## Saturday, February 17, 2007

### 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.

Baseball
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?

Football
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.

Hockey
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.)

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At Monday, February 19, 2007 11:50:00 AM,  JavaGeek said...

Hockey: NHL

Someone once said that home feild advantage in hockey was the result of last change, I didn't buy it so I looked into it:

I found two major factors:

Power Play
It’s interesting to note that there are an additional 405 penalties given (only minors) to the away team (1/3 per game) (8199 vs. 7794), might sound like a little, but this should work out to around 60 goals. If you just look at the more subjective calls (the ones they can ignore) you get a more significant difference of 390 (6457 vs. 6067).

Refereeing is more about the calls they choose to ignore than the ones the make, but that's just my opinion.

The actual goal difference on the PP was 220 goals. Referees can call more 5-3 time for the home team as well [20GF/hr vs. 7GF/Hr]. Also timing probabaly matters [hard to study].

Backup Goalie
Backups play 3 extra games away than at home.

I think if you looked up games where the score was run up, it would more often be at home (so same number of 1 goal games, but a lot more 7-1 games).

Unquantifiable referee factors:
It's my personal belief that referees are more likely to call off/accept a goal in favour of a home team, these are not recorded in the scoresheet so there's no way to know. There are a lot of subjective goal rules.

Also the NHL stated at the beginning of the year [I can't find the article though] that their schedule was designed to get the home team more wins (home teams rests and the away team played the day before).

And 5 is about right (I often use 5.5)

At Friday, February 23, 2007 10:43:00 PM,  Phil Birnbaum said...

Javageek, What's 20GF/hr vs 7GF/hr mean? Is "hr" the amount of time actually spent with a 2-man advantage? I'm confused.

At Tuesday, May 29, 2007 1:54:00 PM,  Anonymous said...

Refree bias is as old as hockey itself but I feel the new NHL rules have given additional leverage to referres to dictate basically who wins or loses a game. And I couldn't agree more with the comment stating that its about what refs don't call then what they do call that counts as bias. The Ottawa vs. Ducks game in Anaheim in the first round of stanely cup finals is a great example of that. Ottawa could have theoretically won that first game...and they were winning until the refs began their offensive in the 3d period. Its impossible to win a game when the deck is competely stacked against you!