## Friday, March 9, 2012

### Does Consistent Play Help a Team Win?

That is the title of a recent post at Fangraphs by Bill Petti. He looked at the volatility of runs scored per game and runs allowed per game for teams. Click here to read it.

I am not totally clear on his technique, but here is one of his conclusions:
"Overall, RS_Vol [game to game runs scored volatility] had a negative relationship to team wins. So the more consistent a team’s run scoring, game to game, the higher their win total. The relationship was the same for RA_Vol [game to game runs allowed volatility], just much stronger."

I did a study a couple of years ago. It is below. I agree that "RS_Vol had a negative relationship to team wins" but disagree that and got the opposite result for runs allowed. I also found that just runs scored per game and runs allowed per game mattered alot more than consistency.

I took both consistency and runs per game (both scored and allowed) into account. He only took volatility (or consistency) into account. I also found that adding in variables for consistency did not improve the accuracy of the model very much.

So here is my study from April 2010

It seems to matter, but maybe much less than simply scoring and preventing runs.

I looked at two periods, 1963-68 and 1996-2000. In each case, I first ran a regression with team winning percentage as the dependent variable and runs per game and opponents' runs per game as the independent variables. Then I added two variables in a second regression which measured consistency. HITCON was the standard deviation (SD) of runs per game divided by runs per game (just the SD would not be right since high scoring teams will have a greater SD). PITCON does something similar on the pitching side.

For 1963-68 (120 teams), the first regression equation was

PCT = .528 + .108*R - .115*OR

Again, R & OR are per game. The r-squared was .903, meaning that the equation explains 90.3% of the variation in the dependent variable. The standard error was .023. For a 162 games, that works out to about 3.73 wins. Now the 2nd regression with the consistency variables added in.

PCT = .493 + .098*R - .103*OR - .084*HITCON + .117*PITCON

The r-squared did rise, but only slightly, to .912 while the standard error fell to 3.59 wins per season. The coefficinet values on the consistency variables seem to make sense. The more consistent hitting teams win more for a given average runs per game while the less consistent pitching teams win more. That may seem strange, but if you allowed 4 runs per game on average you would win at least 81 games if you gave up 0 runs half the time and 8 the other half. You would win some of those 8 runs games, so you would have a winning record. If it were a league that had an average of 4 runs per game, you would win more than expected.

On the surface, it might look like the consistency variables are pretty important. But the coefficient values are only about as high as they are for R & OR because the consistency variables are alot lower. For example, average runs per game was 3.86 while the HITCON average was.73. So the coefficient values have to be relatively high on the consistency variables.

The R & OR variables were more significant, with higher t-values. Here they are for all four:

R: 16
OR: -17.96
HITCON: -2.2
PITCON: 2.99

I also found the number of exta wins that would be generated by a one standard deviation improvement in each variable. That means scoring more runs, giving up fewer runs, scoring more consistently and giving up runs less consistently (because the coefficient on that PITCON was positive).

R: 7.68
OR: 8.12
HITCON: 1.05
PITCON: 1.34

So a one SD improvement in run scoring consistency (HITCON) adds 1.05 wins. That is a lot less that the 7.68 for simply scoring. We could say something similar on the pitching side. So it looks like a team should be more interested in just trying to score runs than being more consistent. Less consistency on the pitching side is desirable, but not nearly as much as simply preventing runs.

For the 1996-2000 period (146 teams), the first regression was

PCT = .500 + .0944*R - .0945*OR

The r-squared was .894 and the standard error worked out to 3.63 wins per season. The second regression was

PCT = .441 + .085*R - .082*OR - .139*HITCON + .202*PITCON

The r-squared was .915 and the standard error worked out to 3.28 wins per season. The results are similar to those of the 1963-68 period. Adding the consistency variables does improve the accuracy of the model, but only slightly. The signs on the coefficients are the same.

The t-values were

R: 22.5
OR: -21.3
HITCON: -3.3
PITCON: 5.3

The number of exta wins that would be generated by a one standard deviation improvement in each variable were:

R: 7.34
OR: 7.4
HITCON: 1.02
PITCON: 1.81

These numbers a very close to the numbers for the 1963-68 period. So again, it looks like it is much more important to score and prevent runs than become more consistent (or less, on the pitching side). This is true for a low scoring era, 1963-68, when the average runs per game was 3.86 as well as for the latter period when it was 4.97.

Sources: Retrosheet, Baseball Reference, Sean Lahman Baseball Archive