Voter Mixing Equals Criterion Mixing

I'm going to talk about basketball and probability again. Wasn't that obvious from the title of this post?

It's apparently never too early to talk about the MVP award for the NBA. We're coming up on the halfway point of the season, and writers have been tracking the MVP candidates for, oh, about half a season. Nobody takes them seriously until about now, though.

One side effect of the question being taken seriously is that some wag will point out that the MVP is not—and has never been—defined precisely. In fact, I can't find anywhere where it's been defined at all by the NBA, precisely or otherwise. That leaves the voters (sportswriters and broadcasters, mostly, plus a single vote from NBA fans collectively) to make up their own definition, a situation that said wag invariably finds ludicrous.

Well, here's one wag that finds this situation perfectly acceptable. Desirable, even.

Listen: There is no way that everybody will ever agree on a single criterion for being the "most valuable player." Most valuable to whom? The team? The league? The fans? Himself? (I can think of a few players who certainly aim to be most valuable to themselves.) And what kind of value? Wins? Titles? Highlights? Basketball is entertainment, after all. There are just too many different ways to evaluate players.

Instead, we might imagine that some writers would get together at some point and define MVP as a mixture of criteria. For instance, the title of MVP could be based in equal parts—or inequal parts, for that matter—on individual output, contributions to team success, and entertainment value.

Except, I'd argue that that is exactly what we've been doing for all these years. We have all these voters, all of whom have differing ideas of what the MVP does (or should) stand for. Some people think it should be based on individual statistics (Hollinger's Player Effectiveness Rating, or PER, is a current favorite). Some people think it should be based, at least in part, on team success, so team wins are an input to the decision (a 50-win minimum is a popular threshold). Still others dispense with explicit criteria altogether and vote based on reputation or flash.

Well, if exactly the same number of voters take each of those different perspectives on MVP, then we will have an MVP based in equal parts on individual output, contributions to team success, and entertainment value. And if more voters lean on individual output than on entertainment value, then the MVP make-up will show that same leaning. Voter mixing equals criterion mixing!

What's more, this criterion mixing is automatic. No committee needs to be formed, and the exact mixture evolves as the voter population evolves. If someday team success becomes more important to the basketball cognoscenti, then it'll automatically have a larger impact on MVP selection. No redefinition is necessary.

Can this equivalence be demonstrated on any kind of formal level? In something as complex as basketball, my guess is not. But it's close enough, and intuitive enough, that I think it just doesn't make sense to gripe about the MVP lacking a precise definition. As long as each voter comes to their own decision about what it stands for, we'll get the mix that we should.