USCL Power Rankings: Final Week

The 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.

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.

Before the 2010 list, let's look at where teams stood in the 2009 list.

Power Rankings 2009 (End of Regular Season)

1 -	New Jersey (8.0 - 1st East)	1.000
2 -	Seattle (7.5 - 1st West)	0.953
3 -	Boston (7.5 - 2nd East)	0.929
4 -	Arizona (6.0 - 3rd West)	0.901
5 -	San Francisco (6.5 - 2nd West)	0.894
6 -	Miami (6.0 - 4th West)	0.879
7 -	New York (5.0 - 3rd East)	0.853
8 -	Chicago (4.0 - 5th West)	0.764
9 -	Philadelphia (4.0 - 5th East)	0.735
10 -	Dallas (3.5 - 6th West)	0.730
11 -	Queens (3.5 - 6th East)	0.726
12 -	Baltimore (4.5 - 4th East)	0.724
13 -	Tennessee (2.0 - 7th West)	0.647
14 -	Carolina (2.0 - 7th East)	0.622

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.

Therefore, here is the final power rankings for the 2010 season.

2010 USCL Power Rankings
End of Regular Season

Rank	Team	Score	Change
1 -	New England	1.000	0
2 -	Boston	0.886	+1
3 -	Arizona	0.857	-1
4 -	Chicago	0.793	+2
5 -	New York	0.793	-1
6 -	Baltimore	0.787	+1
7 -	Miami	0.771	+1
8 -	Seattle	0.760	+2
9 -	St. Louis	0.743	-4
10 -	Los Angeles	0.740	+3
11 -	San Francisco	0.708	-2
12 -	Philadelphia	0.697	+2
13 -	Dallas	0.686	-2
14 -	New Jersey	0.677	-2
15 -	Manhattan	0.638	0
16 -	Carolina	0.607	0

The top eight teams in the power rankings are also the top eight teams in the playoffs. Good luck to all of them.

USCL 2010 Power Rankings Week 9

A little late... okay a LOT late, but I was away.

Notable about this is that New England has completely pulled away from the pack.

Rank	Team	Score	Change
1 -	New England	1.000	0
2 -	Arizona	0.886	0
3 -	Boston	0.857	0
4 -	New York	0.793	0
5 -	St. Louis	0.793	+2
6 -	Chicago	0.787	0
7 -	Baltimore	0.771	-2
8 -	Miami	0.760	+1
9 -	San Francisco	0.743	-1
10 -	Seattle	0.740	+1
11 -	Dallas	0.708	-1
12 -	New Jersey	0.697	+2
13 -	Los Angeles	0.686	-1
14 -	Philadelphia	0.677	+1
15 -	Manhattan	0.638	-2
16 -	Carolina	0.607	0

USCL 2010 Power Rankings Week 8

The 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.

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.

Not even visible to the human eye (only the fourth decimal place) separates Chicago and St. Louis!

Rank	Team	Score	Change
1 -	New England	1.000	0
2 -	Arizona	0.914	0
3 -	Boston	0.846	0
4 -	New York	0.844	0
5 -	Baltimore	0.810	+2
6 -	Chicago	0.799	0
7 -	St. Louis	0.799	+1
8 -	San Francisco	0.794	-3
9 -	Miami	0.769	0
10 -	Dallas	0.728	+3
11 -	Seattle	0.703	-1
12 -	Los Angeles	0.692	-1
13 -	Manhattan	0.679	-1
14 -	New Jersey	0.658	+1
15 -	Philadelphia	0.651	-1
16 -	Carolina	0.632	0

Remainder of Season Simulation: Post-Week 8

Chance to be at least tied for 4th in match/game points, based on 100,000 simulations.

Western Division
100.00% Arizona
_73.15% St. Louis
_72.37% Chicago
_63.15% San Francisco
_51.96% Miami
_26.43% Dallas
_13.62% Seattle
__4.72% Los Angeles

Eastern Division
100.00% New England
_99.65% Boston
_94.25% New York
_92.55% Baltimore
_13.47% Manhattan
__0.78% New Jersey

USCL Simulation after Week 8 Monday

UPDATED! Now includes Western Division!

Chance of making playoffs (100,000 simulated Wednesday Week 8s and Weeks 9 and 10)

Eastern Division

New England	100.00%
Boston	98.85%
New York	97.44%
Baltimore	92.29%
Manhattan	11.27%
New Jersey	0.79%
Philadelphia	0.00%
Carolina	0.14%

Western Division

Arizona	99.99%
Chicago	85.45%
San Francisco	69.28%
St. Louis	35.04%
Seattle	30.48%
Miami	18.73%
Los Angeles	16.68%
Dallas	49.12%

Note that Arizona made the playoffs in 99,991 of the 100,000 simulations!

