Thursday, March 17, 2011

Hacking the PairWise

What happens when you combine a mathematically defined system for selecting the NCAA field, the oldest technological university in the English-speaking world, and two weeks of waiting around to see if said university (or Institute, if you prefer) is going to get a bid to the tournament?

Well, you get this: a program that runs all of the permutations heading into the final three days of games before the field is chosen.

Reilly Hamilton, an enterprising CompSci/Economics major from RPI's Class of 2012 (and a key component of RPI TV's broadcasts as president), took it upon himself to write a program that essentially played the remaining 19 games to each potential overall result, then weighted those results using KRACH, the best statistic available for determining the likelihood of one team beating another (which we've discussed here before).

Those results can be found here.
They include numbers for every team that is either still playing or can still potentially make the tournament. If your team isn't listed here... sorry. Your season's definitively over.

Now, this isn't perfect for a couple of reasons. First, in these calculations, KRACH doesn't change as the games are played. To do that would require a whole new set of calculations taking up a heck of a lot more time... and the games start tonight, so time is something we don't have a lot of. The second is that KRACH really doesn't have a good way of predicting the likelihood of a tie, and there are two games this weekend - the ECAC and CCHA consolation games - that could potentially end in a tie. But they are at the very least a rough estimate of the likelihood of teams making the tournament, and what seed they're likely to be.

The unweighted listings are very simple: they are a list of the total number of scenarios that could result after the 19 games this weekend are played.

Since we're an RPI-centric site, here are the Engineers' results. They are in the tournament in permutations listed in green, out in the ones listed in red.

SeedWeightedUnweightedPermutations
100.0005%0.0058%68
110.4574%1.5599%18401
127.8356%12.7865%150836
1319.9679%24.7119%291514
1428.6039%27.0253%318803
1524.5002%8.2914%97809
SeedWeightedUnweightedPermutations
130.0062%0.5383%6350
140.3022%4.4988%53070
155.2459%13.6443%160955
1611.2954%6.4567%76166
171.7260%0.4508%5318
180.0583%0.0299%353
190.0005%0.0004%5

As you can see, RPI could finish as high as 10th in the PWR, but that's not only highly unlikely (68 possible scenarios out of 1,179,648 overall scenarios), the situation is also fairly fanciful, because the weighted percentage is less than the unweighted percentage.

A simple way to explain this is to look at Colgate's tournament chances. Given that they will only be in the tournament if they win the ECAC title, their unweighted chances of making the tournament are 25%, because in 25% of the possible scenarios, they win the ECAC tournament. However, not all teams are created equal, and in the scope of the entirety of the season, their chances of actually winning the tournament isn't really great.

With that said, the Engineers, according to this model have an 81.3656% chance of playing next weekend. Slightly better than 4 in 5? What's not to be excited about there? It's not a given, which would be better, but beggars can't be choosers. Their unweighted chances are 74.3808%, which means that even if you treated every scenario as being equally likely, they're still in almost 3 times out of 4.

This analysis proves what we already knew about teams that are already in the tournament: Yale, North Dakota, Boston College, Miami, Michigan, Denver, Union, Merrimack, and Minnesota-Duluth can't miss the tournament.

It also shows that the bandied about scenarios of Notre Dame or New Hampshire missing the tournament are extremely fanciful. Barring something extremely, extremely unlikely, both teams are in.

Nebraska-Omaha, for all of its problems, is also almost certainly in.

That leaves the teams that are firmly on the bubble, and that's RPI, Western Michigan, Colorado College, and Dartmouth. Depending on the number of upset champions, there will be between 0 and 3 at-large bids that will go to these teams, discounting the fact that BU, Alaska-Anchorage, and Maine are also alive in this group but with much worse chances of making it. Of that group, the Engineers stand the best chance of emerging in the tournament field. That's a wonderful place to be.

So special thanks to Reilly Hamilton for putting in the time and effort needed to create this program. He has promised some updates over the course of the weekend, and we'll be glad to bring them to you here.

Go Seawolves (tonight)!

No comments:

Post a Comment