Wednesday, March 18, 2009

Tournament Chances (With Math!)

For those of us that want an assessment of what UW's chances are of making the tournament, there's always the opportunity to plug in some scenarios into the YATC widget, as Chuck has already done. These give us hope, as we can see that it's possible for UW to get an at-large bid without winning the Final Five. USCHO's diligent Badger fans have also identidied a couple of other scenarios that get UW in.

Identfiying a scenario is one thing, but what about quantifying the chances of that scenario actually coming to fruition? Enter USCHO poster 'Patman.' Patman's a statistician, so there's no lack of love for the numbers. Patman took the Pairwise formula, the results of the past season, and a mathematical technique known as Poisson regression to determine the chances of each scenario coming to pass. If you follow politics, you may have seen blogger, closet math nerd, and baseball sabremetrician Nate Silver's website FiveThirtyEight.com. There, Silver applied the same methodology to election polling - taking the polls done and using a regression analysis to predict the future, based on chance, in a number of different scenarios. Silver would plug in the poll data, adjust as need be for accuracy, and have the computer run a regression analysis (where it basically ran a fake election 10,000 times). The number of times a certain scenario popped up, divided by 10,000, and that's the percent chance of it happening. Silver was remarkably accurate in his election predictions.

Patman applied the same basic method here, though instead of using polling data, he used the previous game data. He adjusted for home ice advantage and for overtime performance, and used the past results as a basis for predicting the future games. Each run created a scenario where all the remaining games were played, and the PWR is applied at the end to see what happens. He did this 10,000 times, and aggregated the results. Putting things in percentage terms:

                      CHAMPS ATLRGE  NCAA  SEED 1 SEED 2 SEED 3 SEED 4
------ ------ ------ ------ ------ ------ ------
1 Air Force 0.4309 0.0000 0.4309 0.0000 0.0000 0.0001 0.4308
2 Army 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
3 American Intl 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
4 Bentley 0.1269 0.0000 0.1269 0.0000 0.0000 0.0000 0.1269
5 Canisius 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
6 Connecticut 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
7 Holy Cross 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
8 Mercyhurst 0.2407 0.0000 0.2407 0.0000 0.0000 0.0000 0.2407
9 RIT 0.2015 0.0000 0.2015 0.0000 0.0000 0.0000 0.2015
10 Sacred Heart 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
11 Alaska 0.1065 0.0000 0.1065 0.0000 0.0000 0.0000 0.1065
12 Bowling Green 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
13 Ferris State 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
14 Lake Superior 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
15 Miami 0.0000 0.8800 0.8800 0.0000 0.0000 0.3789 0.5011
16 Michigan 0.3716 0.6284 1.0000 0.9150 0.0850 0.0000 0.0000
17 Michigan State 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
18 Nebraska-Omaha 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
19 Northern Michigan 0.0887 0.0000 0.0887 0.0000 0.0000 0.0000 0.0887
20 Notre Dame 0.4332 0.5668 1.0000 1.0000 0.0000 0.0000 0.0000
21 Ohio State 0.0000 0.0881 0.0881 0.0000 0.0000 0.0000 0.0881
22 Western Michigan 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
23 Alabama-Huntsville 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
24 Bemidji State 1.0000 0.0000 1.0000 0.0000 0.0000 0.0000 1.0000
25 Niagara 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
26 Robert Morris 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
27 Brown 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
28 Clarkson 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
29 Colgate 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
30 Cornell 0.2414 0.5415 0.7829 0.0000 0.2041 0.5194 0.0594
31 Dartmouth 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
32 Harvard 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
33 Princeton 0.2393 0.5269 0.7662 0.0000 0.2195 0.4989 0.0478
34 Quinnipiac 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
35 Rensselaer 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
36 St. Lawrence 0.3158 0.3118 0.6276 0.0000 0.1623 0.2312 0.2341
37 Union 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
38 Yale 0.2035 0.7939 0.9974 0.0288 0.6020 0.3200 0.0466
39 Boston College 0.0999 0.0180 0.1179 0.0000 0.0003 0.0885 0.0291
40 Boston University 0.4862 0.5138 1.0000 1.0000 0.0000 0.0000 0.0000
41 Maine 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
42 Massachusetts 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
43 Mass.-Lowell 0.1847 0.0000 0.1847 0.0000 0.0000 0.0215 0.1632
44 Merrimack 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
45 New Hampshire 0.0000 1.0000 1.0000 0.0000 0.1256 0.8744 0.0000
46 Northeastern 0.2292 0.7708 1.0000 0.1966 0.7936 0.0098 0.0000
47 Providence 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
48 Vermont 0.0000 1.0000 1.0000 0.0000 0.6785 0.3215 0.0000
49 Alaska-Anchorage 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
50 Colorado College 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
51 Denver 0.3139 0.6861 1.0000 0.7693 0.2307 0.0000 0.0000
52 Michigan Tech 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
53 Minnesota 0.0784 0.1912 0.2696 0.0000 0.0229 0.1354 0.1113
54 Minnesota-Duluth 0.1345 0.4782 0.6127 0.0000 0.0690 0.2893 0.2544
55 Minnesota State 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
56 North Dakota 0.2458 0.7542 1.0000 0.0903 0.8064 0.1033 0.0000
57 St. Cloud State 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
58 Wisconsin 0.2274 0.2503 0.4777 0.0000 0.0001 0.2078 0.2698

The first column is the percentage of scenarios in which a team wins their conference tournament. The second column is the chance that they get an at-large bid. The third is the combination of the first two - the total chance of making the tournament. The last four columns then break that down by potential seed.

This shows us a comple of things. Several teams are locks to make the tournament, either by winning their tournaments or by getting an at-large bid. Michigan, Bemidji State, Boston University, New Hampshire, Northeastern, Vermont, Denver, and North Dakota are all locks. Of those, only Bemidji has actually secured an Automatic Qualifier (AQ) by winning the CHA tournament.

Wisconsin, according to this model, has a 22.74% chance of winning the Final Five, and a 25.03% chance of receiving an at large bid if they don't - for a total 47.77% chance of making the NCAAs.

Obviously, this is future performance based on past results. It can't take into account things like Denver's injured forwards, or the potential for lazy play given that the two top seeds in the WCHA have tournament bids locked up, or Wisconsin's desperation to continue their season. Nevertheless, the overall numbers are quite high, especially for the at large bid.

The overall chances that each WCHA team has of winning the Final Five are as follows:

Denver: 31.39%
Minnesota: 7.84%
UMD: 13.45%
North Dakota: 24.58%
Wisconsin: 22.74%

Anyway, many thanks to Patman for putting these numbers together and adding some factual basis to fan speculation.