# Stats to the Limit

Via True Hoop, Jonathan Weiler has an informative run-down of the state of play in terms of NBA quantitative analysis. The point he makes about interaction effects keeps coming up in critiques of *The Wages of Wins* and I thought one potentially better way to make the point would just be to observe that the linear analysis *WoW* employs just produces results that are obviously mistaken even on its own terms. You can see this if you look at any *Wow* evaluations and then imagine an outlandish situation. As they note in the book, their methods, if employed literally, suggest that a team of sufficiently good players would win more than 82 games.

Since there are only 82 games to win, it's obviously not the case that the right personnel will give you 90 wins. Similarly, *WoW* implies that a sufficiently bad team could wrack up a negative win total, which is also false. If we lives on Karl Popper's dream planet we could just see that this model implies things which are false, and then reject the theory out of hand. The growth of knowledge in the real world, however, doesn't work like that. It's clear from those examples -- examples you can find in the book -- that the linearity assumption isn't actually correct. The trouble is that if you relax that assumption, the math becomes much more difficult and it's still totally unclear how you can improve the model. This, in turn, stems from the fact that though thought-experiments about extreme situations can show us that team wins have to add up to 82 or fewer wins, we have very little *actual data* about extreme situations.

Looking at *WoW* I think something almost all basketball fans have trouble with is the seeming implication that if you put five high-efficiency, low-volume shooters who were good at rebounding and avoiding turnovers on the floor simultaneously that you'd have a really effective team. This seems wrong to most of us; it seems as if in that situation the team would either see turnovers skyrocket (shot clock violations) or else shooting efficiency decline. And it would be good to have a formula that took that sort of thing into account. To construct a formula like that, though, you'd either need to *just guess* what would happen, or else you'd need much more data out of which to try and build an empirically grounded non-linear analysis. But since as best I can tell no coaches actually field lineups like that (they, like most people, are just assuming it wouldn't work) there isn't much to be done.