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December 15, 2005

Crooked Numbers

Deviation from Standards

by James Click

A few years ago on this very website, Gary Huckabay briefly discussed the manner of the presentation of information. As an exercise, he presented the 2002 Angels’ stats as percentages of plate appearances, noting that perhaps certain round numbers would catch our eye if they were typically presented that way. Everyone knows 100 RBI or a .300 batting average, but there are countless ways in which we can view current and past baseball statistics that dramatically change the location of those eye-catching round numbers in relation to player value.

One of the main points is that we’re all working with a learned scale of context. If you’re Clay Davenport and you’re developing EqA, you can take advantage of it by mapping the scale of your metric to the construct that all baseball fans find familiar. Or, if you’re perhaps pushing OPS as the next best offensive metric, you just have to talk about it enough and show OBP+SLG enough that people start to develop that scale. I would argue that they haven’t. For example, how good is an .800 OPS? League average? All-star level?

Actually, it could be either. A player with a .400 OBP and a .400 SLG is highly valuable. One with a .320 OBP and .480 SLG--despite having the same OPS--is not quite as valuable, or at least not to the league average team. This, of course, is one of the problems with OPS, but let’s leave that to another article.

Instead, just as an exercise, I want to discuss an alternative method of looking at player statistics taking advantage of standard deviations and the league average or mean. For example, here’s how the distribution of batting averages shook out this past year for all players with at least 200 ABs:

And some vital statistics about the distribution:

Min                 .202
Quartile            .252
Mean                .270
Quartile            .289
Max                 .335
Standard Deviation  .026