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What to Make of a Small Sample

Trevor Story already has seven home runs. Should you sell "high," and if so what's high? Is it a player like Christian Yelich or Nelson Cruz? The answer depends on what meaning you extract from Story's mind-blowing one-week sample. In February, I emphasized how a sample's size was only one factor, its amplitude being the other. If Story hit three homers last week, it would still be a strong start, and the sample would still be one week, but it would easier to chalk up to variance. Seven home runs per week is obviously not sustainable even for Babe Ruth on steroids in Coors, but it's more likely we're looking at a 25-homer baseline player (in Colorado) than it was before the season. All but the most irrationally-stubborn Story-faders would concede that, but how much more likely? Are there stats we can use to determine whether a power spike is for real?

At Fangraphs (building on Russell Carleton's work), you can see how far into the season(s) particular stats "stabilize." By that they mean, you have a pretty good sense of the stats being indicative of the player's skills. By "pretty good sense" they mean starts to correlate reliably to future performance, showing us his likely baseline skill level. By "reliably" they mean the correlation is .7 among the entire pool of players. (It's possible I'm misstating these definitions slightly, but the gist is that after a given number of plate appearances/batters faced, a player's skills come into focus. Before such time, the preponderance of the player's performance is equally or more likely to be explained by variance, i.e., luck.)

For home run rate (HR/PA) to stabilize, you need 170 plate appearances. Through six games, Story has only 28. Plainly, Story's 25 percent rate of home runs per plate appearance is not "stable." If it were, we'd expect him to hit 150-plus home runs this year. Were Story to have 43 HR 170 plate appearances into the year, we'd have to take the possibility seriously. So Story's seven-homer week is mostly luck and not remotely indicative he's the greatest player of all time by a wide margin. But that information isn't especially useful. No serious fantasy owner even in a 10-team mixed league would leave Story on waivers until the 170-plate-appearance threshold before picking him up. What we need more than the .70 correlation standard is a sliding scale where 25 plate appearances means it's 10 percent likely to be skill/90 percent luck, 50 means 20/80 and so on until we get to 170 when it's greater than 50/50. Because players on waivers (or those you draft in the middle and late rounds) are like stock options. You're buying once the threshold hits five or 10 or 15 percent (ownership styles vary), hoping the player's performance leaves you in the money.

So we need to have an idea of what a small performance sample says about the possibilities - not the likelihood - regarding a player's skill set. The best fantasy owners live in that sweet spot - not picking up every random player who hits an odd home run or two, and also not waiting forever for proof.

Of course, any system that uses a sliding scale to calculate when a player is five or 10 or 15 percent likely to have developed a new skill has to take into account not only the number of plate appearances (sample size), but also the magnitude. It might be five percent likely Story has a 25-homer power level after three home runs in a week, but 30 percent likely that's so after seven. This isn't an easy thing to model, and that's not even taking into account scouting information about the player, venue, age, etc. Bottom line, for now you're largely on your own. Every year certain players will produce at a level not commensurate with anything they've done before, and there's no magic formula (yet) to tell you when it's for real. The best owners will spot plausible upside before it costs much a little sooner than everyone else and pounce.