Inspired by Sax's graph of the "Druw Jones Industrial Average", I decided to take a closer look at the conventional wisdom that says Russell Martin's '07 was superb until the last month, at which point the wear and tear of the season took its toll.
Certainly a perfunctory look at his batting average by month seems to support this theory:
Why, he batted no lower than 0.284 in any month until his horrid 0.259 in September! Furthermore, looking at his running cumulative average, one might fixate on the fact that throughout the season his average wavered between 0.366 and 0.288, and conclude that because his season-ending average of 0.293 was near the nadir, it further supports the theory that he got worse as the season wore on.
While both monthly average and cumulative batting average are oft-used and easy-to-digest metrics when attempting to identify temporal trends, I dislike both. I dislike monthly average because:
- The analysis ends up being defined by arbitrary boundaries (i.e., when each month begins and ends).
- It removes any continuity. Analysis becomes limited to 6 discreet data points, which removes the ability to see any intra-monthly and almost all inter-monthly trends.
And I dislike looking at cumulative averages because as the season goes on and at-bats pile up, one's batting average becomes less and less sensitive, which removes both chronological symmetry and the ability to decipher much past the all-star break.
So let's take a look at my preferred metric - the progressive average of Martin's trailing 20 games - and graph it against cumulative average:
With the cumulative average, you will see the wide swings at the beginning, but once you get to about August, the at-bat denominator gets so big that his average hardly moves and any trend becomes very difficult to identify. However, with the trailing twenty games average, you can see that while he definitely sucked the last two weeks if the season, he had two earlier periods of equal or greater suckitude, and each time came back strong.
Presented another way, if one looked only at the cumulative average graph, could Martin's early-August swoon be spotted? After all, his average hovered just below 0.300 that whole time. And similarly, looking at only monthly averages, his 0.303 July and 0.300 August also completely hide this swoon.
Anyhow, I am very late for a meeting and don't want to get fired today so I will leave it at this.