Year End Rankings

I'm not really into ranking teams that much (because match-ups depend on many more factors), but I came up with a new (and I think better) rating system today and here's how it ranks the Top Twenty:

Rank	Team	Rating
1	North Carolina	131.6
2	Kansas	129.6
3	Michigan State	126.9
4	West Virginia	125.3
5	Virginia	117.9
6	Villanova	114.9
7	Oregon	112.1
8	Xavier	110.4
9	Purdue	109.3
10	Louisville	108.9
11	Arizona	106.1
12	Duke	105.4
13	Kentucky	105.2
14	SMU	104.0
15	Indiana	103.9
16	Oklahoma	103.7
17	Miami Florida	99.9
18	Maryland	97.9
19	Baylor	97.7
20	Wichita State	97.4

I'm not entirely sure what I think of this.  The top of the rankings isn't too surprising, although I think most folks wouldn't have UNC ahead of Kansas and MSU.  Oklahoma is much lower than the #2 seed they received.  Wichita State is also a surprise at 20 -- although they seem to be handling Vanderbilt tonight so maybe there's something to that.

And I guess you could conclude that it's a bad year for Louisville and SMU to be on probation -- they were both very solid this year.

Does Coaching Experience Matter?

One of the things I investigated in the run-up to the Tournament this year was whether coaching experience matters.  My approach was pretty simplistic -- I offered my prediction model information on how a team/coach had performed the previous year in the Tournament to see if that information had any predictive value.  It didn't -- at least for my model.

Over at Harvard Sports Analysis Collective (worth reading, by the way), Kurt Bullard takes a better look at the same question.  He looks at how coaches perform relative to their seeding over their coaching lifetime.  If experience matters, you'd expect coaches with more experience to do better.  But that's not the case -- there's no correlation between how well a coach does and how much experience he has.  (Alternatively, it could be that his experience is factored into the seed his team gets, although I'd argue that's probably not the case.)

At any rate, you might want to be leery of analysts who say that "Michigan State is going to do well in the Tournament because Coach Izzo has more experience than anyone in the Tournament."  Michigan State probably is going to do well -- but that's because the Committee mis-seeded them, not because of Coach Izzo's experience.

That's Not Really A Number

Suppose that you're competing in the Kaggle competition and you're using team win ratios and average scoring for the season to predict who is going to win a game.  Your input to your model might look something like this:

Team	Win Ratio	Ave. Score	Team	Win Ratio	Ave. Score
Michigan	0.75	86.5	UCLA	0.73	81

Your results are mediocre, so you decide to improve your model by adding more information about each team.  The seeding of the team -- the NCAA Tournament committee's assessment of team strength -- seems like it would be useful for prediction, so you add each team's seeds to your inputs:

Team	Win Ratio	Ave. Score	Seed	Team	Win Ratio	Ave. Score	Seed
Michigan	0.75	86.5	5	UCLA	0.73	81	14

You've just made a mistake.  Do you see what it is?

The way you've added the seeding information, many machine learning tools / models are going to treat the seed as a number¹, not any different from the Win Ratio or the Average Score.  And that's a problem, because the seed is not really a number.  It's actually what statisticians would call a categorical variable, because it can take one value out of a fixed set of arbitrary values.  (Machine learning types might be more likely to call it a categorical feature.)  If you're not convinced about that, imagine replacing each seed with a letter -- the #1 seed becomes the A seed, the #2 seed becomes the B seed and so on.  This is perfectly reasonable -- we could still talk about the A seeds being the favorites, we'd know in the first round the A seeds play the P seeds and so on.  It wouldn't make any sense to try to do that with a numeric feature like (for instance) the Average Score.

Another difference between numeric and categorical features that merely look like numbers is that real numeric features have a fixed scale, while categorical features have an arbitrary scale.  The difference between an Ave. Score of 86.5 and an Ave. Score of 81 is 5.5 points, and that's the same amount as the difference between an Ave. Score of 78.8 and 73.3.  But the difference between a 16 seed and a 15 seed might be quite different than the difference between a 1 seed and a 2 seed.  (Not to mention that the difference between a 16 seed and a 15 seed might be quite different than between the 16 seed and a different 15 seed!)

So if I've convinced you that team seeds are not really numbers but just look like numbers, then how should your represent them in your model?

