983407292011-10-15T03:10:00.000-07:002011-10-15T04:02:50.069-07:00USCL Season Simulation 2011Last year, I created a simulation of possible outcomes for the remainder of the United States Chess League season, to project the chances each team has of making the playoffs.<div><br /></div><div>As there are three weeks left, I decided to run another set of simulations this year.<div><br />Once again, here are the assumptions.<br /><ol><li>All teams have the same strength. Therefore, they have the same chances in each match against their opponents.<br /></li><li>The game point results of the match follow the historical distribution of USCL matches (which is <a href="http://www.uschessleague.com/Stats.html">here</a>). That is, 2.5-1.5 is more common than 3-1, which is more common than 3.5-0.5, etc.</li><li>If a team was tied for a playoff spot with the same match and game points, I said they both would make the playoffs -- I didn't go beyond the first tiebreaker.</li></ol>I ran 100,000 simulations for both the Eastern and Western division. Here are the results.</div><div><br /><span style="font-weight: bold; ">Western Division</span><br /><font="courier"><br /><table cellpadding="2"><tbody><tr><td align="left"><span class="Apple-style-span">Team</span></td><td align="right"><span class="Apple-style-span">Playoffs</span></td><td align="right"><span class="Apple-style-span"> Top 2</span></td><td align="right"><span class="Apple-style-span">Number 1</span></td></tr><tr><td align="left"><span class="Apple-style-span">Arizona</span></td><td align="right"><span class="Apple-style-span">39.322%</span></td><td align="right"><span class="Apple-style-span">6.648%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Chicago</span></td><td align="right"><span class="Apple-style-span">100.000%</span></td><td align="right"><span class="Apple-style-span">99.995%</span></td><td align="right"><span class="Apple-style-span">99.596%</span></td></tr><tr><td align="left"><span class="Apple-style-span">San Francisco</span></td><td align="right"><span class="Apple-style-span">65.377%</span></td><td align="right"><span class="Apple-style-span">16.010%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">St. Louis</span></td><td align="right"><span class="Apple-style-span">0.905%</span></td><td align="right"><span class="Apple-style-span">0%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Seattle</span></td><td align="right"><span class="Apple-style-span">11.293%</span></td><td align="right"><span class="Apple-style-span">0.889%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Miami</span></td><td align="right"><span class="Apple-style-span">19.010%</span></td><td align="right"><span class="Apple-style-span">1.242%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Los Angeles</span></td><td align="right"><span class="Apple-style-span">90.735%</span></td><td align="right"><span class="Apple-style-span">51.724%</span></td><td align="right"><span class="Apple-style-span">0.381%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Dallas</span></td><td align="right"><span class="Apple-style-span">80.074%</span></td><td align="right"><span class="Apple-style-span">28.023%</span></td><td align="right"><span class="Apple-style-span">0.146%</span></td></tr></tbody></table><p><span class="Apple-style-span"><span style="font-weight: bold; ">Eastern Division</span></span></p><font="courier"><table cellpadding="2"><tbody><tr><td align="left"><span class="Apple-style-span">Team</span></td><td align="right"><span class="Apple-style-span">Playoffs</span></td><td align="right"><span class="Apple-style-span"> Top 2</span></td><td align="right"><span class="Apple-style-span">Number 1</span></td></tr><tr><td align="left"><span class="Apple-style-span">New England</span></td><td align="right"><span class="Apple-style-span">39.508%</span></td><td align="right"><span class="Apple-style-span">1.464%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Boston</span></td><td align="right"><span class="Apple-style-span">27.179%</span></td><td align="right"><span class="Apple-style-span">0.501%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">New York</span></td><td align="right"><span class="Apple-style-span">99.982%</span></td><td align="right"><span class="Apple-style-span">93.277%</span></td><td align="right"><span class="Apple-style-span">43.467%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Baltimore</span></td><td align="right"><span class="Apple-style-span">38.095%</span></td><td align="right"><span class="Apple-style-span">1.378%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Manhattan</span></td><td align="right"><span class="Apple-style-span">67.278%</span></td><td align="right"><span class="Apple-style-span">9.757%</span></td><td align="right"><span class="Apple-style-span">0.357%</span></td></tr><tr><td align="left"><span class="Apple-style-span">New Jersey</span></td><td align="right"><span class="Apple-style-span">0.045%</span></td><td align="right"><span class="Apple-style-span">0%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Philadelphia</span></td><td align="right"><span class="Apple-style-span">99.988%</span></td><td align="right"><span class="Apple-style-span">94.578%</span></td><td align="right"><span class="Apple-style-span">57.171%</span></td></tr><tr><td align="left"><span class="Apple-style-span">Carolina</span></td><td align="right"><span class="Apple-style-span">31.810%</span></td><td align="right"><span class="Apple-style-span">0.792%</span></td><td align="right"><span class="Apple-style-span">0%</span></td></tr></tbody></table><br /><p>Any scenarios you want me to run? Things like: If NJ wins the remainder of their matches 4-0, what's their chance to get in the playoffs... things like that....<br /><br />Let me know in the comments...</p><p><br /></p></font="courier"></font="courier"></div></div>Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com2tag:blogger.com,1999:blog-35277765.post-44457187714577491122011-10-15T02:14:00.000-07:002011-10-15T02:25:05.815-07:00USCL Power Rankings Week 7<div><br /></div><div>The power rankings are finally here this week!</div><div><br /></div><div>No big changes at the top and the bottom. Chicago and its perfect record outpace the rest of the field, with Philadelphia and New York in second and third. </div><div><br /></div><div>There is a logjam in the middle of the Eastern Division standings, with four teams having 3.0 match points, with their tiebreaking game points ranking them as follows: New England, Baltimore, Carolina, Boston. However, the power rankings say that the most powerful team in of these four is not New England, but Baltimore instead, and indeed, Boston is more powerful than Carolina.</div><div><br />Until next week!