By Daniel Alpert and Timothy Pugh

Every year, Baseball-Reference comes out with statistics showing each team’s total wins above average (WAA), but also that WAA broken down by position. For those unfamiliar with WAA, it is the amount of WAR a player generates relative to the average player, or basically WAR above average. For example, the table below shows the breakdown for the 2017 Boston Red Sox. In total, their players combined for 8.4 WAA—it’s clear that their pitching carried them, as their pitchers combined for 8.7 WAA, while the non-pitchers combined for -0.3 WAA.

Looking through this data for each team since the 2000 season, we wanted to know if all positions are made equal. In short, we want to know if each position contributes equally to a team’s end of season win total. Hypothetically, each WAA is worth exactly one win, so we should see that no matter which position that WAA comes from, it should contribute exactly one win to the end of season total.

The first task is to prove that one team WAA is actually worth one win to a team’s end of season total. We can do this by regressing total WAA on a team’s wins. We collected each team’s positional and total WAA data as well as their win totals from the past 18 seasons (2000-2017) to run the following regressions.

We find that each team WAA is worth 0.991 wins and that is zero WAA will win about 80 games. So we essentially find that a team that is zero wins above average is about .500 and each positional WAA increases the team’s wins by 1—very in line with what we expect.

If we regress each positional WAA on total wins, we should find that an increase in 1 WAA for each position should increase the total wins total by 1—i.e. each coefficient should be about 1, just as we saw in the first regression.

The table above shows the results of three regressions—one for the full league, one for just the AL (which includes DH), and one for just the NL. We expected that each coefficient would be 1. For example, for each WAA that your first basemen (1B) increases by, we expect the team’s win total to go up by 1 as well. What we found, however, shows slightly different results. Nearly every position has a coefficient of about 1, but slightly above. For example, in the all-league regression, first base has a coefficient of 1.14, indicating that your first basemen improving by 1 WAR actually improves the team by 1.14 wins. This is interesting but not altogether crazy given that the data can be pretty variable.

To test the variability of the data we constructed 95% confidence intervals for each coefficient for each position for each league. The results are displayed in the table below.

The surprising results come with catcher. The three regressions suggest that catcher has the highest coefficient. This means that on average for each WAA your catcher improves, the team gains 1.37 wins.

Intuitively it makes sense that catcher has the highest coefficient as the catcher is involved with every pitch defensively. The recent statistical advances in measuring pitch framing promote the idea that catcher should have the highest coefficient as they greatly affect pitcher performance. One reason that the position is undervalued by conventional WAA is that, for a long time, pitch framing was not factored into a player’s value. As such, good defensive catchers were likely not valued highly enough by old models.

It’s also interesting to note that there is no overlap between the confidence intervals for the coefficient of catcher in the AL and in the NL. We have no explanation for why catcher might be more important to an AL team than to an NL team. This may also be a result of randomness or variation from the data. By definition, 95% confidence intervals are not completely perfect. If we were to construct 100 different 95% confidence intervals using the same method but with different samples of data, then 5 of those intervals would not contain the true WAA coefficient. So there is a small chance that the true WAA coefficient for catcher is outside of our respective AL and MLB confidence intervals. That being said, even in the unlikely case that the true WAA coefficient for AL catchers is outside of our confidence interval it is even more unlikely that its true WAA coefficient is equal to or less than 1.00 since that is significantly outside of our interval of 1.39 to 2.02.

While our data suggests that catcher has the highest coefficient and shortstop has the lowest our conclusion would become more concrete by examining more than the 18 seasons worth of data that made up our study. In addition to that, there can be a lot of randomness associated with wins and it can be argued that for a more accurate result we could have run the regression using Pythag W-L or BaseRuns Wins. That being said, 18 years still provides us with 540 data points and 283 data points for the NL and 257 for the AL. The large number of data points should also account for the randomness and luck associated with wins to balance out.

For executives looking to upgrade at different positions in the offseason, it would be tough with sparse data to say which position is most important, but one thing is clear—focus on upgrading the catcher position before upgrading at shortstop.

If you have any questions for Daniel or Timothy, please reach out to them at alpert@college.harvard.edu or tpugh@college.harvard.edu

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