On Ceilings and Floors and Betting

Harrison Barnes has exceeded most Warriors' fans expectations though 9 games this season. He's looked especially good in the last copule of games. This has prompted some fans to re-visit the classical sports discussion regarding a player's  "ceiling" and "floor". While the topic is one of the oldest in the book, the criteria for selecting a ceiling and floor for a player is not very clear (to me, anyway).

I think that most people see it as equivalent to asking following question:

Who is the best current or former player that Player X has *some* possibility of becoming better than?

The key word here is *some*. When a fan suggests a ceiling that is deemed too low, the response is always something like, "How can you say he doesn't have *some* chance to be better than that player!?" Well, my reply is, of course, there's *some* chance. I'm going to illustrate why this is a problematic foundation for the discussion.

I think it's fair to say that, ideally, we would like to have debates that have some objectivity to them. One way to constrain a debate to be more objective is simply to introduce a bet. A bet invariably has to be settled by some objective criteria, otherwise, neither party would agree. If we want to debate which team is better, we should bet on the outcome of a game or maybe a season. That might not truly settle the debate, but at least it's an objective approach. If I pick Team A and you pick Team B, we bet against each other, and the winner is easy to declare.

So let's think about how we might construct a bet on the ceiling for a player (the floor could be done in a similar way). Here's one way to do it. The player in question is Player X. I propose that Player A is his ceiling. You propose that Player B is his ceiling. First, we need some objective criterion, i.e. a "stat". For the sake of argument, I'll just choose a stat that most everyone reading this has heard of: Hollinger's PER. (This is not the time to debate the merit of PER. You can substitute any stat you would like, as it won't materially change the point at hand.) Ok, so with per as the base metric, the winner of the bet is the one who picks the ceiling that is closest to Player X.

Let me demonstrate with some numbers. Say that Player A's highest PER was 25 and Player B's highest PER was 30. Let's have one scenario where Player X ends up with a PER of 24. In this case, I win the bet because Player A meets two important criteria: 1) Player X did not achieve a PER higher than Player A (which would mean Player A was by definition too low a ceiling); and 2) In absolute terms, the difference between Player X and Player A is smaller than between Player X and Player B.

Now, say we have another scenario where Player X ends up with a PER of 26. In that case - and again, according to how I would set up the bet - you would win simply because Player X achieved a PER higher than the ceiling I set for him. The fact that my ceiling was closer (in absolute terms) doesn't make a difference.

Does that make sense? Let me re-iterate that this is just one way to construct the bet. Obviously, there are others. We could just take the absolute difference and not worry about whether Player X ends up higher or lower than our ceilings. I don't like that approach, because I'm used to thinking about the games from the Price is Right, where you had to guess the price *without going over*. It makes even more sense to have that rule here, because the whole point of choosing a ceiling is that we're saying that is the player's LIMIT.

The problem I have with the original (and seemingly more popular) approach to the ceiling/floor discussion is that there's really now way to evaluate it objectively. Let's use Harrison Barnes as the example. I'll say that his ceiling is Danny Granger. You say that his ceiling is LeBron James. Who would win that bet ? If Barnes never becomes "better" than LeBron, do you win? If that's the case, what exactly is the incentive of choosing any player other than arguably the best SF of all time? The ceiling for every SF would then either be Bird or James, right?

Now, I think most people inherently understand that dilemma, so they pick someone not quite as good as that for Barnes. But the criteria for doing so is usually ad hoc. It's basically, "Well, I think he has some chance of being better than this player, but no chance of being better than this player."

My point is let's bet on it. Let's put some numbers on it. The challenge here is not to pick *some* player that is the absolute ceiling (which is easy and trivial). The challenge (for me, anyway) is to pick the *worst* player that you think will be *better* than the player in question (Player X). Because otherwise, as I said, there's no incentive to pick anyone other than the best player of all time. In math, they would say that's an "ill-posed" problem. In order to make it a well-posed problem, it seems to me the logical solution is to construct it as a bet. From there everything else follows.

I know, that was a lot of words. But next time you enter into the ceiling/floor debate or listen to it on tv, just remember the main point here: Pick the guy that you would be willing to bet on.