<br /><br /><table cellpadding="2"><tbody><tr><td align="center"><b> Rank </b></td><td><b> Team </b></td><td><b> Score </b></td><td align="center"><b> Change </b></td></tr><tr><td align="center"> 1 - </td><td> Chicago </td><td> 1.000 </td><td align="center"> 0 </td></tr><tr><td align="center"> 2 - </td><td> Philadelphia </td><td> 0.860 </td><td align="center"> 0 </td></tr><tr><td align="center"> 3 - </td><td> New York </td><td> 0.845 </td><td align="center"> 0 </td></tr><tr><td align="center"> 4 - </td><td> Los Angeles </td><td> 0.794 </td><td align="center"> +1 </td></tr><tr><td align="center"> 5 - </td><td> Dallas </td><td> 0.745 </td><td align="center"> +2 </td></tr><tr><td align="center"> 6 - </td><td> San Francisco </td><td> 0.743 </td><td align="center"> 0 </td></tr><tr><td align="center"> 7 - </td><td> Manhattan </td><td> 0.739 </td><td align="center"> -3 </td></tr><tr><td align="center"> 8 - </td><td> Baltimore </td><td> 0.707 </td><td align="center"> 0 </td></tr><tr><td align="center"> 9 - </td><td> New England </td><td> 0.700 </td><td align="center"> +5 </td></tr><tr><td align="center"> 10 - </td><td> Arizona </td><td> 0.681 </td><td align="center"> +1 </td></tr><tr><td align="center"> 11 - </td><td> Boston </td><td> 0.678 </td><td align="center"> -2 </td></tr><tr><td align="center"> 12 - </td><td> Miami </td><td> 0.671 </td><td align="center"> -2 </td></tr><tr><td align="center"> 13 - </td><td> Carolina </td><td> 0.664 </td><td align="center"> -1 </td></tr><tr><td align="center"> 14 - </td><td> Seattle </td><td> 0.653 </td><td align="center"> -1 </td></tr><tr><td align="center"> 15 - </td><td> St. Louis </td><td> 0.594 </td><td align="center"> 0 </td></tr><tr><td align="center"> 16 - </td><td> New Jersey </td><td> 0.555 </td><td align="center"> 0 </td></tr></tbody></table><br /><br /></div>Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com0tag:blogger.com,1999:blog-35277765.post-24400062386850644482011-10-06T17:14:00.000-07:002011-10-06T17:19:07.718-07:00USCL Power Rankings Week 6<div><br /></div><div><br /></div><div>Because interdivisional week just completed, the power rankings are now combined into one table.</div><div><br /></div><div>Unsurprisingly, Chicago holds the top spot, with a huge gap between them and the second place team. Indeed, teams two, three, and four are all from the Eastern Division, with Philadelphia barely edging out New York for second. Los Angeles is more powerful than San Francisco, even though the Mechanics are ahead of the Vibe in the official standings. In the battle of the basement, the Knockouts fall below the Arch Bishops.</div><div><br /></div><div><b><span class="Apple-style-span" >COMBINED POWER RANKINGS</span></b><br /><br /><table cellpadding="2"><tbody><tr><td align="center"> Rank </td><td> Team </td><td> Score </td><td align="center"> Change </td></tr><tr><td align="center"> 1 - </td><td> Chicago </td><td> 1.000 </td><td align="center"> 0 </td></tr><tr><td align="center"> 2 - </td><td> Philadelphia </td><td> 0.837 </td><td align="center"> 0 </td></tr><tr><td align="center"> 3 - </td><td> New York </td><td> 0.836 </td><td align="center"> 0 </td></tr><tr><td align="center"> 4 - </td><td> Manhattan </td><td> 0.789 </td><td align="center"> 0 </td></tr><tr><td align="center"> 5 - </td><td> Los Angeles </td><td> 0.774 </td><td align="center"> 0 </td></tr><tr><td align="center"> 6 - </td><td> San Francisco </td><td> 0.760 </td><td align="center"> 0 </td></tr><tr><td align="center"> 7 - </td><td> Dallas </td><td> 0.748 </td><td align="center"> 0 </td></tr><tr><td align="center"> 8 - </td><td> Baltimore </td><td> 0.706 </td><td align="center"> 0 </td></tr><tr><td align="center"> 9 - </td><td> Boston </td><td> 0.697 </td><td align="center"> 0 </td></tr><tr><td align="center"> 10 - </td><td> Miami </td><td> 0.693 </td><td align="center"> 0 </td></tr><tr><td align="center"> 11 - </td><td> Arizona </td><td> 0.678 </td><td align="center"> 0 </td></tr><tr><td align="center"> 12 - </td><td> Carolina </td><td> 0.661 </td><td align="center"> 0 </td></tr><tr><td align="center"> 13 - </td><td> Seattle </td><td> 0.661 </td><td align="center"> 0 </td></tr><tr><td align="center"> 14 - </td><td> New England </td><td> 0.657 </td><td align="center"> 0 </td></tr><tr><td align="center"> 15 - </td><td> St. Louis </td><td> 0.579 </td><td align="center"> 0 </td></tr><tr><td align="center"> 16 - </td><td> New Jersey </td><td> 0.560 </td><td align="center"> 0 </td></tr></tbody></table><br /><br /></div>Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com0tag:blogger.com,1999:blog-35277765.post-32282800596420801972011-09-28T21:31:00.000-07:002011-09-28T21:48:31.353-07:00USCL Power Rankings Week 5<div><br /></div><div>Exciting baseball tonight. My Orioles (always #1 to me) pulled off a great victory against the Red Sox (my #2 team). Sox collapsed, and the Rays have more of a chance to crush the hapless and worthless Yankees.</div><div><br /></div><div>Oh wait, this is chess.</div><div><br /></div><div>So, week 5 in the power rankings show the continued dominance of Chicago in the West. The California teams are closely knotted in second and third, Dallas and Miami are separated by a mere 0.004 in fourth and fifth, and Seattle and Miami by an even smaller 0.001 in sixth and seventh.</div><div><br /></div><div>In the East, the surprising Philadelphia Inventors grab the top spot in the power rankings, with the NYC teams (Knights and Applesauce) following in second and third. But notice that the power differential between first place Philadelphia and cellar-dwelling eighth place New Jersey is very close to the differential between the first (Chicago) and fourth (Dallas) place teams in the West. This suggests that the East teams are closer in strength to each other, while the West teams are more variable.