Playing with stats: What was your Fantasy Average?

I'm weak. Intellectually, I get that batting average paints an incomplete picture of an offensive player. I know that on-base percentage, OPS+, wOBA paint a better picture of a player's offensive value, that ignoring walks and extra bases and all that jazz is all very Murray Chass-ian.

But .300 just looks so damn pretty.

See, I love the new era of statistical analysis. I'm constantly baffled by the people who insist that everything we need to know about baseball we knew in 1934, like the Wright Brothers made three planes and that was it for NASA. No, we should always be learning, always working to figure out better ways to understand what we love. Anyone who argues that ... well, they're wrong.

On the other side, though, is that I'm 30. I grew up with batting average. Runs batted in, wins, saves. Ask me what a good batting average is, and I say .300. 100 RBI, 20 wins, 50 saves. Ask me what a good wRC+ is, and you gotta give me a second. Is that one of the ones scaled to 100? Or is it like slugging percentage, you want .500? Maybe it's like standard OPS, with 1.000 threshold.

Look, I get the stat. I understand it. As much as a guy who didn't get past Calc 2 in college can, I understand them all. I'm just sayin', aesthetics, man. Aesthetics.

Along with that, I have a question for you. Who was more valuable in standard 5x5 fantasy in 2013: Elvis Andrus or Mark Trumbo? Trumbo crushed Andrus in home runs and RBI, but Andrus smoked Trumbo in average and stolen bases. Runs were close enough so as to make no difference. All things being equal, what was more valuable? We can ballpark it, personal-preference it. The various sites' player raters have quantified these values, but I gotta tell you, when I look at ESPN's and see that Miguel Cabrera's number was a 15.04, I don't have the first clue what that means. It's a number, sure, but it's not analogous to anything I've ever seen before.

So I've been playing with a system of my own for assigning a player one true, overall number for his 2013 fantasy value. "Miguel Cabrera was worth X." And I've scaled that number directly to batting average. So when you see that, for example, Pedro Alvarez scored .281 in fantasy value in 2013, you know what it means. Alvarez was good. He wasn't the best, but even with his low batting average and minimal steals, his run production kept his overall fantasy value high.

For hitters, this system isn't even that complicated. A 502-PA threshold is fine for batting-title consideration, but too strict for fantasy contributions, so I took every offensive player with at least 400 plate appearances a year ago, and calculated their average and standard deviations of production (thanks Excel!) at all five standard offensive fantasy categories. From there, it's a simple process of finding out how many SDs above or below the mean a player was in each category and scaling that to the mean batting average.

For example, Joey Votto scored 101 runs last year, while the average 400-PA guy scored 65.7 with a standard deviation of 18.05. That puts Votto slightly less than 2 SDs better than the mean in runs scored. The same number of SDs better than the mean batting average (.266) would give Votto a .324, so his "runs scored batting average" - and yes I have to work on a name for that - would be .324. He scored a .294 in home runs, a .280 in RBI, a .258 in stolen bases, and of course he had a .305 batting average. Since all five categories count the same in fantasy, then, it's as simple as averaging the five contributions, and in fantasy in 2013, Joey Votto was a .292 player.

This system isn't adding anything new to the world of fantasy. Everything that was true of Votto before I told you that number is true now. Just like WAR, the Fantasy Average (better name?) is little but a sorting tool. But it's one that should give a number to the varying forms fantasy contributions take.

So, again, would you rather have Andrus or Trumbo? My complete guess is that the majority would take Trumbo and his power and his RBI last year over Andrus and his speed and batting average. And in the end, they were very close. But according to Fantasy Average, Andrus contributed a .287 in 2013, while Trumbo was a .286. A minuscule difference to be sure, but if Trumbo would have been the overwhelming favorite, as I guess, then even a tiny win for Andrus is significant.

(***Like I said, I did this for every hitter with 400+ plate appearances in 2013. It was a simple, solid threshold. Yes, a .300 batting average in 600 plate appearances is more valuable than the same in 400. Ultimately, though, those contributions are similar enough as to be rendered comparable. The problem I've run into with my Fantasy Average, though, is the other side of the ball. I could not figure out how best to factor pitchers into this little game. If I set the minimum at, say, 130 innings, then I'm eliminating all relievers, and that's worthless. But if I make it 40, I'll be scaling a 40-inning ERA against a 220-inning, and those simply aren't comparable. If you have a suggestion for how to apply Fantasy Average to pitchers, toss them in the comments; I'm all ears.***)

((Or just tell me this whole system is dumb. It could be. But I find it interesting.))

Anyway, below is the Fantasy Averages for all 204 hitters with at least 400 plate appearances in 2013. I don't expect any huge surprises in the rankings here, but I do think it's interesting to see little tidbits like Andrus-versus-Trumbo:

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