The basic approach is something called "one hot encoding" (the name derives from a type of digital circuit design).  The idea behind one hot encoding is to represent each possible value of the categorical feature as a different binary feature (with value 0 or 1).  For any particular value of the categorical feature, one of these binary features will have the value 1 and the rest will be zero.  (Hence "one hot".)  To represent the seeds, we need 16 binary features:

Team	Win Ratio	Ave. Score	Seed_1	Seed_2	Seed_3	Seed_4	Seed_5	...	Seed_16	Team	Win Ratio	Ave. Score	Seed_0	...
Michigan	0.75	86.5	0	0	0	0	1	...	0	UCLA	0.73	81	0	...

This representation gives your model much more flexibility to learn the differences between the seeds.  For example, it could learn that being a 5 seed is every bit as valuable as being a 4 seed.  If you represented the seed as a number, it would be impossible to learn that.

One drawback about this representation is that it has a tendency to rapidly increase the number of  input features.  Seeds added 32 features to the model -- adding the Massey ordinals to your model could add many thousands of features!  That can be bad for several reasons.  First, the increased dimensionality will slow down the training of your model.  This may or may not be a problem, depending upon the overall size of your training data and the computational power you have for training.  A more significant problem is that it will encourage your model to overfit.  Even if you use the Tournament data all the way back to 1985 (which I do not encourage) there may be only a few games for unlikely pairings such as (say) a #8 seed plays a #16 seed.  That may cause your model to learn a rule for those games that is too specific.

Now it may be that you disagree with the very premise of this posting.  You really do think that seeds can be treated like numbers.  The good news for you is that it is very easy to do that -- just include the seed as both a numeric feature and a categorical feature.  You can look at the size of your model coefficients or other components to see whether treating the seed as a number has any value or not.

---

1 This is admittedly a simplification.  Some machine learning models (such as tree-based models) may be flexible enough to treat numeric variables in ways that mimic categorical variables.  But many models (and notably linear and logistic regressions) will not.^↩

Machine Madness 2016

This is just a quick post to announce the return for the 7th year of the Machine Madness contest, for machine predictors to compete in a traditional bracket-style March Madness competition.  Details can be found on this page.  Last year, Dr. Amanda Schierz (aka "Bluefool") won the competition and ESPN immediately (*) sent a film crew all the way to England to interview her.  Don't miss out on your chance to be a media star!

(*) If by immediately you mean a year later.

Please come compete, and let me know if you have any questions!

Scoring the Kaggle Contest

In this previous post, I talked briefly about whether competitors in the Kaggle March Madness contest should "gamble" with their entries.  The short answer is "yes" -- if your goal is to win money, then your best strategy is to gamble with at least some of your game predictions.  (How many games you should gamble with is an interesting question for another time.) In my opinion, that's a sign that the contest is broken.  Rather than testing who can make the best predictions about the NCAA Tournament, the contest is testing who can formulate the best meta-strategy for winning the contest.  

So, is it possible to fix the contest so that the results more accurately identify the best predictions?

The log-loss scoring function asks competitors to provide a confidence in their predictions, and then scores them based upon how confident their correct (or incorrect) prediction was.  If you analyze this scoring approach, you find that the best strategy in the long run is for the competitors to set their confidence in each prediction to exactly their real confidence.  And that's exactly what you want for a fair and accurate scoring system.

The problem is that this contest is not a "long run".  In fact, it's anything but a long run -- there are only 63 games being scored.  That's a lot compared to predicting (say) just the Superbowl, but for a contest like this it's not nearly long enough to ensure that true predictions are the best strategy.  

So, how can we fix the scoring to better reward true predictions?

The obvious fix of having the teams play a few thousand games is probably a non-starter.  But it does point towards the necessary condition:  We want the competitors to be making many choices instead of just 63.  My suggestion is to have the competitors predict the Margin of Victory (MOV) for each game, and score them on how close they get to the actual MOVs.  Now instead of making 63 binary predictions, the competitors are making 63 predictions with many more choices, and -- crucially -- they don't have control over how much they will win/lose on each prediction.