<br /></div><div><br /></div><div><b>EASTERN DIVISION</b><br /><br /><table cellpadding="2"><tbody><tr><td align="center"> Rank </td><td> Team </td><td> Score </td><td align="center"> Change </td></tr><tr><td align="center"> 1 - </td><td> Philadelphia </td><td> 1.000 </td><td align="center"> +4 </td></tr><tr><td align="center"> 2 - </td><td> New York </td><td> 0.981 </td><td align="center"> -1 </td></tr><tr><td align="center"> 3 - </td><td> Manhattan </td><td> 0.951 </td><td align="center"> -1 </td></tr><tr><td align="center"> 4 - </td><td> Baltimore </td><td> 0.847 </td><td align="center"> 0 </td></tr><tr><td align="center"> 5 - </td><td> Carolina </td><td> 0.831 </td><td align="center"> +1 </td></tr><tr><td align="center"> 6 - </td><td> Boston </td><td> 0.826 </td><td align="center"> -3 </td></tr><tr><td align="center"> 7 - </td><td> New England </td><td> 0.769 </td><td align="center"> +1 </td></tr><tr><td align="center"> 8 - </td><td> New Jersey </td><td> 0.705 </td><td align="center"> -1 </td></tr></tbody></table><br /><br /></div><div><b>WESTERN DIVISION</b><br /><br /><table cellpadding="2"><tbody><tr><td align="center"> Rank </td><td> Team </td><td> Score </td><td align="center"> Change </td></tr><tr><td align="center"> 1 - </td><td> Chicago </td><td> 1.000 </td><td align="center"> 0 </td></tr><tr><td align="center"> 2 - </td><td> San Francisco </td><td> 0.780 </td><td align="center"> 0 </td></tr><tr><td align="center"> 3 - </td><td> Los Angeles </td><td> 0.777 </td><td align="center"> +2 </td></tr><tr><td align="center"> 4 - </td><td> Dallas </td><td> 0.753 </td><td align="center"> -1 </td></tr><tr><td align="center"> 5 - </td><td> Miami </td><td> 0.671 </td><td align="center"> -1 </td></tr><tr><td align="center"> 6 - </td><td> Seattle </td><td> 0.668 </td><td align="center"> 0 </td></tr><tr><td align="center"> 7 - </td><td> Arizona </td><td> 0.614 </td><td align="center"> 0 </td></tr><tr><td align="center"> 8 - </td><td> St. Louis </td><td> 0.568 </td><td align="center"> 0 </td></tr></tbody></table><br />Next week is Inter-division Week, and the power rankings will be combined into one list.</div><div><br /></div>Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com0tag:blogger.com,1999:blog-35277765.post-21350981393034028972011-09-21T22:02:00.000-07:002011-09-21T22:16:13.897-07:00USCL Power Rankings Week 4<div><br /></div><div>Power rankings this week show a lot of movement in the Eastern Division, but holding steady at the top of the Western Division.</div><div><br /></div><div>In the East, the New York Knights take the top spot away from Boston, which dropped to third. The New Jersey Knockouts move out of the cellar, leaving the Nor'easters in that dubious spot, but just barely, with only 0.005 Power Points separating them.</div><div><br /></div><div>In the West, the Chicago Blaze remain at the top, but with an astounding 0.220 Power Points separating them from the Mechanics, which remain number two. Despite Finegold's excellent individual record, the Arch Bishops remain at the bottom.</div><div><br /></div><div><b>Eastern Division</b></div><div><br /></div><div><table cellpadding="2"><tbody><tr><td align="center"> Rank </td><td> Team </td><td> Score </td><td align="center"> Change </td></tr> <tr><td align="center"> 1 - </td><td> New York </td><td> 1.000 </td><td align="center"> +2 </td></tr> <tr><td align="center"> 2 - </td><td> Manhattan </td><td> 0.944 </td><td align="center"> 0 </td></tr> <tr><td align="center"> 3 - </td><td> Boston </td><td> 0.931 </td><td align="center"> -2 </td></tr> <tr><td align="center"> 4 - </td><td> Baltimore </td><td> 0.912 </td><td align="center"> +2 </td></tr> <tr><td align="center"> 5 - </td><td> Philadelphia </td><td> 0.902 </td><td align="center"> 0 </td></tr> <tr><td align="center"> 6 - </td><td> Carolina </td><td> 0.831 </td><td align="center"> -2 </td></tr> <tr><td align="center"> 7 - </td><td> New Jersey </td><td> 0.669 </td><td align="center"> +1 </td></tr> <tr><td align="center"> 8 - </td><td> New England </td><td> 0.664 </td><td align="center"> -1 </td></tr></tbody></table> <br /><br /></div><div><b>Western Division</b></div><div><br /></div><div><table cellpadding="2"><tbody><tr><td align="center"> Rank </td><td> Team </td><td> Score </td><td align="center"> Change </td></tr> <tr><td align="center"> 1 - </td><td> Chicago </td><td> 1.000 </td><td align="center"> 0 </td></tr> <tr><td align="center"> 2 - </td><td> San Francisco </td><td> 0.780 </td><td align="center"> 0 </td></tr> <tr><td align="center"> 3 - </td><td> Dallas </td><td> 0.777 </td><td align="center"> 0 </td></tr> <tr><td align="center"> 4 - </td><td> Miami </td><td> 0.753 </td><td align="center"> +2 </td></tr> <tr><td align="center"> 5 - </td><td> Los Angeles </td><td> 0.671 </td><td align="center"> -1 </td></tr> <tr><td align="center"> 6 - </td><td> Seattle </td><td> 0.668 </td><td align="center"> +1 </td></tr> <tr><td align="center"> 7 - </td><td> Arizona </td><td> 0.614 </td><td align="center"> -2 </td></tr> <tr><td align="center"> 8 - </td><td> St. Louis </td><td> 0.568 </td><td align="center"> 0 </td></tr></tbody></table> <br /></div><div>Until next week!</div><div><br /></div>Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com0tag:blogger.com,1999:blog-35277765.post-69500870612242894422011-09-14T21:45:00.000-07:002011-09-14T21:55:58.338-07:00USCL Power Rankings Week 3<div><br /></div><div><br /></div><div>United States Chess League, Power rankings. Week 3... Not much surprise this week, as the power rankings exactly match the standings.</div><div><br /></div><div>Power is pretty evenly spaced in the Eastern Division, except at the top, where Manhattan barely trails Boston. </div><div><br /></div><div>Chicago sits atop the Western Division, followed by San Francisco and Dallas, with a tightly spaced pack from fourth to seventh.</div><div><br /></div><div><br /></div><div><b>Eastern Division</b></div><div><br /><table cellpadding="2"><tbody><tr><td align="center"> Rank </td><td> Team </td><td> Score </td><td align="center"> Change </td></tr><tr><td align="center"> 1 - </td><td> Boston </td><td> 1.000 </td><td align="center"> +1 </td></tr><tr><td align="center"> 2 - </td><td> Manhattan </td><td> 0.973 </td><td align="center"> +2.5 </td></tr><tr><td align="center"> 3 - </td><td> New York </td><td> 0.889 </td><td align="center"> -2 </td></tr><tr><td align="center"> 4 - </td><td> Carolina </td><td> 0.827 </td><td align="center"> -2 </td></tr><tr><td align="center"> 5 - </td><td> Philadelphia </td><td> 0.782 </td><td align="center"> +1 </td></tr><tr><td align="center"> 6 - </td><td> Baltimore </td><td> 0.728 </td><td align="center"> -1.5 </td></tr><tr><td align="center"> 7 - </td><td> New England </td><td> 0.667 </td><td align="center"> 0 </td></tr><tr><td align="center"> 8 - </td><td> New Jersey </td><td> 0.524 </td><td align="center"> 0 </td></tr></tbody></table><br /><br /></div><div><b>Western Division</b></div><div><br /></div><div><table cellpadding="2"><tbody><tr><td align="center"> Rank </td><td> Team </td><td> Score </td><td align="center"> Change </td></tr><tr><td align="center"> 1 - </td><td> Chicago </td><td> 1.000 </td><td align="center"> 0 </td></tr><tr><td align="center"> 2 - </td><td> San Francisco </td><td> 0.904 </td><td align="center"> +0.5 </td></tr><tr><td align="center"> 3 - </td><td> Dallas </td><td> 0.836 </td><td align="center"> +1 </td></tr><tr><td align="center"> 4 - </td><td> Los Angeles </td><td> 0.712 </td><td align="center"> -1.5 </td></tr><tr><td align="center"> 5 - </td><td> Arizona </td><td> 0.671 </td><td align="center"> +1 </td></tr><tr><td align="center"> 6 - </td><td> Miami </td><td> 0.658 </td><td align="center"> +2 </td></tr><tr><td align="center"> 7 - </td><td> Seattle </td><td> 0.630 </td><td align="center"> -2 </td></tr><tr><td align="center"> 8 - </td><td> St. Louis </td><td> 0.507 </td><td align="center"> -1 </td></tr></tbody></table><br /><br /></div><div>Until next week!