Hot Hands in Cold Water: the Advanced Stats of Water Polo

And the Wages of Wins coverage of the Western Economics Association continues! Jill Harris, who currently lectures on Economics at Pitzer College and has over a decade of experience in economics consulting, has taken on the charge of advanced statistics for water polo! What follows is a review of the her paper Hot Hands in Cold Water: An Investigation of the “Myth” Using NCAA Division I Water Polo.

Advanced stats have exploded in many sports. Economist Jill Harris decided to expand to water polo. Unlike other sports, which have tons of data publicly available, water polo is a bit more opaque. Using video data provided by James Graham, Dr. Harris went frame by frame to collect statistics “from the most recent season of men’s and women’s water polo at a top 20 Division 1 program” . In short, Dr. Harris is a one person Synergy Sports for collegiate water polo!

As Dr. Harris says in the paper

The “sabermetric” revolution has not quite taken hold in water polo; most coaches and programs keep stats of some form, but there is no standardization.

As such, this paper is definitely the start of what is hopefully a larger data explosion. The sample size is small, but it is in this data where Dr. Harris found some very intriguing results.

Yay Points!

The most important model in most sports is explaining scoring. Dr. Harris’ looked at many variables to answer a question – given a shot in a game, can we predict if it will go in? Here’s where it gets fun.

Things that were statistically significant in explaining if a shot would go in.

Variables in bold imply a positive influence, non-bold a negative.

• If the shot was a penalty shot.
• If it was the fourth (final) period of the game.
• What year the student was in college (Freshman through Senior)
• If it was the third period of the game.
• Where the player took the shot from.
• What sequence the shot was.

Some noticeably absent variables that you’d think might matter were

• If the shot was taken during a 6 on 5 (think power play, hockey fans)
• The gender of the player. (Stats were taken from both the men and women teams)
• If a foul was called on the shot.
• The player’s shooting percentage for the season.
• The player’s goals per game for the season.

As a note, while the model found did help to explain scoring, there are many other factors that appear to influence if a shot goes in. Dr. Harris produced two models, a Heteroskedasticity Corrected Model and a Probit Model. Both explain somewhere in the neighborhood of 10% of scoring. Other factors may help improve the explanation — the advanced stats of water polo are young, but already I suspect the defense flag will rear its head.

The Hot Hand?

Looking at the scoring model above, a fascinating set of variables should stand out. As a player makes more shots, the odds of a goal increase. What’s more, as the game goes on, the odds of scoring go down. Basically, it looks like players may “warm up” and “tire out”. And this leads to the coolest part of the paper.

One of the most popular questions in sports is the hot hand. Do players suddenly start scoring “at will”? In fact, this very subject was very popular at last year’s WEA. Given that the sequence of shots and time of game seemed to impact scoring, could the very streak of the player matter? The answer is a solid Mythbusters-style plausible.

Dr. Harris did a runs test for each player. This works as follows. Each series of consecutive hits is a run, each series of consecutive misses is a run. Based on the total number of shots a player takes, we can estimate how many “runs” they should have. If they have fewer runs than expected, then the idea that players can “get hot” or “get cold” becomes a very real possibility.

What were the results? Four players on the team (out of twelve total players) had fewer runs than expected by a significant margin! And on the whole, the team had many fewer runs than expected. A majority of these were scoring runs. Again, this is only one team for one season, but the initial results suggest that there are many hot hands in the cold water (which is also one of the coolest titles for a paper ever)

Summing Up

This was an amazing level of advanced stats found in one season from one very dedicated economist. The hot hand, which economists have spent decades debating and looking for, may have been in the water this whole time. Dr. Harris’ hope is that many more colleges will become convinced to start keeping track of more standardized stats (Lee Meade would be proud). So if you’re a water polo fan out there and want more exciting research, I urge you to follow Jill Harris (@jillharris). And if you happen to work with college level water polo, you could definitely help make the data for next year’s WEA even stronger!

-Dre