The WGOM

Just how inconsistent is your offense?

September 5th, 2007 by ubelmann

Since the very beginnings of baseball, fans have complained about their offense being too inconsistent. Well, I don't know that for certain, but at the end of the post, I'll give you an example of a team that I think will convince you.

If someone says an offense is good or bad, it's easy to point at how many runs they've scored as a measure of their quality. However, when someone claims an offense is inconsistent, there aren't any readily available stats to address that question.

Ideally, our measuring stick for consistency would be really simple. The simplest measure I can think of is the standard deviation of runs scored. If you've ever taken (or at least passed) a stats and probability class, you probably know about this. Those interested in the details of calculating the standard deviation should look elsewhere, but it's fairly easy to understand conceptually.

Say we have three hypothetical teams that each score 5 runs per game. The Steady Stans score exactly 5 runs in every game. Since every observation is exactly the same as the mean, their standard deviation is zero. The Jekyll/Hyde Psychopaths score 0 runs in half of their games and 10 runs in half of their games. Their standard deviation is five. The Average Joes score anywhere from 0 to 10 runs in each game, and thus have a standard deviation somewhere between zero and five.

So basically, the larger your standard deviation is, the more inconsistent your offense is. This jives with the idea of consistency because we tend to think of something as consistent when it is nearly the same each time out and we think of things as inconsistent when wildly different outcomes are commonplace.

Consistency as measured by standard deviation

Armed with the run distribution for each team and a spreadsheet, I can calculate each team's standard deviation:

The standard deviation is in units of runs. As a simple but rough way to classify the offenses, I divided the 30 teams into 3 groups of 10: inconsistent, typical, and consistent. The Twins, as we might expect, fall in the inconsistent category.

Henry Blanco Syndrome

Those astute readers will have noticed that many of the above inconsistent offenses score a lot of runs. The Yankees, Tigers, and Red Sox have essentially the three best offenses in the AL and all are considered inconsistent by this measure. It turns out that this seems to be a pattern:

We could do a linear regression analysis here, but just by looking at the graph, we can see a pretty strong relationship between a team's runs scored per game and the standard deviation of their runs scored. [Technical side note: The variance for each team is 2-3 times as large as the mean, so the run scoring distribution doesn't seem to be all that well approximated with a Poisson Distribution.]

For those who prefer charts, I divided the offenses into three groups (good, average, bad) according to how many runs per game they scored:

This gets me finally to Henry Blanco Syndrome. It is easy for a hitter to be consistent, or at least, it's easy for a hitter to be consistently bad. Because Blanco's mean is low (a .220 batting average) it's easy for him to be consistently close to his mean.

The same thing generally holds true for team offense. If you have a crappy offense that scores an average of one run per game by always scoring 0, 1, or 2 runs, it would have a very low standard deviation--it's consistently bad. Now, if you want to have an offense that averages 7 runs per game to have the same standard deviation, they are going to have to essentially score 6, 7, or 8 runs per game. I think we can all agree that it'd be a lot harder to score at least 6 runs per game than it would be to average 7 runs per game overall.

This raises some quesions:

1) Is standard deviation a good way to measure offensive inconsistency? To a degree, I think that the standard deviation is giving us an accurate reflection of how fans/players/managers/etc. view the game. Pitching and defense are highly valued because good pitching and defense are by nature consistent, while good offense is less valued because it can "disappear."

2) How much do teams control their consistency? Just by looking at the data above, one might hypothesize that there's no difference between having a high scoring average and having a high standard deviation. Thanks to GreekHouse's excellent three-part series on Piranhas versus Sharks, we have some indication that teams that depend mostly on singles are less consistent than teams that depend mostly on home runs, even if they have the same scoring average. Of course, GreekHouse examined the most extreme cases possible, so it remains to be shown how large we should expect that effect to be in a real life offense.

3) Can we devise a measure of consistency that is (mostly) independent of scoring average? The simplest thing to do here is to just divide the standard deviation by the scoring average (runs per game). I'll call this 'scaled consistency.'

This might be over-correcting the problem, since no bad offenses manage to get listed as consistent, but at least one good, average, and bad offense gets classified as inconsistent.

There are other questions to ask here regarding how this correlates to team power, how much of this is just dumb luck, and just how valuable it is to be consistent anyway. But those are questions for another day.

Back in my day, we walked uphill both ways

I earlier asserted that since the beginnings of professional baseball, fans have complained about inconsistent offenses. As supporting evidence, I present the 1871 Troy Haymakers (great name, by the way.) They finished third (of nine) in scoring that season with 12.1 R/G, well above the league average of 10.5 R/G. How they got there was a different question altogether, though. Check out their runs scored by game:

5, 29, 3, 5, 25, 20, 8, 5, 11, 3, 33, 37, 9, 3, 10, 13, 11, 4, 17, 4, 5, 5, 17, 16, 13, 3, 13, 5, 19 (And yes, the numbers on the board are correct.)

Of their 29 games all season, the Haymakers played in 2 one-run games and 17 games decided by 5 or more runs. I think it's safe to say that their fans considered the offense (and probably the whole team) a tad inconsistent.

For those old-timers out there yearning for the days when men were men and pitchers finished what they started, I present the Haymakers' John Mullin, a lefty who started every game that season and pitched all but one of the team's 250 innings on defense. His 12/75 SO/BB ratio doesn't look terribly appealing, though, even considering that the league as a whole had 175 SO and 393 BB. (And yes, perhaps I'm distracting myself with the oddities of baseball in the 1800's, but at the moment it's more amusing than perusing Twins statistics.)

This entry was posted by ubelmann on Wednesday, September 5th, 2007 at 3:00 pm and is filed under Guest Writers, MLB, Minnesota Twins, Stat Geekery, ubelmann. It is one of 640 entries by the author. We are no longer accepting Letters to the Editor on this post.