</div><div><br /></div>Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com0tag:blogger.com,1999:blog-35277765.post-90506331321878225602011-09-11T19:05:00.000-07:002011-09-11T20:41:25.606-07:00USCL Power Rankings Week 2<div><br /></div><div>Welcome to the 2011 USCL season.</div><div><br /></div><div>Here are the weekly power rankings for the conclusion of Week 2. Note: Week 1 power rankings were not published (the lack of data makes them rather silly).</div><div><br /></div><div>The methods to calculate power rankings are the same as in previous years. Until there is inter-divisional play, the rankings will remain separate.</div><div><br /></div><div>Without further ado...</div><div><br /></div><div><b>Eastern Division</b></div><div><br /></div><div><table cellpadding="2"><tbody><tr><td align="center">Rank </td><td>Team </td><td>Score </td><td align="center">Change </td></tr><tr><td align="center">1 - </td><td>New York </td><td>1.000 </td><td align="center">+1 </td></tr><tr><td align="center">2 - </td><td>Carolina </td><td>0.963 </td><td align="center">0 </td></tr><tr><td align="center">3 - </td><td>Boston </td><td>0.863 </td><td align="center">-1 </td></tr><tr><td align="center">4-5 - </td><td>Manhattan </td><td>0.795 </td><td align="center">+0.5 </td></tr><tr><td align="center">4-5 - </td><td>Baltimore </td><td>0.795 </td><td align="center">+2.5 </td></tr><tr><td align="center">6 - </td><td>Philadelphia </td><td>0.727 </td><td align="center">-1.5 </td> </tr><tr><td align="center">7 - </td><td>New England </td><td>0.627 </td><td align="center">0 </td> </tr><tr><td align="center">8 - </td><td>New Jersey </td><td>0.590 </td><td align="center">-1 </td></tr></tbody></table></div><div><br /><br /></div><div><b>Western Division</b></div><div><div><br /><table cellpadding="2"><tbody><tr><td align="center">Rank</td><td>Team</td><td>Score</td><td align="center">Change</td></tr><tr><td align="center">1 -</td><td>Chicago</td><td>1.000</td><td align="center">0</td></tr><tr><td align="center">2-3 -</td><td>Los Angeles</td><td>0.797</td><td align="center">+2</td></tr><tr><td align="center">2-3 -</td><td>San Francisco</td><td>0.797</td><td align="center">0</td></tr><tr><td align="center">4 -</td><td>Dallas</td><td>0.786</td><td align="center">+0.5</td></tr><tr><td align="center">5 -</td><td>Seattle</td><td>0.759</td><td align="center">+3</td></tr><tr><td align="center">6 -</td><td>Arizona</td><td>0.649</td><td align="center">-3.5</td></tr><tr><td align="center">7 -</td><td>Saint Louis</td><td>0.535</td><td align="center">-0.5</td></tr><tr><td align="center">8 -</td><td>Miami</td><td>0.508</td><td align="center">-1.5</td></tr></tbody></table><br /></div></div><div><br /></div><div><br /></div><div><br /></div>Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com0tag:blogger.com,1999:blog-35277765.post-59382181041190320262011-05-26T16:46:00.000-07:002011-05-26T16:48:51.855-07:00Earth versus Space Chess Match<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEid3SDnTVJfMASjdf-ov57SXlKfPMXInDpwJ7AODIeShnY6SKWgl8qaSydu4B06j6r5oNhUkqSgUyMKt_7dtgDGtlJDYdyXvFTI7IGyExKwAaXlokIvIs3mwNm-q6Z7L9oAj1Xh/s1600/earthvsspace.png"><img style="float: left; margin: 0pt 10px 10px 0pt; cursor: pointer; width: 242px; height: 250px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEid3SDnTVJfMASjdf-ov57SXlKfPMXInDpwJ7AODIeShnY6SKWgl8qaSydu4B06j6r5oNhUkqSgUyMKt_7dtgDGtlJDYdyXvFTI7IGyExKwAaXlokIvIs3mwNm-q6Z7L9oAj1Xh/s400/earthvsspace.png" alt="" id="BLOGGER_PHOTO_ID_5611175946464986642" border="0" /></a><br /><br />There is an Earth versus Space chess match going on. It is an interesting concept, but poorly executed. They even have a Facebook page, but there's no indication on the FB page of what the current position actually is.<br /><br />How sad.Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com0tag:blogger.com,1999:blog-35277765.post-63504518080532261532011-04-11T19:52:00.000-07:002011-04-11T20:05:59.736-07:00Recipe: Coconut Pumpkin PieI found some handwritten recipes in two books in some stuff in my garage. Both are in old, spiral bound notebooks. One was my mom's (who died in 1992) and the other is my grandmother's (I'm pretty sure it is hers - she died in 1978).<br /><br />Anyway, I'm certainly not much of a cook, but I thought I would post these recipes here, as once they go into the cloud, they are likely not lost forever. And who can resist a Coconut Pumpkin Pie? This one if from my grandmother's recipe book.<br /><br />Note that I am not changing or correcting the spelling or punctuation, because I think it is interesting from a historical perspective.... like in the recipe below, she spells "separated" incorrectly.<br /><br /><span style="font-weight: bold;">Coconut Pumpkin Pie</span><br /><br />1 1/3 c. cooked or canned pumpkin<br />2/3 c. brown sugar<br />1 tsp. cinnamon<br />1/4 tsp. ginger<br />1/4 tsp. nutmeg<br />1/2 tsp. salt<br />2 eggs seperated<br />2 c. bottled milk or 1 c. evap. milk and 1 c. water<br />1/2 c. shredded coconut<br />1 9 in pastry lined pie plate.<br /><br />Combine the pumpkin, brown sugar, cinnamon, ginger, nutmeg, salt and slightly beaten egg yolks. Mix well and add the milk. Fold in the egg whites, beaten stiff, and pour into the lined pie plate. Bake in a very hot oven 450°F for 10 min. The reduce to 325° for 15 min. Sprinkle coconut over top of pie and bake 15 min. longer.Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com0tag:blogger.com,1999:blog-35277765.post-75293841729521585992011-01-24T18:12:00.000-08:002011-02-24T18:50:21.250-08:00USCL Game of the Year Judging AnalysisI performed some statistics on the judging in <a href="http://usclnews.blogspot.com/2010/12/2010-game-of-year-contest.html">United States Chess League's 2010 Game of the Year</a> contest.<br /><br />There were five judges: Hess, Gustafsson, Johannesson, Melekhina, Young. I will refer to them by the first letter of their last name.<br /><br />Several analyses were completed.<br /><br /><span style="font-size:130%;"><span style="font-weight: bold;">What are the games for which the judges agreed most and disagreed most?</span></span><br /><br />This can be calculated by looking at the standard deviations of the scores on each game.<br /><br />The <span style="font-style: italic;">most agreed</span> upon games were:<br /><ol><li>#20, Sammour-Hasbun vs. Kaplan (sd = 2.51)</li><li>#2, Sammour-Hasbun vs. Kacheishvili (sd = 2.61)</li><li>#4, Rosen-Guo (sd = 2.97)</li></ol> The <span style="font-style: italic;">most disagreed</span> upon games were:<br /><ol><li>#13 Schroer vs. Kacheishvili (sd = 7.99)</li><li>#19 Galofre vs. Milat (sd = 7.80)</li><li>#12 Friedel vs. Akobian (sd = 7.36)</li></ol> <span style="font-size:130%;"><span style="font-weight: bold;">Which judges were most different?