March Madness Bracketeering

Methodology Sports
  1. March Madness Bracketeering
  2. Applied Bracketeering: Modeling March Madness
  3. Bracketeering update: Mascot randomness is beating the pants off RPI after round 2
  4. Applied Bracketeering: So, who saw that final four coming?
  5. Applied bracketeering wrapup: Highly-rated team wins in shocking finale
  6. Applied Bracketeering: Does our model also work for the NCAA Women’s tournament?
  7. Applied Bracketeering, 2018 Edition: Do streaks matter?
  8. Applied Bracketeering, 2018: Streaky Clean
  9. Bracketeering Sweet 16 update: The Infallible Braculator agrees to never speak of this past weekend again
  10. Bracketeering Final Four update: Round of the Usual Suspects (and Loyola)
  11. Bracketeering Finale: Much ado about nothing or A tale of four regions
  12. What countries punch above their demographic weight at the World Cup (and can this be predictive)?
  13. World Cup Predictions: in a bonkers first round of games, even the best models get just over 50%
  14. World Cup Predictions: Most models underestimate the chance of a tie.
  15. World Cup Predictions: Knockout round madness
  16. World Cup Predictions: The final countdown
  17. World Cup predictions wrap-up: Vive le France!
  18. The Insufferable Braculator™ Strikes Again. Can your NCAA Women’s Tourney predictions beat it?
  19. The Insufferable Braculator models NCAA Women’s basketball, chapter 2: Concerning chalk

By: Richard W. Sharp

Something fascinating about March Madness is that the smart money always loses. You’ll always do respectably in the office pool, but you’ll never beat that guy who went to Davidson in 2008 and was Steph Curry’s roommate. Unless you pick some upsets, usually based on irrational faith in your alma mater, you’ll finish in the middle of the pack.1

In order to produce a more widely useful pseudoscientific method we’re going to add a tried and true wildcard factor to the analysis: mascots. Yes, there have been plenty of “let’s rank the mascots articles” in the past, but we’re not here to talk about the past, we’re here to settle the most important question of the day. We’ll start with a model based on the safe bets, then mix things up a bit (but not too much) by factoring in our own, highly-biased-toward-wildcats mascot ranking.

The question

So how much randomness is the right amount? What dosage of crazy maximizes your potential outcome?

The smart money

First things first, how do we generate a consensus among the experts? Who are the experts? That at least isn’t too difficult to answer. There are many team ranking systems out there. Top 25 polls, like the AP poll are well known, but not very useful for us. We’ll need a ranking that at least covers all of the teams in the tournament. The best known of these is probably RPI, but there are literally dozens of others.2 Fortunately, a large selection of these polls have been recorded for posterity by the folks at Massey Ratings. From RPI to BPI to 7OT they’ve got you covered.

Next we’ll need to see how these rankings fared in the past. For that we turn to the folks at Kaggle, who hosted a contest on this very subject last year, complete with handy historical data. We’ll score each ranking system by first turning the ranking into a bracket (for each pair of teams, the top ranked one moves on to the next round). For each correct pick, points are awarded. There are lots of schemes out there, but we’ll keep it simple: play-in games are excluded, and the points-per-correct-pick in each round are as follows: 1, 2, 4, 8, 16, 32 (for a consistent total of 32 possible points each round).

Each of the polls was scored for the 2010-2015 seasons and the results compiled in the chart below. There’s quite a bit of variation from year to year, but it’s clear that some polls are better than others. RPI does not impress (keep scrolling, scrolling, scrolling… there it is!).

Ranking the models: How much better are they than RPI?
Ranker 2010 2011 2012 2013 2014 2015 mean pts (of 192) mean %possible pts mean % above RPI
Sagarin 85 46 135 116 64 96 90.3 47.0% 34.2%
Doktor Entropy 88 49 127 114 59 99 89.3 46.5% 32.7%
Bobcat 85 46 129 117 65 90 88.7 46.2% 31.7%
Whitlock 84 51 130 117 60 84 87.7 45.7% 30.2%
Kirkpatrick 89 50 119 115 60 90 87.2 45.4% 29.5%
Pigskin 85 46 125 114 68 84 87.0 45.3% 29.2%
Sport Theory 85 47 118 116 61 90 86.2 44.9% 28.0%
Pomeroy 110 50 132 83 60 78 85.5 44.5% 27.0%
Sagarin-Elo 65 47 122 116 68 90 84.7 44.1% 25.7%
Rothman 67 47 121 113 61 94 83.8 43.7% 24.5%
Wilson 67 46 132 111 68 78 83.7 43.6% 24.3%
Wrathell CPA 79 46 130 87 56 103 83.5 43.5% 24.0%
Massey 66 51 122 109 67 83 83.0 43.2% 23.3%
Pugh 67 45 120 108 68 87 82.5 43.0% 22.5%
Dance Card 72 59 130 80 65 87 82.2 42.8% 22.0%
Cheong 79 47 125 86 57 99 82.2 42.8% 22.0%
Moore 88 51 78 115 64 88 80.7 42.0% 19.8%
Daniel Curry Index 86 48 79 115 61 86 79.2 41.2% 17.6%
LRMC 86 45 131 69 61 73 77.5 40.4% 15.1%
Krach 66 45 126 64 69 89 76.5 39.8% 13.6%
Wobus 66 46 126 60 68 91 76.2 39.7% 13.1%
Dolphin 65 49 118 64 69 91 76.0 39.6% 12.9%
Wrathell CPA Retrodiction 52 41 140 67 62 92 75.7 39.4% 12.4%
Bihl 66 49 118 60 68 91 75.3 39.2% 11.9%
RoundTable 86 43 67 100 50 105 75.2 39.1% 11.6%
Rewards 61 48 113 55 66 106 74.8 39.0% 11.1%
Wolfe 66 45 117 59 62 91 73.3 38.2% 8.9%
Nolan 68 51 109 55 56 76 69.2 36.0% 2.7%
Colley 66 51 85 52 68 84 67.7 35.2% 0.5%
Snapper’s World 80 49 80 52 62 82 67.5 35.2% 0.2%
Real-Time RPI 69 48 82 56 61 88 67.3 35.1% 0.0%
RPI 69 48 82 56 61 88 67.3 35.1% 0.0%

