Take a look at total hits. It's that simple.
Not extra-base hits, not average bases per hit, just plain old hits. For reference, here are the bivariate correlations of various statistics with total fantasy points for the 2010 season (in my league, scoring system detailed here):
Hits: 0.965
Plate Appearances: 0.939
At-bats: 0.927
Runs: 0.950
HR: 0.735
RBI: 0.890
Stolen Bases: 0.364
BB: 0.749
Strikeouts: 0.601 (yes, it's positive- more K means more points)
Batting Average: 0.546
OBP: 0.536
OPS: 0.6317
It's important to note that hits/runs/HR/RBI/steals/BB/K actually generate value in and of themselves in most points leagues, so they will almost always have a high correlation. You get a point for an RBI, and so RBIs will correlate positively with points.
But hits is far and away the single biggest indicator, and here's why: hits make the most things happen. If a player gets a hit, they get a point for that. If they get extra bases on that hit, then they get more points. Home runs are incredibly valuable (they are a hit, four total bases, a run, and at least one RBI for a 7 point minimum), but they are also a subset of hits. A hit is efficient at generating an RBI; sacrifice RBI require a runner on third while a BB RBI requires the bases to be full. But on a hit, a player can score from third, second, or even first if it's a good hit. For a player to steal a base, he has to first get on base. That is most likely to happen because of a hit as opposed to BB, fielder's choice, HBP, etc.
Hits are also relatively independent; that is, they rely less on a player's situation than many other statistics. True, a player will not get many great pitches to hit if he's surrounded in the lineup by scrubs (why give him something he can do damage with when the players behind him are easy outs). But runs and RBI require other people to get hits or get on base, respectively. Home runs vary a lot by ballpark, for the simple fact that a 370-foot fly ball to left-center is a homer if the wall is 365 feet out but an out if the wall is 400 feet out (detailed much better over at fangraphs). Batting average and on-base percentage are rate stats; someone with an OBP of 0.500 in twenty plate appearances isn't going to generate many points, even if he is doing plenty with the plate appearances given. These stats are going to have the correlation then mitigated by playing time (plate appearances, games missed due to rest/injury), and would correlate better only if everyone had equal playing time.
One last example concerning the value of hits: Ichiro Suzuki has consistently been one of the most valuable fantasy outfielders; since entering the league he's never had a fantasy season less than 600 points. He also consistently paces the league in hits. His lowest total is 206 in 2005, while his highest total is a major-league record 262. His average is 224.4 hits per season, with a standard deviation just under 18. Every year, he just amasses hits. He's done this for Mariner's teams that have won 116 games and teams that have lost 100+ games. And every year, he's one of the most valuable outfielders. The hits are always there. And that's why hits are such a good shorthand.
A few other notes on the correlations. First, homers don't correlate as well as their point value should indicate because many power hitters hit for low average; they do (fantasy) damage when they connect but they don't connect often enough. Strikeouts correlate positively in large part because a) power hitters strike out more, and those hitters do damage; and b) more importantly, you have to come up to the plate to strikeout and more plate appearances means more opportunities to create positive value. The correlation on steals is abysmal, which jives with the research showing that steals generally don't create real in-game value either; a steal is only worth attempting in very specific situations.
Counting stats (hits, walks, home runs, etc) tend to have good correlations in points leagues because the more times you perform an action, the more points the player accumulates. However, rate stats are good indicators of production given a number of plate appearances. To that end, OPS is the best stat to look at. In a points league, you get extra points for extra bases, plus points for walks. Batting average (H/AB) doesn't take into account extra bases or walks, slugging percentage doesn't account for walks (TB/AB), and on-base percentage doesn't account for total bases ((H+BB)/PA). OPS takes into account hits, extra bases, and walks, and scales that by PA*AB (a full explanation is here). So if you're not concerned with the total accumulation of counting stats, OPS is the best indicator of points league value given playing time. That is, a player who hits ten home runs (controlling for other stats) gets the same number of points if it's done in 20 or 200 plate appearances. The player with 200 plate appearances will likely generate more value, but the player with 20 plate appearances has the higher OPS and is generating points at a better rate. In general, if you believe playing time is being under- or over-projected, then OPS is the best stat to look at.
Lastly, and most important, the correlation on plate appearances is worth noting. It's one of the stats that doesn't generate value in and of itself, but it still has a high correlation (.939); this number is best among all stats that don't create points in and of themselves by a wide margin. It's even better than the correlation for some stats that do create value; in fact, it's better than all stats listed except hits. The reason for this is simple: plate appearances are opportunities. Each time a player steps into the box, he can get a hit, walk, home run, stolen base, etc. If he's sitting on the bench, he can't do any of these things. That means people who will get a large number of plate appearances are the ones most worth targeting in a points league. Players who bat down in the order or who tend to be injured will amass fewer plate appearances; unless their production rates are stellar they are going to be less valuable than someone who produces at a worse rate but gets more opportunities. Incidentally (and I'll get to this in a later post), this is why I have Josh Hamilton outside the top 50 for hitters, let alone top 50 overall.
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