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Expected Return Vs. Volatility

During a lengthy debate on the wisdom of my Mike Stanton pick in the fourth round of the 14-team Yahoo! Friends and Family League, a couple of the commenters panned the pick due to the possibility (they estimated 20 percent) Stanton would struggle would due to his low contact rate and get sent down to the minors. Whether or not that's true (I think 20 is too high, and if so, that would mean he was playing badly enough to get sent down which means getting sent down would hardly make things worse), the argument boils down to: "Stanton is a bad pick in the fourth round of a 14-team mixed league because his non-injury-related floor is too low." Setting aside the merits of the argument about Stanton in particular (which are laid out in detail in the debate linked above), I think the argument misses a key point generally.

When we project players, we necessarily have to assume they'll perform at the 50th percentile given all of their possible 2011 seasons. After all, a player is equally likely to exceed or fall short of his mean level of production. For that reason, players with significant downsides are likely to suffer in most projected-stats-based rankings. But is trying to draft the best team assuming every player in the league had his average season the optimal strategy for winning an actual league where the variance is all over the map? In other words, should rankings be based strictly on expected returns, or can a player with a lower mean season but a higher 90th percentile one give you a better chance to win your league?

I would argue that the shallower the league, i.e., the higher the level of replacement value, the more important it is to focus on a player's ceiling than his floor. In other words, given two players with equal 50th percentile projections, the one with greater volatility should be worth more in shallower formats. That's because you can always replace him with someone adequate if he fails, and if he succeeds, he greatly boosts your chances of winning the league. At some point, of course, the difference in mean expected value is large enough that the lower ceiling/higher floor player is worth more - even in a shallow league. And the expected return of players in the fourth round tends to be high. But the more volatile the player, the less likely that his full potential for profit is priced in even if you draft him far higher than his 50th percentile projections would warrant.

A player's volatility then is an important consideration not captured by his mean projection and one that increases his value in inverse proportion to the depth of your league. The bottom line: don't needle me about what could go wrong - I'm focused on what could go right.

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