</span></span><br /><br />I calculated which of the judges were "most different" than the combined wisdom of all the judges together. The judges that were the most different could be considered outliers.<br /><br />There are several ways to do this. I will demonstrate two approaches.<br /><br /><span style="font-weight: bold;">FINDING THE OUTLIER JUDGES</span><br /><br />First, I compared the score a judge gave to the average of all the judges, but tempering that by the amount of disagreement of all the judges. For instance Judge Y gave 2 points (19th place) to Schroer-Kacheishvili, while the average number of points was 9.2, and the standard deviation (the amount of disagreement) was 7.99. Therefore, For that game, Judge Y would receive the absolute value of (2 - 9.2)/7.99 or 0.80 "difference points". For each of the twenty games, add up the difference points. The more the difference points, the more different the judge was from the other judges. <br /><br />The total number of difference points were...<br />Judge Y: 17.49<br />Judge J: 11.09<br />Judge M: 19.40<br />Judge G: 12.80<br />Judge H: 16.96<br /><br />Therefore, Judge Y and Judge M were the most different from the other judges.<br /><br />Then, we could discard the scores of these two judges, and rescore the contest.<br /><br />See below for how the results would have changed.<br /><br /><br /><span style="font-weight: bold;">COMPUTE THE MIDDLE SCORES FOR EACH GAME</span><br /><br />Another way of rescoring the contest is to do it on a "per game" basis, as opposed to throwing judges as a whole. Instead, discard the high and low scores given to each game, and create a new total.<br /><br />For example, Golfre-Milat received scores of 1, 1, 1, 5, and 19. If we were to use this method, we would throw out one of the 1s and the 19, and the game would received a revised score of 7.<br /><br />. . .<br /><br />The table below shows the original place for each game, as well as the place it would have come it if you used the "Three Judges Only" method, or the "No Hi-Lo" method. Ties were not broken for these alternate methods.<br /><br /> <table style="width: 556px; height: 432px; font-family: courier new;" border="0" cellpadding="0" cellspacing="0"><col style="width: 157pt;" width="209"> <col style="width: 54pt;" width="72"> <col style="width: 69pt;" width="92"> <col style="width: 54pt;" width="72"> <tbody><tr style="height: 15pt;" height="20"> <td style="height: 15pt; width: 157pt;" height="20" width="209">GAME</td> <td style="width: 54pt;" width="72">Original</td> <td style="width: 69pt;" width="92">Three Judges</td> <td style="width: 54pt;" width="72">No Hi-Lo</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Sammour-Hasbun vs Kaplan</td> <td class="xl63">20</td> <td class="xl63">19</td> <td class="xl63">19</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Galofre vs Milat</td> <td class="xl63">19</td> <td class="xl63">20</td> <td class="xl63">20</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Gurevich vs Barcenilla</td> <td class="xl63">18</td> <td class="xl63">18</td> <td class="xl63">18</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Akobian vs Friedel</td> <td class="xl63">17</td> <td class="xl63">T13-14</td> <td class="xl63">17</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Rosenthal vs Thompson</td> <td class="xl63">16</td> <td class="xl63">T15-17</td> <td class="xl63">15</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Krasik vs Balasubramanian</td> <td class="xl63">15</td> <td class="xl63">T13-14</td> <td class="xl63">16</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Hungaski vs Schroer</td> <td class="xl63">14</td> <td class="xl63">T15-17</td> <td class="xl63">13</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Schroer vs Kacheishvili</td> <td class="xl63">13</td> <td class="xl63">T15-17</td> <td class="xl63">14</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Friedel vs Akobian</td> <td class="xl63">12</td> <td class="xl63">T11-12</td> <td class="xl63">12</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Shulman - Felecan</td> <td class="xl63">11</td> <td class="xl63">T11-12</td> <td class="xl63">11</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Rensch - Abrahamyan</td> <td class="xl63">10</td> <td class="xl63">T4-5</td> <td class="xl63">T7-10</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Shankland vs Becerra</td> <td class="xl63">9</td> <td class="xl63">8</td> <td class="xl63">T7-10</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Stripunsky vs Erenburg</td> <td class="xl63">8</td> <td class="xl63">10</td> <td class="xl63">T7-10</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Christiansen vs Kraai</td> <td class="xl63">7</td> <td class="xl63">T6-7</td> <td class="xl63">T7-10</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Schroer vs Christiansen</td> <td class="xl63">6</td> <td class="xl63">T4-5</td> <td class="xl63">4</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Kacheishvili vs Shankland</td> <td class="xl63">5</td> <td class="xl63">9</td> <td class="xl63">T5-6</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Rosen vs Guo</td> <td class="xl63">4</td> <td class="xl63">T6-7</td> <td class="xl63">T5-6</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Shulman vs Khachiyan</td> <td class="xl63">3</td> <td class="xl63">2</td> <td class="xl63">2</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Sammour-Hasbun vs Kacheishvili</td> <td class="xl63">2</td> <td class="xl63">3</td> <td class="xl63">3</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Akobian vs Shulman</td> <td class="xl63">1</td> <td class="xl63">1</td> <td class="xl63">1</td> </tr> </tbody></table><br /><br />Readers are invited to make their own conclusions.Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com0tag:blogger.com,1999:blog-35277765.post-36796759975987016202010-12-13T08:22:00.000-08:002010-12-13T08:25:30.213-08:00Ratings ContestA website called Kaggle have regular contests where they give people a data set, and have them to predict something about the data set. They have done it for a variety of topics (e.g., tourism prediction, grant application success) and, of course, they just finished one for chess ratings.<br /><br />Spurred on by Jeff Sonas (the Chessmetrics guy), there were a lot of entries, and suffice it to say, someone came up with a method that is 6.6% better than standard Elo ratings.<br /><br />You can read all about it <a href="http://kaggle.com/blog/2010/12/13/summary-of-elo-chess-ratings-competition-stage-set-for-part-ii/">here</a>, and wait for the follow up contest in January.Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com0tag:blogger.com,1999:blog-35277765.post-82687240749043266182010-10-28T17:32:00.000-07:002010-10-28T17:45:33.365-07:00USCL Power Rankings: Final WeekThe final week of the United States Chess League regular season has come and gone, and the playoffs are set. The power rankings only are for the regular season, so the rankings below are the final ones for this year.<br /><br />The last week really shook up the rankings, with St. Louis plummeting four places and other teams jockeying for a better position. In the end, the newcomers, the New England Nor'easters are far above the remainder of the field. Interestingly the bottom three places of the rankings are filled by Eastern Division Teams.<br /><br />Before the 2010 list, let's look at where teams stood in the 2009 list.<br /><br /><span style="font-weight: bold;">Power Rankings 2009 (End of Regular Season)</span><br /><table style="border-collapse: collapse; width: 451px; height: 284px;" border="0" cellpadding="0" cellspacing="0"><col style="width: 48pt;" width="64"> <col style="width: 71pt;" width="95"> <col style="width: 48pt;" width="64"> <tbody><tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt; width: 48pt;" height="17" width="64">1 -</td> <td style="width: 71pt;" width="95">New Jersey (8.0 - 1st East)<br /></td> <td class="xl65" style="width: 48pt;" align="right" width="64">1.000</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">2 -</td> <td>Seattle (7.5 - 1st West)<br /></td> <td class="xl65" align="right">0.953</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">3 -</td> <td>Boston (7.5 - 2nd East)<br /></td> <td class="xl65" align="right">0.929</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">4 -</td> <td>Arizona (6.0 - 3rd West)<br /></td> <td class="xl65" align="right">0.901</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">5 -</td> <td>San Francisco (6.5 - 2nd West)<br /></td> <td class="xl65" align="right">0.894</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">6 -</td> <td>Miami (6.0 - 4th West)<br /></td> <td class="xl65" align="right">0.879</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">7 -</td> <td>New York (5.0 - 3rd East)<br /></td> <td class="xl65" align="right">0.853</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">8 -</td> <td>Chicago (4.0 - 5th West)<br /></td> <td class="xl65" align="right">0.764</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">9 -</td> <td>Philadelphia (4.0 - 5th East)<br /></td> <td class="xl65" align="right">0.735</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">10 -</td> <td>Dallas (3.5 - 6th West)<br /></td> <td class="xl65" align="right">0.730</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">11 -</td> <td>Queens (3.5 - 6th East)<br /></td> <td class="xl65" align="right">0.726</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">12 -</td> <td>Baltimore (4.5 - 4th East)<br /></td> <td class="xl65" align="right">0.724</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">13 -</td> <td>Tennessee (2.0 - 7th West)<br /></td> <td class="xl65" align="right">0.647</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">14 -</td> <td>Carolina (2.0 - 7th East)<br /></td> <td class="xl65" align="right">0.622</td></tr></tbody></table><br />How some teams fortunes have changed in a year, especially New Jersey which went from the top in 2009 to near the bottom this year.<br /><br />Therefore, here is the final power rankings for the 2010 season.<br /><br /><span style="font-weight: bold;font-size:180%;" >2010 USCL Power Rankings<br />End of Regular Season</span><br /><br /> <table border="0" cellpadding="0" cellspacing="0" width="287"><col style="width: 48pt;" width="64"> <col style="width: 71pt;" width="95"> <col style="width: 48pt;" width="64"> <col style="width: 48pt;" width="64"> <tbody><tr style="height: 12.75pt;" height="17"> <td class="xl65" style="height: 12.75pt; width: 48pt;" height="17" width="64">Rank</td> <td class="xl65" style="width: 71pt;" width="95">Team</td> <td class="xl67" style="width: 48pt;" width="64">Score</td> <td class="xl66" style="width: 48pt;" width="64">Change</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl65" style="height: 12.75pt;" height="17">1 -</td> <td class="xl63">New England</td> <td class="xl67">1.000</td> <td class="xl68">0</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl65" style="height: 12.75pt;" height="17">2 -</td> <td class="xl63">Boston</td> <td class="xl67">0.886</td> <td class="xl68">+1</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl65" style="height: 12.75pt;" height="17">3 -</td> <td class="xl63">Arizona</td> <td class="xl67">0.857</td> <td class="xl68">-1</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl65" style="height: 12.75pt;" height="17">4 -</td> <td class="xl63">Chicago</td> <td class="xl67">0.793</td> <td class="xl68">+2</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl65" style="height: 12.75pt;" height="17">5 -</td> <td class="xl63">New York</td> <td class="xl67">0.793</td> <td class="xl68">-1</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl65" style="height: 12.75pt;" height="17">6 -</td> <td class="xl63">Baltimore</td> <td class="xl67">0.787</td> <td class="xl68">+1</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl65" style="height: 12.75pt;" height="17">7 -</td> <td class="xl63">Miami</td> <td class="xl67">0.771</td> <td class="xl68">+1</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl65" style="height: 12.75pt;" height="17">8 -</td> <td class="xl63">Seattle</td> <td class="xl67">0.760</td> <td class="xl68">+2</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl65" style="height: 12.75pt;" height="17">9 -</td> <td class="xl63">St. Louis</td> <td class="xl67">0.743</td> <td class="xl68">-4</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl65" style="height: 12.75pt;" height="17">10 -</td> <td class="xl63">Los Angeles</td> <td class="xl67">0.740</td> <td class="xl68">+3</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl65" style="height: 12.75pt;" height="17">11 -</td> <td class="xl63">San Francisco</td> <td class="xl67">0.708</td> <td class="xl68">-2</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl65" style="height: 12.75pt;" height="17">12 -</td> <td class="xl63">Philadelphia</td> <td class="xl67">0.697</td> <td class="xl68">+2</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl65" style="height: 12.75pt;" height="17">13 -</td> <td class="xl63">Dallas</td> <td class="xl67">0.686</td> <td class="xl68">-2</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl65" style="height: 12.75pt;" height="17">14 -</td> <td class="xl63">New Jersey</td> <td class="xl67">0.677</td> <td class="xl68">-2</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl65" style="height: 12.75pt;" height="17">15 -</td> <td class="xl63">Manhattan</td> <td class="xl67">0.638</td> <td class="xl68">0</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl65" style="height: 12.75pt;" height="17">16 -</td> <td class="xl63">Carolina</td> <td class="xl67">0.607</td> <td class="xl68">0</td> </tr> </tbody></table><br />The top eight teams in the power rankings are also the top eight teams in the playoffs. Good luck to all of them.Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com1tag:blogger.com,1999:blog-35277765.post-19169306440146742132010-10-26T18:21:00.000-07:002010-10-26T18:23:20.794-07:00USCL 2010 Power Rankings Week 9A little late... okay a LOT late, but I was away.<br /><br />Notable about this is that New England has completely pulled away from the pack.<br /><br /> <table border="0" cellpadding="0" cellspacing="0" width="287"><col style="width: 48pt;" width="64"> <col style="width: 71pt;" width="95"> <col style="width: 48pt;" width="64"> <col style="width: 48pt;" width="64"> <tbody><tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt; width: 48pt;" height="17" width="64">Rank</td> <td class="xl66" style="width: 71pt;" width="95">Team</td> <td class="xl69" style="width: 48pt;" width="64">Score</td> <td class="xl68" style="width: 48pt;" width="64">Change</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">1 -</td> <td class="xl70">New England</td> <td class="xl69">1.000</td> <td class="xl71">0</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">2 -</td> <td class="xl67">Arizona</td> <td class="xl69">0.886</td> <td class="xl71">0</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">3 -</td> <td class="xl67">Boston</td> <td class="xl69">0.857</td> <td class="xl71">0</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">4 -</td> <td class="xl67">New York</td> <td class="xl69">0.793</td> <td class="xl71">0</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">5 -</td> <td class="xl70">St. Louis</td> <td class="xl69">0.793</td> <td class="xl71">+2</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">6 -</td> <td class="xl67">Chicago</td> <td class="xl69">0.787</td> <td class="xl71">0</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">7 -</td> <td class="xl67">Baltimore</td> <td class="xl69">0.771</td> <td class="xl71">-2</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">8 -</td> <td class="xl67">Miami</td> <td class="xl69">0.760</td> <td class="xl71">+1</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">9 -</td> <td class="xl67">San Francisco</td> <td class="xl69">0.743</td> <td class="xl72">-1</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">10 -</td> <td class="xl67">Seattle</td> <td class="xl69">0.740</td> <td class="xl71">+1</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">11 -</td> <td class="xl67">Dallas</td> <td class="xl69">0.708</td> <td class="xl71">-1</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">12 -</td> <td class="xl67">New Jersey</td> <td class="xl69">0.697</td> <td class="xl71">+2</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">13 -</td> <td class="xl70">Los Angeles</td> <td class="xl69">0.686</td> <td class="xl71">-1</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">14 -</td> <td class="xl67">Philadelphia</td> <td class="xl69">0.677</td> <td class="xl71">+1</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">15 -</td> <td class="xl70">Manhattan</td> <td class="xl69">0.638</td> <td class="xl71">-2</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl66" style="height: 12.75pt;" height="17">16 -</td> <td class="xl67">Carolina</td> <td class="xl69">0.607</td> <td class="xl71">0</td> </tr> </tbody></table>Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com0tag:blogger.com,1999:blog-35277765.post-76681136314529599622010-10-14T17:57:00.000-07:002010-10-14T18:01:33.987-07:00USCL 2010 Power Rankings Week 8The power rankings show that New England is clearly the class of the league, with a huge lead in strength over second place Arizona. Baltimore and Dallas were the big gainers this week, while San Francisco took a big tumble.<br /><br />Only a whisker separates Boston and New York, and when these teams likely play in the playoffs in the first round, it should be a close match.<br /><br />Not even visible to the human eye (only the fourth decimal place) separates Chicago and St. Louis!<br /><br /> <table border="0" cellpadding="0" cellspacing="0" width="287"><col style="width: 48pt;" width="64"> <col style="width: 71pt;" width="95"> <col style="width: 48pt;" width="64"> <col style="width: 48pt;" width="64"> <tbody><tr style="height: 12.75pt;" height="17"> <td class="xl64" style="height: 12.75pt; width: 48pt; font-weight: bold;" height="17" width="64">Rank</td> <td class="xl64" style="width: 71pt; font-weight: bold;" width="95">Team</td> <td class="xl67" style="width: 48pt; font-weight: bold;" width="64">Score</td> <td class="xl66" style="width: 48pt; font-weight: bold;" width="64">Change</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl64" style="height: 12.75pt;" height="17">1 -</td> <td class="xl68">New England</td> <td class="xl67">1.000</td> <td class="xl69">0</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl64" style="height: 12.75pt;" height="17">2 -</td> <td class="xl65">Arizona</td> <td class="xl67">0.914</td> <td class="xl69">0</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl64" style="height: 12.75pt;" height="17">3 -</td> <td class="xl65">Boston</td> <td class="xl67">0.846</td> <td class="xl69">0</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl64" style="height: 12.75pt;" height="17">4 -</td> <td class="xl65">New York</td> <td class="xl67">0.844</td> <td class="xl69">0</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl64" style="height: 12.75pt;" height="17">5 -</td> <td class="xl65">Baltimore</td> <td class="xl67">0.810</td> <td class="xl69">+2</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl64" style="height: 12.75pt;" height="17">6 -</td> <td class="xl65">Chicago</td> <td class="xl67">0.799</td> <td class="xl69">0</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl64" style="height: 12.75pt;" height="17">7 -</td> <td class="xl68">St. Louis</td> <td class="xl67">0.799</td> <td class="xl69">+1</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl64" style="height: 12.75pt;" height="17">8 -</td> <td class="xl65">San Francisco</td> <td class="xl67">0.794</td> <td class="xl69">-3</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl64" style="height: 12.75pt;" height="17">9 -</td> <td class="xl65">Miami</td> <td class="xl67">0.769</td> <td class="xl70">0</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl64" style="height: 12.75pt;" height="17">10 -</td> <td class="xl65">Dallas</td> <td class="xl67">0.728</td> <td