USCL 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.

Once again, the chances that the team will make the playoffs, be in the top 2, and win the division.

Here are the results (to three significant digits).

Western Division (based on 100,000 simulations)

Team	Playoffs	Top 2	Number 1
Arizona	35.0%	2.20%	0%
Chicago	100%	100%	100%
San Francisco	71.0%	6.23%	0%
St. Louis	0%	0%	0%
Seattle	0.339%	0%	0%
Miami	44.2%	1.45%	0%
Los Angeles	99.9%	90.0%	0%
Dallas	55.9%	2.78%	0%

Eastern Division (based on 100,000 simulations)

Team	Playoffs	Top 2	Number 1
New England	33.1%	0%	0%
Boston	51.1%	0.239%	0%
New York	100%	92.6%	41.4%
Baltimore	17.8%	0%	0%
Manhattan	90.9%	16.0%	0.728%
New Jersey	0%	0%	0%
Philadelphia	100%	92.6%	58.9%
Carolina	9.95%	0.792%	0%

Again, if you have suggested scenarios, please comment with your requests.

USCL Season Simulation Midweek 8

It is middle of week 8 in the USCL, and half the teams have played their matches this week. Therefore I ran simulations again.

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!

Here are the results.

Western Division (based on 100,000 simulations)

Team	Playoffs	Top 2	Number 1
Arizona	35.4%	1.67%	0%
Chicago	100%	99.981%	99.0%
San Francisco	71.1%	5.67%	0%
St. Louis	1.14%	0%	0%
Seattle	0.584%	0%	0%
Miami	20.6%	0.366%	0%
Los Angeles	99.68%	81.4%	1.22%
Dallas	79.3%	14.9%	0.122%

Eastern Division (based on 2,500,000 simulations)

Team	Playoffs	Top 2	Number 1
New England	37.7%	0.763%	0%
Boston	51.0%	0.274%	0%
New York	99.989%	96.0%	41.6%
Baltimore	38.3%	0.654%	0%
Manhattan	66.4%	7.06%	0.252%
New Jersey	0.0568%	0%	0%
Philadelphia	99.99996%	96.6%	58.9%
Carolina	10.5%	0.792%	0%

A scenario has been requested, and I will mention it in the comments.

USCL Season Simulation 2011

Last 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.

As there are three weeks left, I decided to run another set of simulations this year.

Once again, here are the 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.
3. 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.

I ran 100,000 simulations for both the Eastern and Western division. Here are the results.

Western Division

Team	Playoffs	Top 2	Number 1
Arizona	39.322%	6.648%	0%
Chicago	100.000%	99.995%	99.596%
San Francisco	65.377%	16.010%	0%
St. Louis	0.905%	0%	0%
Seattle	11.293%	0.889%	0%
Miami	19.010%	1.242%	0%
Los Angeles	90.735%	51.724%	0.381%
Dallas	80.074%	28.023%	0.146%

Eastern Division

Team	Playoffs	Top 2	Number 1
New England	39.508%	1.464%	0%
Boston	27.179%	0.501%	0%
New York	99.982%	93.277%	43.467%
Baltimore	38.095%	1.378%	0%
Manhattan	67.278%	9.757%	0.357%
New Jersey	0.045%	0%	0%
Philadelphia	99.988%	94.578%	57.171%
Carolina	31.810%	0.792%	0%

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...

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?