Is the D-backs Offense Particularly Feast or Famine?

Thanks in part to playing a majors-high 56 games (thanks, Australia), the D-backs are actually tied at 13th for runs scored in the majors so far this year. Switch to runs scored per game, and the team ranks just 21st in the bigs and 8th in the NL. That’s not bad, but it clearly has not been enough to carry a pitching staff that is dead last in runs allowed per game.

Us Inside the ‘Zona guys never seem to run out of things to check on or questions to ask or answer, but there are only three brains coming up with article ideas — it’s nice to get some other brains to ask questions for us, too (reach out to us in the comments, or on Twitter!). Last week, Devan of Cover Those Bases wondered if an inconsistent offense was partly to blame for the D-backs’ lack of success this year. I responded that I wasn’t sure the D-backs offense actually was inconsistent, but pledged to look into it. It turns out that it’s a more complicated question than I thought.

I logged the runs scored of each of the 30 teams, per game, to help me arrive at an answer. My first approach was to calculate the standard deviation of runs scored per game for each of the 30 teams. Standard deviation could stand in as a number representation of “inconsistent.” Based on a “normal distribution,” also known as a bell curve, we would expect 68% of the runs totals from particular games to be within 1 standard deviation of the same team’s average number of runs per game (and 95 % within 2 standard deviations).For example, a team that scored an average of 4 runs per game in 50 games by scoring 2 runs half the time and 6 runs the other half of the time would show a standard deviation of 2.02. A different team that also scored an average of 4 runs per game, but which always scored either 0 runs or 8 runs, would have a standard deviation of 4.04.

The standard deviation for runs scored in all MLB games through Wednesday is 2.92. In other words, there’s about a 68% chance that the runs total for a particular team in a particular game was within 2.92 runs of the average number of runs scored per game: 4.16. We could also infer that there would be a 68% chance of any particular team scoring within 2.92 runs of 4.16 in each game moving forward.

The standard deviation for runs scored by the Diamondbacks in their games is 3.07. That may mean they’re a little more “inconsistent” than average. That 3.07 figure ranks 11th among the 30 MLB teams, so if standard deviation means “inconsistent,” then the D-backs are a little more inconsistent than average, but so much so that it’s remarkable.

But that’s a big “if.” It turns out that there’s a fairly strong link between the standard deviation of a team’s runs in individual games and its overall average of runs scored — I calculate the “R” score, which measures correlation, at 0.556 (0 meaning “no relationship,” 1 meaning “perfect relationship,” and -1 meaning “perfectly opposite relationship”). Essentially, the more runs a team scores overall, the wider the spread of scores in individual games.

This makes a lot of sense. Runs scored in individual games don’t get distributed in a normal distribution or bell curve. I’ve expressed standard deviation to the hundredths place with decimals because they aren’t very meaningful without them — but at the same time, no team could ever score exactly 4.16 runs per game, or exactly 2.92 runs more or less than 4.16. Runs are integers. And teams can never score a number of runs two standard deviations under 4.16, because it’s impossible in the game of baseball to score less than 0 runs.

This matters because extreme games can only be extreme in one direction — up. The Rockies lead the majors in runs scored per game (5.02). But while they can never put up a runs total lower than 5 runs below that average, they can post runs totals higher than 5 above. In fact, the Rockies have scored 11 or more runs in five games this season.

If teams could put up negative runs totals, then I’m not sure there’d be a correlative relationship between runs scored per game and standard deviation of runs scored per game. But because the most extreme game scores can only be high game scores, the high standard deviation teams also tend to be teams that had high-scoring games, and teams that had high-scoring games tend to have high runs scored per game averages.

I tried a number of other methods to look for inconsistency; instead of using a mean for “average,” I tried using the median runs scored (for the D-backs, that was 4), and also the mode, or most frequent game score for each team (the D-backs’ most frequent runs scored total was 5, which was true for only one other team, the Brewers). I tried segregating extreme examples, counting games with runs scored totals either below 2 or above 6. But none of these methods seemed to lend any insight to the analysis, because they tended to make the sample size actually or virtually smaller. At that point, single games made huge differences, and that seems to say a lot less about the nature of teams’ offenses.

The best example of the effect that a single high-score outlier can have is actually the Diamondbacks. Remember the party they threw at Chase Field the last Saturday that the Dodgers were in town? If we remove that 18-run game from the data set, the standard deviation of runs scored in D-backs games drops all the way from 3.07 (which was somewhat, but not particularly “inconsistent”) to 2.41. That 2.41 figure would have ranked the D-backs just 27th in the majors — even with the 12-run performance on Wednesday. In other words, without that single 18-run game, the D-backs offense would have been the fourth most consistent offense in the majors.

Of course, being “consistent” doesn’t necessarily mean “consistently good,” and so consistency can be a bad thing if it means being consistently bad. But as Jeff explored yesterday, the D-backs offense hasn’t been tied to home runs, necessarily, and one would at least expect that it’s the teams that rely largely on walks and home runs that are least “consistent” from game to game (the team with the highest combined walk and HR rates, the Oakland Athletics, do indeed have the second-largest standard deviation in runs scored per game). But the D-backs are doing it their own way. That might mean some low runs totals, but at least it keeps things interesting.