class="xl69">+3</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl64" style="height: 12.75pt;" height="17">11 -</td> <td class="xl65">Seattle</td> <td class="xl67">0.703</td> <td class="xl69">-1</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl64" style="height: 12.75pt;" height="17">12 -</td> <td class="xl68">Los Angeles</td> <td class="xl67">0.692</td> <td class="xl69">-1</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl64" style="height: 12.75pt;" height="17">13 -</td> <td class="xl68">Manhattan</td> <td class="xl67">0.679</td> <td class="xl69">-1</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl64" style="height: 12.75pt;" height="17">14 -</td> <td class="xl65">New Jersey</td> <td class="xl67">0.658</td> <td class="xl69">+1</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl64" style="height: 12.75pt;" height="17">15 -</td> <td class="xl65">Philadelphia</td> <td class="xl67">0.651</td> <td class="xl69">-1</td> </tr> <tr style="height: 12.75pt;" height="17"> <td class="xl64" style="height: 12.75pt;" height="17">16 -</td> <td class="xl65">Carolina</td> <td class="xl67">0.632</td> <td class="xl69">0</td> </tr> </tbody></table>Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com0tag:blogger.com,1999:blog-35277765.post-81296866553208905892010-10-14T10:51:00.001-07:002010-10-14T11:00:35.707-07:00Remainder of Season Simulation: Post-Week 8Chance to be at least tied for 4th in match/game points, based on 100,000 simulations.<br /><br /><span style="font-weight: bold;">Western Division</span><br /><span style="font-family:courier new;"> 100.00% Arizona</span><br /><span style="font-family:courier new;"> _73.15% St. Louis</span><br /><span style="font-family:courier new;"> _72.37% Chicago</span><br /><span style="font-family:courier new;"> _63.15% San Francisco</span><br /><span style="font-family:courier new;"> _51.96% Miami</span><br /> <span style="font-family:courier new;">_26.43% Dallas</span><br /><span style="font-family:courier new;"> _13.62% Seattle</span><br /><span style="font-family:courier new;">__4.72% Los Angeles</span><br /><br /><span style="font-weight: bold;">Eastern Division</span><br /><span style="font-family:courier new;"> 100.00% New England</span><br /> <span style="font-family:courier new;">_99.65% Boston</span><br /><span style="font-family:courier new;"> _94.25% New York</span><br /><span style="font-family:courier new;"> _92.55% Baltimore</span><br /><span style="font-family:courier new;"> _13.47% Manhattan</span><br /><span style="font-family:courier new;">__0.78% New Jersey</span><br /><br /><span style="color: rgb(136, 136, 136);"><br /></span>Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com2tag:blogger.com,1999:blog-35277765.post-54957090023540430562010-10-11T21:02:00.001-07:002010-10-12T06:18:34.829-07:00USCL Simulation after Week 8 Monday<span style="font-style: italic;"><span style="font-weight: bold;">UPDATED!</span> Now includes Western Division!</span><br /><br />Chance of making playoffs (100,000 simulated Wednesday Week 8s and Weeks 9 and 10)<br /><br /><span style="font-weight: bold;">Eastern Division</span><br /><table border="0" cellpadding="0" cellspacing="0" width="149"><col style="width: 66pt;" width="88"> <col style="width: 46pt;" width="61"> <tbody><tr style="height: 15pt;" height="20"> <td style="height: 15pt; width: 66pt;" height="20" width="88">New England</td> <td class="xl63" style="width: 46pt;" align="right" width="61">100.00%</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Boston</td> <td class="xl63" align="right">98.85%</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">New York</td> <td class="xl63" align="right">97.44%</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Baltimore</td> <td class="xl63" align="right">92.29%</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Manhattan</td> <td class="xl63" align="right">11.27%</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">New Jersey</td> <td class="xl63" align="right">0.79%</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Philadelphia</td> <td class="xl63" align="right">0.00%</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Carolina</td> <td class="xl63" align="right">0.14%</td></tr></tbody></table><br /><br /><span style="font-weight: bold;">Western Division</span><br /> <table style="width: 179px; height: 184px;" border="0" cellpadding="0" cellspacing="0"> <col style="width: 48pt;" span="2" width="64"> <tbody><tr style="height: 15pt;" height="20"> <td style="height: 15pt; width: 48pt;" height="20" width="64">Arizona</td> <td class="xl63" style="width: 48pt;" align="right" width="64">99.99%</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Chicago</td> <td class="xl63" align="right">85.45%</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">San Francisco</td> <td class="xl63" align="right">69.28%</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">St. Louis</td> <td class="xl63" align="right">35.04%</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Seattle</td> <td class="xl63" align="right">30.48%</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Miami</td> <td class="xl63" align="right">18.73%</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Los Angeles</td> <td class="xl63" align="right">16.68%</td> </tr> <tr style="height: 15pt;" height="20"> <td style="height: 15pt;" height="20">Dallas</td> <td class="xl63" align="right">49.12%</td> </tr> </tbody> </table><br />Note that Arizona made the playoffs in 99,991 of the 100,000 simulations!<br /><br /><br /><br /><br /><table border="0" cellpadding="0" cellspacing="0" width="149"><tbody><tr style="height: 15pt;" height="20"><td style="height: 15pt; width: 66pt;" height="20" width="88"><br /></td><td class="xl63" style="width: 46pt;" align="right" width="61"><br /></td></tr><tr style="height: 15pt;" height="20"><td style="height: 15pt;" height="20"><br /></td><td class="xl63" align="right"><br /></td></tr><tr style="height: 15pt;" height="20"><td style="height: 15pt;" height="20"><br /></td><td class="xl63" align="right"><br /></td></tr><tr style="height: 15pt;" height="20"><td style="height: 15pt;" height="20"><br /></td><td class="xl63" align="right"><br /></td></tr><tr style="height: 15pt;" height="20"><td style="height: 15pt;" height="20"><br /></td><td class="xl63" align="right"><br /></td></tr><tr style="height: 15pt;" height="20"><td style="height: 15pt;" height="20"><br /></td><td class="xl63" align="right"><br /></td></tr><tr style="height: 15pt;" height="20"><td style="height: 15pt;" height="20"><br /></td><td class="xl63" align="right"><br /></td></tr><tr style="height: 15pt;" height="20"><td style="height: 15pt;" height="20"><br /></td><td class="xl63" align="right"><br /></td> </tr> </tbody></table>Bionic Limehttp://www.blogger.com/profile/15056656079490255005noreply@blogger.com2