How much referee bias would it take to account for home field advantage?
One more thought on the subject of whether the home field advantage (HFA) could simply be due to refereeing bias: it occurred to me that you can measure *how much* bias it would take to account fully for the HFA.
For baseball, most of umpiring is ball/strike calls. The home winning percentage in MLB is about .540, an "excess" of .040. To convert .040 losses into wins, you need about .4 runs. That's about three strikes turned into balls (or vice-versa, when the visiting team bats).
Does that seem reasonable? How many borderline calls are there in a game, and are there really enough that the home team could get three more in its favor than the visiting team?
The NFL home winning percentage is, I think, around .590. It takes about 400 yards to equal one win, so the home advantage is about 36 yards. Are there enough controversial calls (or non-calls) in a game to add up to a net of +36 home yards? This one, it seems to me, is harder to answer – there's so much simultaneous action in the game that it would be hard to notice missed infractions.
Assume that referee discretion in basketball is mostly foul calls. A foul on the offense that leads to two foul shots turns an expected one point (teams score about a point per possession) into about a point and a half (75% foul shooting percentage times two shots). So a foul is worth half a point.
It takes 30 points to turn a loss into a win, and the NBA home winning percentage is .625. That means the refereeing has to favor the home team by almost four points a game – which is eight foul calls (or non-calls). Seems high, but I don't really know.
The NHL home winning percentage last year was .573 (not considering the bonus point for a "regulation tie"). I don't know how many goals it takes to turn a loss into a win – but, to be conservative, let's suppose it's 5. That means the home team has an advantage of .36 goals per game.
Assuming a minor penalty is worth .18 goals (which looks like a typical power-play conversion percentage), that would require referee bias of an extra two penalties per game to the visiting team. That seems a bit high to me.
But I have to emphasize that I don't really know – I don't watch enough games to know the frequency of controversial or missed calls for sure. Just going by my intuition, and what the TV announcers say, I'd guess that referees don't make enough biased calls to account for the home field advantage.
I suppose you could study this by listening to both the home and away broadcasts of games, and counting the number of times the announcers or commentators question a call.
I'd be interested in what others think. Have you noticed any apparent bias in officiating? If so, how much do you think there is?
(And please correct my numbers above, if I've used incorrect ones, which I probably have.)
Labels: home field advantage