Yesterday, while watching the last five minutes of the All-Ireland Hurling championships, it occurred to me that statistical analysis might be entirely absent from the GAA and Irish sports.
To set the stage: Kilkenny was awarded a penalty with about three minutes to go in regular time. In hurling, you receive three points for scoring a goal and one point by hitting the ball over the bar and through goal posts. It was a tie match. One point was enough to put Kilkenny ahead with two minutes left in normal time and about three minutes of extra time. In hurling, it's more likely than not that someone will score in five minutes of play. One point isn't much of a lead at all, but three points, with less than five minutes, is an overwhelming advantage.
Rather than go for a goal, the Kilkenny hurler hit the ball over the bar for a single point. It was the smart play, everyone around me said.
Why?
A simple expected value analysis shows that it was almost certainly not the smart play.
If you assume that a championship calibre player scores a goal on a penalty 50% of the time, that yields an expected value of 1.5 points every time you shoot for a goal. Plus, if you assume that a goalie might re-direct a shot on goal above bar the 10% of the time, that yields an extra .1 of expected value. Plus, if a goalie re-directs the shot out of bounds, then the player gets a free, which they would likely convert, say, 90% of the time. That's an extra .09 expected value.
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| I could have won the game for my team, but I didn't |
Add it up, and a player who goes for goal has an expected value of 1.69 for every penalty attempt. If a player who goes for a point converts 99% of the time, the expected value for the conservative route is only .99.
Unless my estimates are radically off, that means that Kilkenny's decision to go for a point was not the smart play, regardless of conventional wisdom.
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I googled sabermetrics and the GAA and I found nothing. There's a company called Avenir Sports that has software that analyzes video for the major county teams, but on their website didn't give any additional details on how they conduct their analyses.
These kinds of analyses are becoming mainstream in North American sports, and they are increasingly common at the international club level for soccer. Do they exist at all in hurling?
If not, they should.
If not, they should.
Send it to Brian Cody manager of Kilkenny. If anyone would listen it would be him.
ReplyDeleteI found this from Facebook, and was pleasantly surprised and enjoyed reading several of the posts. It's refreshing writing and insight from the monotonous litany of the running Blog stuff (guilty, here).
ReplyDeleteBut I chose to comment on this one -- a topic I know almost nothing about!
One complaint I have is calling advanced statistical analysis "sabermetrics." I feel like I've seen this a lot in regard to derived* statistics. *And there's no such as a derived statistic, either, as all statistics are some sort of function on raw, measured data.
Otherwise, I would argue that a simple expected value analysis is insufficient in these cases. The increased risk of gaining /nothing/ may exceed the conservative play of being nearly guaranteed to gain /something./ An extreme example: wagering your life savings with a 51% chance of doubling it.
More salient to this case, in a sport in which I admittedly don't understand: what's the optimal strategy when there is only 1 second left? 10 seconds left? etc. The remaining time is clearly a factor. Now it sounded like there was plenty of time left for more scoring, but why would we expect the advantage in the remainder to be tilted toward either team? Another factor that would come into play would be if it's a high-scoring shootout or defensive match, and possibly home-team advantage. Without any evidence otherwise, that should be a wash. The difference is, the conservative play allows for an almost guaranteed increase probability of winning.
Your intuition may still be correct, though, but I think what you'd want is to take the probability of winning with a lead of 3 times the probability of converting, vs. the probability of winning with a lead of 1 times the near certainty of converting. Those probabilities would be based, then, on previous games and simulations, more than instantaneous expected value.
My opinion. Good stuff!
Hey Mike.
DeleteAs I was writing this, I thought to myself, "you know, the correct analysis isn't anywhere near this simplistic," but then I figured no one would read it and I just posted with the most simplistic approach. My ultimate objection was to the announcers' immediate characterization of the decision as a smart play.
But, lo and behold, if you post something wrong on the internet, people will find you and hunt you down:)
Upon closer reflection, I think that my original intuition was, in fact, wrong. Kilkenny was right to go for only one point rather than three. But only because Kilkenny was a heavy favorite in the match, and because Kilkenny would be heavily favored in the replay as well. (Irish sports have full-game replays in the event of a draw). If the only consideration were winning on the same day rather than drawing, going for 3 would have given them a better chance of winning (and losing, as it's a higher volatility play), but as a heavy favorite, a conservative approach may have been wise.
Here's my take on a more precise probability distribution:
Odds of winning by going for one point with five minutes remaining:
Odds of winning on same day: 60%
Odds of losing on same day: 3%
Odds of drawing on same day: 37%
Odds of winning replay: 66%
Overall odds of winning: 60 + (37 * .66) = 85ish%
Estimated odds of winning by going for 3:
Odds of winning same day: 65%
Odds of losing same day: 10%
Odds of drawing same day: 25%
Odds of winning replay: 66%
Odds of winning overall by going for 3:
65 + (25 * .66) = 82ish%
If Kilkenny were the underdog, the EV calculation flips around and you're better off going for 3 rather than 1.
And, more closely to your point, the closer to the end of time, the more the probability distribution shifts where you just want to be in the lead, no matter how marginal the lead may be. With one minute remaining, it would make sense for either team to go for one. With 30 minutes remaining, it would make sense for either team to go for 3. The question is at what stage the calculus shifts. I think this is a pretty close call, but upon closer reflection, I think they probably did get it right.
As an addendum, they won the replay, so they are the champions!