The team on top

In the comments section of Keith Law's post on the Angels' bizarre and misguided signing of Tori Hunter, user thoyt06 makes this comment:

I'm excited to see Torii Hunter as an Angel. K Law, as always, makes a good statistical argument which is all you can do at this point, but special teams that end up on top often supersede their statistical averages. For that we'll have to wait and see.

This comment elicited a raised eyebrow from me. On the one hand, I would doubt, though I only speculate, that Mr. thoyt06 has done the research to demonstrate his claim that the teams that end up on top often exceed their expected performance. On the other hand, he's right, but not for the reason he probably thinks he is.

Let's take a step back. If we have three teams with the same level of expected performance, which team will end up "on top" at the end of any series of trials? By definition, the team with the best actual performance will also be the team that exceeds its expected performance by the largest amount. This must be so, because the teams were expected to finish at the same level. In order to finish higher or lower than the other teams, that team will need to beat or fail to meet expectations.

Of course, in real life, all teams do not have the same expected level of performance. However, it is still the case that exceeding expectations will boost your chances of being "on top." For example, if an expected 95 win team under-performs by 5 wins (not at all uncommon) and an expected 87 win team over performs by 4 wins, the expected 87 win team will be "on top," despite the fact that it is objectively not as good as the expected 95 win team.

So the question isn't whether or not teams that end up "on top" tend to exceed expectations. On the contrary, they almost have to exceed expectations. The question really is: do some teams consistently outperform their expectations? In other words, can we identify discernible qualities or strategies that "special" teams employ that cause them to exceed expectations? If so, then it is possible that the Angels are a "special" organization and that Hunter is a "special" player.

But how do you demonstrate this? You can't use past results, because as we have shown here, you will almost always find that the teams that won exceeded expectations, simply because exceeding expectations increases the likelihood of being "on top." If you create an alternate model that identifies teams that are likely to exceed expectations, then all you've really done is created a better expectation. It may change your view of a team's strategy, but it won't change the basic premise: teams that are "on top" are likely to have exceeded expectations.

No, the ultimate problem here, particularly as fans, is to look back and attribute past over-performance to something other than chance because we want to believe that our guys are "special." We make the argument that the rules of expected performance are different for "special" teams because it allows us to claim that our guys are inherently better than your guys. They didn't win because fate smiled on them. They won because they had more "heart," or "grit," or "guts," or whatever vacuous term you choose to use to explain an unexpected result in a positive light.

So should we just "wait and see" if the Angels are a "special" team? No, not really. If the Angels outperform expectation one of two things will be true. Either they just got lucky, or they are smarter than the rest of us and have a better model of expected performance. Either way, it won't be because they have a special, magical quality to their team.