Wednesday, February 21, 2007

Is home advantage in boxing because of biased judging?

Here's still another study from the Home Field Advantage issue of "Journal of Sports Sciences," this one called "Do judges enhance home advantage in European championship boxing?"

In boxing, if one fighter does not knock out his opponent, the winner of the fight is determined solely by the opinions of judges – that is, entirely subjectively. If the "home field advantage" in sports is partly the result of biased officials, you would expect that boxing would show a very large HFA, compared to similar sports where judges are not as large a factor.

In the paper, authors N. J. Balmer, A. M. Nevill, and A. M. Lane look at the issue by, in effect, comparing boxing to itself. Specifically, they compare fights in which there was a knockout, to fights in which the judges decided the winner. Since knockouts are independent of the judges' scoring decisions, the authors argue that if HFA is larger in decisions than in knockouts, this represents evidence of judge bias.

And, after a bunch of logistic regressions that adjust for boxer quality, that's indeed what they found.

"For equally matched boxers, expected probability of a home win was 0.57 for knockouts, 0.66 for technical knockouts, and 0.74 for points decisions. ... We suggest that interventions should be designed to inform judges to counter home advantage effects."

But there's a big problem getting from the numbers to the conclusion. Specifically, there is no reason why you should expect the HFA in knockouts to equal the HFA in decisions.

For instance: suppose that when a boxer knows he's losing on points, late in a fight, he knows the only way he can win is to knock out his opponent. So he takes lots of chances, hoping to land a lucky punch for the knockout. The opponent who's leading, on the other hand, concentrates only on defense, hoping to protect himself from a knockout to win the fight on points.

If that scenario is the cause of most actual knockouts, then it's the *weaker* boxer, not the stronger, who wins the most knockouts. It's perfectly possible that the HFA might even be *negative* on fights that ended in knockouts. And that would be the case whether or not the judges were biased in the other 90% of the fights.

In general, selectively sampling games based on *after-the-fact* criteria can give you almost any HFA at all.

For instance, suppose you want to find a category of hockey games in which the intrinsic home winning percentage is over .900. Here's one, based on a simplified model of hockey:

Suppose team A and team B are equal. Overall, they each get 30 shots on goal per game, with a shooting percentage of .100 overall. But that's an average of the home team actually shooting .120, and the visiting team shooting .080 (for an expected score of 3.6 to 2.4).

I ran a simulation of this game, and, counting a tie has half a win, the home team has an overall winning percentage of around .695.

But, you can easily show, using the binomial theorem, that the home team will have a winning percentage of .906 in games in which either team scores exactly eight goals.

How often will each team score exactly 8 goals? By the binomial theorem, for the home team, it's

p(home) = .120^8 * .880^22 * C(30,8) = 1/66

For the visiting team, it's

p(road) = .080^8 * .920^22 * C(30,8) = 1/637

1/66 divided by (1/66 + 1/637) equals .906. (This ignores 8-8 ties, which I didn't bother accounting for.)

And so:

-- in hockey games as a whole, the HFA is .195.
-- in hockey games where one team scores a "knockout" of at least 8 goals, the HFA is .406.

Compare this to what the boxing study found:

-- in boxing matches by a decision, the HFA is .24.
-- in boxing matches by a knockout, the HFA is .06.

In the hockey case, the results are due to the structure of the game, not any bias on the part of the referees. And the same could be true in the boxing case. Which means, that, unfortunately, the conclusion that boxing judges are biased is not supported by the evidence.

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