I know I probably should just shut up about this stats-based stuff, but I can't let go without one more note.
"Batting Champion" is similarly arbitrary, based as it is on batting average. But what do you think would be more effective in terms of team production, a 400 AB .340 hitter, or a 650 AB .320 hitter? What kind of ridiculous moves have managers made at the season's end to try to secure batting titles for their players, benching players so they don't risk having their average drop when somebody 3 or 4 points back is in hot pursuit? The batting champion should be determined by a player's "Hits above average", not by simple percentage of hits per at bats, which is meaningless statistically. (By the way, a .340 hitter with 400 at bats is 28 hits above average; a .320 hitter with 650 at bats is 32.5 hits above average.)
Here's an example: as of yesterday morning, Todd Helton was 129 for 399, for a batting average of .3233. This is 21 hits above average. Miguel Tejada was 148 for 466, .3176 BA, but 22 hits above average. I favor Tejada, though Helton is considered by most people to be the slightly better hitter (as evidenced by old-timey Sunday morning listings of the top 100 batting averages.)
But the real key to understanding why Tejada's performance is better is this; start with the player with fewer at bats, and determine what he would need to do to attain the other's achievement. Which player is better should be determined by whether the difference in the performances is above or below average. In order for Helton to exactly match Tejada, he would have to go 19 for 67. 19/67 = .284. Since Helton's got to turn in over-average performance to reach Tejada, Tejada's better (with a smaller batting average.) If Helton could reach Tejada with a sub-standard performance, Helton must have started higher.
Similarly, in the pitching discussion, Haren's allowed 143 baserunners in 161 innings, Lincecum's at 176 BR in 172 IP, Carpenter's at 128 BR in 131 IP. For Haren to "reach" Lincecum, he can allow 33 baserunners in 11 innings, a WHIP of 3.000; Haren's WAY ahead of Lincecum. For Carpenter to "reach" Haren, he can only allow 15 BR in 15 IP, a phenomenal WHIP of 1.000, so Haren's ahead of Carpenter; and for Carpenter to "reach" Lincecum, he can only allow 45 BR in 48 IP, less than one baserunner per inning, so Lincecum's ahead of of Carpenter; and so on. The beauty of the single "Innings above average" stat is that for every pair of pitchers you choose, the one with the higher IAA will ALWAYS be better in this regard.
I am similarly tortured by non-sports ranking methods.