It should be obvious that this makes it more difficult to "gamble" for an improved score.  Consider last year, where Kentucky was viewed as an overwhelming favorite coming into the Tournament.  Under the current scoring system there was an easy and obvious "gambling" strategy -- predict that Kentucky would win every game and set your confidence in each of those games very high.  (And in fact, if Kentucky had won the championship game, a gambling strategy would probably have won the contest.)  However, under the Margin of Victory scoring system, how would you "gamble" to improve your chances of winning the contest?  It's hard to imagine any approach that would work better than submitting your actual best predictions.

The Kaggle contest is a fun diversion and I think the results have provided some interesting insight into predicting college basketball games.  But I think the contest would be improved by using a scoring system that more accurately identified the best predictor, and I'll continue my low-key lobbying efforts (*) for that change.

(*) Which consist entirely of posting something like this every year :-)

To Gamble or Not To Gamble, That is the Question

Or at least that's "a" question -- one that comes up yearly in the Kaggle competition.  Here's a version of it that popped up this year.

The Kaggle competition (for those who aren't aware) uses log-loss scoring.  Competitors predict which team will win as a confidence level (e.g., 95% certain of a win by Kentucky) and then are rewarded/punished accordingly.  And since the scoring is logarithmic, you are punished a lot if you make a very confident wrong decision.

The question that plagues competitors is whether forcing their predictions to be more conservative or less conservative will improve their chances of winning the contest.  (Or at least finishing in the top five and receiving a cash prize.)  Note that this is only concerned with winning the contest, not with improving the predictions.  Presumably your predictions are already as accurate as you can make them, and artificially changing them would make them worse -- in the long run.  But the Kaggle contest isn't concerned with the long run -- it's only concerned with how you perform during this particular March Madness.


As a thought experiment, let's assume that you could change your entry right before the final game.  You can see the current standings, but not any of the other entries.  Would you change your entry?  And if so, how?

Well, if you see that you're in first place with a big lead, you might not change it at all.  Or maybe you'd make your pick more conservative so that you could be sure you wouldn't lose much if your pick was wrong.  But if you didn't have a big lead (and in general the farther away from first place you were) you'd probably want to gamble on getting that last game correct.  At that point "average" performance cannot be expected to move you ahead of the team's ahead of you, and even "good" performance might be passed by someone behind you who was willing to gamble more than you.

Since it's much more likely that you will be losing the contest going into the final game than in first place with a big lead, I think this argues that (if your goal is to maximize your expected profit) you should "gamble" on at least the last game.  It's left to the reader to apply this reasoning recursively to games before the final game :-).

As a concrete example of this, last year Juho Kokkala submitted entries based upon "Steal This Entry" but with Kentucky's probabilities turned up to 1.0.   The non-gambling "Steal This Entry" finished in 42nd place, but if Kentucky had won out, Juho would have probably placed in the top two and collected some prize money. 

More Kaggle News, ESPN Irritates Me

As a follow-up to this previous post, the Kaggle competition is officially back.  A good deal of data is available, and the forums have been moderately active.  The new Kaggle Notebooks feature is getting some exercise, too:  there are 116 scripts for this competition at the moment, although I'm unclear on what they all are.  There are at least a couple of scripts to calculate ELO ratings and similar things.  Might be worth a look if you're just getting started in this area.

Prizes this year are considerable -- $20K split 10/6/4/3/2.  I suggested awarding prizes for the best performance on each round of the Tournament, but that might have been too hard to implement quickly.  At any rate, spreading the prizes down to 5th place is a good improvement.  The contest is basically random amongst about the top 100 or so contestants, so weighting all the money at the top makes it even more of "random number lottery."

On a completely unrelated note, the NetProphet predictor broke on me last night.  It turned out that ESPN has changed the format of its box scores.  You can see the new format here.  The change seems to have also broken all the past seasons.  If you go to (say) November 2014 the scoreboard and schedule pages will claim that no games were played.

ESPN has been modifying their page formats for a while now, and I was expecting a change at some point.  The scoreboard page had earlier been modified to run from JSON data embedded in the page, and I was expecting to see something similar happen with the box scores and other game pages.  But interestingly enough, although the page formats have changed, they haven't gone to using embedded JSON data on these pages.  That's too bad, because pulling the JSON data out of the page, parsing it and then using it is more straightforward -- and probably a lot more robust -- than pulling data out of the HTML.