The stupid money: Mascots

To introduce a little chaos to the order of the various polls, we’ve ranked the mascots of the top 100 teams using a patented infallible method: our gut. Hey, we’re trying to pick something random that has no bearing on team performance!

In a two-step process, mascots were ranked by category, then the categories were modified as we pleased. There were some simple rules: originality is to be rewarded, and mascots should be nouns (that’s bad news for Syracuse). So at the top we find forces of nature (hurricanes) and we progress all the way down to colors (again, mascots should be nouns).

Some mascots are deserving of extra praise or scorn, which is added or subtracted from their base category. Bonuses were awarded for fierceness (e.g., Wolverines, Yellow Jackets). Yosemite Sam style characters (aggressive caricatures of men such as Mountaineers or Trojans) were generally penalized for unoriginality. Gandhi-like pacifists (Friars, or if the Quakers ever make it back) got a bonus for guts, and extra points for any team that knows you either go big or go home (Buffaloes, Bison!).

Mascot power rankings by category
Mascot types, from highest to lowest weight.

Putting it all together

Finally, we need an ugly method or two for combing the good and the bad.  Two methods showed some promise for adding the randomness we need to win a pool to the mix.

The first is a way to combine multiple polls through a voting procedure: for each team, a specified number of polls are chosen at random (with replacement) and the team is assigned the average rank among them. This is similar to just taking the average between all of the polls, but it gives us some idea of the range of potential outcomes that are possible, instead of just the center of the range. Early exploration also revealed a case in which two heads are better than one: combining the Kirkpatrick and Pigskin polls can outperform the Sagarin poll (the highest-average performer).

However, we’ll use a second, simpler approach to add in the mascots. We’ll grade on a curve by adding zero-mean normally distributed noise to the top individual polls. The mascot ranking can be scaled to this bell curve once we decide how wide to make it (standard deviation is now related to the number of steps in the ranking we’re willing to let a team rise or fall at random).

But how much randomness should we pour on the fire? Let’s find out.

We know that no noise at all won’t do us any good, but also, too much noise would just produce a random bracket which wouldn’t be very useful either. Our goal is to win the pool as often as possible, not just get the highest average number of points, as many pools award no cash for second place. We’re trying to maximize money, not correct picks.

So, we need to use enough noise to maximize our chance of a significant improvement over the model. We want to look for the best best-case scenarios and accept that these will blow up in our faces more often than the models but also more often turn up winning brackets (nothing ventured, nothing gained). The chart below shows the 90th percentile of points gained through adding randomness at different noise levels (standard deviation).

All three schemes below show a clear peak somewhere around 4 to 6 on our noise scale. Bingo!

Maximizing noise in tourney predictions
The sweet spot to maximize your bracket wins: That hump between 4-6.

Coming soon

Over the next couple days we will produce a large number of brackets combining some of the top polls with mascot seeded randomness (games start Thursday, 3/16). We’ll track these through the tournament and report back in a couple weeks.

Notes:

1 As a Northwestern alum, I think it’s finally my year in more ways than one. Look out, fellow bracketeers. ^
2 One personal favorite is the LRMC model. It’s Bayesian at heart and based primarily on point difference outcomes from all regular season: simple in concept, complex in spreadsheet.^

About The Author

Richard is a Seattle area data scientist who builds predictive models and the services that deliver them. He earned a PhD in Applied and Computational Math from Princeton University, and left academia for the dark side of science (industry) in 2010, following his wife to the land of flannel. Fan of coffee, beer, backpacking and puns. Enjoys a day on the lake fishing, and, better, cooking up the catch for a crowd.

No Comments on "March Madness Bracketeering"

Leave a Comment