Remainder of Season Simulation

I have expanded on my prior projects to determine the likelihood that a team will make the playoffs this season. As I said previously, the ability to be comprehensive in all possibilities of match outcomes eats into years of computing time, so simulation is an obvious answer.

I created a simulation that attempts to model all the matches in the remainder of the USCL season.

The goal was the same -- what is the chance that a team will make the playoffs. This time, however, I included by match points and the game points tiebreaker. (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.)

To do this, I made several other assumptions.

1. All teams have the same strength. Therefore, they have the same chances in each match against their opponents.
   
2. The game point results of the match follow the historical distribution of USCL matches (which is here). That is, 2.5-1.5 is more common than 3-1, which is more common than 3.5-0.5, etc.

I ran 100,000 simulations for both the Eastern and Western division. Here are the results, where the percentages indicate a tie for fourth place or better.

Eastern Division (Chance to make playoffs)

New England	100.00%
Boston	98.43%
New York	97.49%
Baltimore	70.27%
Manhattan	24.79%
New Jersey	6.92%
Philadelphia	2.69%
Carolina	0.61%

Western Division (Chance to make playoffs)

Arizona	97.18%
Chicago	86.54%
San Francisco	78.07%
St. Louis	45.24%
Seattle	35.50%
Miami	27.39%
Los Angeles	23.44%
Dallas	12.92%

I also included the chance that a team will receive draw odds in the first round of the playoffs (tied for second place or better).

Eastern Division (Chance have draw odds first round of playoffs)

New England	98.37%
Boston	55.19%
New York	41.63%
Baltimore	4.90%
Manhattan	0.23%
New Jersey	0.00%
Philadelphia	0.00%
Carolina	0.00%

Western Division (Chance have draw odds first round of playoffs)

Arizona	80.94%
Chicago	50.92%
San Francisco	40.50%
St. Louis	13.13%
Seattle	7.55%
Miami	6.01%
Los Angeles	3.60%
Dallas	1.25%

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....

Let me know in the comments...

USCL Western Division: Playoff Hunt

In my previous post, I posted the chances of at least tying for fourth place in the USCL Eastern Division. You can read about the method I used in that post.

I ran the same thing for the Western Division. Here is the percentage that each team will finish in at least a tie for fourth in match points.

99.14% Arizona
95.70% Chicago
82.20% San Francisco
61.70% St. Louis
35.96% Seattle
35.69% Miami
34.61% Los Angeles
15.31% Dallas

USCL Eastern Division: Playoff Hunt

There are three weeks to go in the USCL regular season. What are the chances that any particular team will be in playoff contention?

Let's assume for the moment that all teams are equally matched, and that all teams have an equal chance to win, draw, or lose a match with every other team. Therefore, each match can have three possible results.

In the Eastern Division of the USCL, there are twelve matches left and therefore there are 3^12 (three to the twelfth power) possible results (in terms of match results). That's 531, 441 possibilities.

If we make the criterion for "possibly in the playoffs" to be tied for fourth or better, then the percentages below indicate what a team's chances to possibly be in the playoffs.

100.00% - New England
99.55% - Boston
98.27% - New York
74.75% - Baltimore
41.28% - Manhattan
10.32% - New Jersey
3.05% - Philadelphia
1.21% - Carolina

Now, if we take game points (the first tiebreaker) into consideration, that increases the number of possibilities to 9^12 power, which is actually 531,441 times bigger than the last time. Since the simulation presented here took about 4 seconds to run on my computer, the code for including game points is about 50% more complex (increasing time to completion by about 50%), it would take over 553 days for the simulation to run!

I think I'll wait for the actual results.

Anyone interested in me doing this for the Western Division too?

USCL 2010 Power Rankings Week 7

Only three weeks left in the season, and the races are tightening.

New England keeps the top spot in the rankings, while Arizona jumps four places to number two. Miami also makes a big jump up to number nine. Several pairs of teams are almost indistinguishably close in their score. San Francisco and Chicago are five and six; Miami and Seattle are nine and ten; Manhattan, Dallas, and Philadelphia are twelve, thirteen, and fourteen.

Will New England keep their top spot in the rankings at the end of the regular season? Only time will tell.

Rank	Team	Score	Change
1 -	New England	1.000	0
2 -	Arizona	0.912	+4
3 -	Boston	0.889	-1
4 -	New York	0.878	-1
5 -	San Francisco	0.849	0
6 -	Chicago	0.845	-2
7 -	Baltimore	0.803	0
8 -	St. Louis	0.771	+2
9 -	Miami	0.756	+4
10 -	Seattle	0.755	-2
11 -	Los Angeles	0.739	-2
12 -	Manhattan	0.686	+3
13 -	Dallas	0.685	-2
14 -	Philadelphia	0.683	-2
15 -	New Jersey	0.668	-1
16 -	Carolina	0.607	0