Sunday, January 07, 2007

Vinovich Better For Underdogs?

Here's a hypothesis: The rate a home team wins might be unrelated to the referee, but some refs are better for favorites than others.

I've tried to see which ref characteristics hold up over the course of a season by comparing the first half of 2006 with the second half. If they don't hold up, it seems less likely it was related to the refs as opposed to an outside factor. (I won't get into the disclaimers to this simple test.)

How about the rate that home teams win? Probably not related to the ref -- only a correlation of -0.058 between first-half home win rates and second-half home win rates by referee.

How about whether some refs are better for favorites? Yes, probably some relation to the ref. Let me get into the stats then some theories why this might be true.

The stats: using a sampling of 5 of the 17 refs, how well the net points scored matched up to how big a team was a favorite had some correlation to which referee it was. This is true whether the yardstick of determining which team is a favorite is by the team's final record (excluding the game in question) (0.186 correlation) or using net DVOA from (0.229 correlation).

Who is good for favorites? Jeff Triplette: 0.699 correlation by final record and 0.723 correlation by net DVOA.

Which had results that didn't match up as well to expected team strengths? Bill Vinovich: 0.104 by final record and 0.349 by net DVOA.

The theory: Hard to know why this would be true, but here's a theory -- some refs call the games differently from others and that makes the final result less predictable according to how the teams ordinarily do. For example, if 90% of the refs call the game one way, but 10% of the refs call it another way, then the results for those 10% of the refs will not match up well to the results from the rest of the season. Let's say 90% of the refs almost never call holding but 10% of the refs call it by the book. Results for the strict refs will be skewed to favor teams that know how to obey the rules. Results will be different from how well those teams do over the course of the season because for most of the season, following the rules strictly wouldn't matter. You can see how could make a game less predictable if a 5% of the refs call defensive holding strictly but the others don't.

So, with some refs, the favorites do better than with other refs. I will analyze many other statistics such as over/under (total points scored) to see which characteristics really look like it's related to the ref, as proven over the course of the 2006 NFL season. Post some comments if you have questions or ideas.


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