FanPost

Can't Remember How This Got Started: Models of NL Scoring Volatility Related to Win Percentage

"They just can't score." "This offense is so inconsistent!" "You can't win in the playoffs with slumps like this."

Etc.

This has been a familiar refrain about the Brewers this year, despite the fact that they're the #2 run-scoring team in the National League behind the altitude-powered Rockies. In fact, their scoring trend is slightly up over the course of the season, and with Troy Tulowitzki and Carlos Gonzalez out for the rest of the year, it's not crazy to think the Brewers might take the #1 spot by the end of game 162.

So, OK, maybe they're scoring a lot overall, but if they're doing that with a mix of feast and famine, they're not helping themselves win lower-scoring games. By playing slightly better than their pythagorean record, the Brewers look to be using their runs efficiently. But how do they compare to the rest of the league on this score? Below, I present analysis of run-scoring up to and including July 28, when I pulled down this data; that was the Brewers' 107th game of the season.

The first concern is figuring out how to measure volatility. I take two approaches. First is a simple standard deviation. This is a measure of dispersal around the mean that, importantly, assumes all cases represent the same thing -- that is, it doesn't take fundamental differences in cases into account. So if a team gains or loses a key player in May, their scores from April and June are still seen as representing the same thing. It also doesn't link subsets of cases together, and thus can't take "streaks" into account. This is a particular problem, because I'm interested in both offensive consistency and perceived offensive consistency. Because perceived consistency should be much more affected by day-to-day movement than in season-long distribution, I also created a measure I'll call mean absolute score change (MAbCh), which is simply how different the run total for game 2 is from the run total for game 1. This measure allows long-term change to emerge with a smaller day-to-day effect. If this is correct, you'd expect, for instance, to see the Reds have a higher SD than MAbCh because losing Votto and Phillips would alter the "true" run potential of the team's roster.

But there's one more twist on both measures -- scoring more runs increases them. So to account for this, I finally divide each measure by the team's mean runs scored. Below is a table with each team's win percentage, runs scored SD and SD/M, runs scored MAbCh and MAbCh/M, and just for fun, runs allowed SD and SD/M. For each of the mean-neutralized measures, a regression coefficient and R2 are provided.

win pct. scored SD scored SD/M scored MAbCh scored MAbCh/M allowed SD allowed SD/M
MIL 0.551 2.852 0.656 2.953 0.676 2.875 0.704
CHC 0.413 3.067 0.795 3.068 0.788 2.907 0.675
CIN 0.495 2.688 0.716 2.606 0.688 2.757 0.748
PIT 0.533 2.903 0.697 3.558 0.849 2.591 0.627
STL 0.538 2.449 0.662 2.680 0.719 3.061 0.851
ATL 0.547 2.787 0.724 2.971 0.765 2.617 0.726
WSN 0.553 2.806 0.666 3.088 0.741 2.597 0.743
MIA 0.495 2.841 0.684 3.010 0.735 2.731 0.629
NYM 0.481 2.638 0.679 2.648 0.686 2.604 0.688
PHI 0.434 2.845 0.739 3.286 0.876 3.068 0.688
LAD 0.557 2.562 0.614 2.848 0.681 3.089 0.844
SFG 0.538 2.752 0.713 3.066 0.804 2.544 0.694
COL 0.410 3.281 0.698 3.448 0.728 3.276 0.630
SDP 0.438 2.626 0.854 2.740 0.891 2.446 0.706
ARI 0.434 3.100 0.773 3.133 0.776 2.639 0.565
ß -.69 -.39 .56
R2 48.0% 14.8% 31.0%

(Least volatility in bold, second-least in italics.)

Let's visualize:

Vol-scored-sd_zps745ab545_medium

Vol-scored-ch_zpsfb1a0484_medium

Vol-allow-sd_zps83094b86_medium

The big takeaway here is that the Brewers and Dodgers are the most and second-most consistent offenses by each measure (each team wins one); they are also, respectively, the #3 and #1 NL team by win percentage. But, plain SD is a much better predictor of wins than day-to-day consistency is, even though the latter measure probably contributes more to fan perceptions. But even on the non-neutralized day-to-day measure, the Brewers are #6 in the league, and that's being driven by their outburst games. So be happy, Brewers fans!

If you do need something to be unhappy about, however, here's a little extra analysis. Let's take a look at three-game rolling averages of runs scored, runs allowed, and then the difference between the two:

Vol-trends_zps6cd2af0c_medium

Vol-diff_zps809afc74_medium

The offense has gotten a bit better over time. That's good! But the pitching has gotten quite a bit worse.

That's bad.