One of the perplexing things about the first half of the 2009 season for the Rays has been the run differential, which is seemingly indicative of a great performance but not necessarily reflected in the W-L record for the Rays.

A potential source of the discrepancy between expected W-L and actual W-L is found in bad luck, which the Rays have been party to this year. This includes performance in close "1-run" games, high leverage situations ("runners in scoring position") and other such areas of chance.

Another source, however, may be found in the Rays run variance. The Rays have experienced the following:

Runs scored per game (standard deviation): 5.35 (3.56)
Runs allowed per game (standard deviation): 4.49 (2.84)

Runs scored per win (standard deviation): 7.40 (3.31)
Runs allowed per win (standard deviation): 2.84 (2.00)

Runs scored per loss (standard deviation): 2.95 (2.04)
Runs allowed per loss (standard deviation): 6.12 (2.82)

We have exhibited a pretty high level of variance in runs scored. In fact, the RS standard deviation represents more than 1/2 of the mean, which means that we'll observe rather useless results like: about 68% of the time, we score between 1.79 and 8.91 runs. Wow! So we're scoring between about 2 and 9 runs per game most of the time. Even if we try to squeeze the interval, it's very tough - the standard deviation (and therefore variance) in runs scored is ridiculously high, especially in our wins. So, that would help to explain some of the seeming discrepancy in our run differential.

Ideally, we'd like to score as many runs as possible, but additionally, we'd like to be consistent - that is, we want to capture a reasonable 68% or 95% interval for our RS. For example, between a team that scores 4.5 RPG with a .5 SD and a team that scores 5.5 RPG with a 3.0 SD, which would you pick? Tricky question: The 68% interval (1 SD) for the first team captured 4.0 - 5.0 RPG, while the 68% interval for the second captures 2.5 - 8.5 RPG. Which is more valuable? More than likely the first, as teams are pretty close to "as likely to win" with 5 runs as they are with 8, but much disadvantaged when they score 2.5 or 3 runs as opposed to 4.

via i29.tinypic.com

In the next part, I will examine how the Rays stack up to the other teams in the major leagues in terms of run variance and try to reconcile our run differential with the results. After taking a preliminary look at the numbers, it appears that the Rays are by and far in the lead in terms of runs scored variance.