The Sabermetric Revolution: Assessing the Growth of Analytics in Baseball by Benjamin Baumer, Andrew Zimbalist

model from part 1 with the metrics constructed in part 2.
    The presence of meaningful associations between the residuals from the first model and the sabermetric intensity metrics is a method for detecting the presence of and quantifying the impact of sabermetrics among clubs.
Modeling Team Performance as a Function of Payroll
    Our first task is to understand the role of team payroll upon performance. Our data set contains performance statistics obtained from Retrosheet, 1 as well as team year-end payroll data (in nominal dollars) obtained from MLB’s Labor Relations department and used with permission. The data contains complete information on all major league clubs (768 team-seasons) from 1985 to 2011.
    Next, we want to contextualize the payroll data. We do this by defining PAY as the share of a team’s payroll relative to the league average share, which is by definition the total amount spent divided by the number of clubs. Notethat this correction is necessary, since the number of clubs has not remained constant over the time period in question. 2 Thus, PAY implicitly controls for both U.S. inflation and for baseball salary inflation simultaneously. In order to characterize the relationship between payroll and winning percentage, we run a regression model for winning percentage (WPCT) as a function of PAY, PAY 2 , and team fixed effects. 3 The details from this model are shown in Table 20 .
    Table 20. Relationship Between Win Percentage and Payroll, with Team Fixed Effects

    Our model satisfies the conditions for multiple linear regression well. Although the quadratic term was not statistically significant at the 5 percent level, we chose to include it so as to incorporate the desirable notion of diminishing returns to payroll. Moreover, analysis of the residuals favored the model that included the quadratic term.
Measuring Sabermetric Intensity
    In the previous section we described a model for a team’s winning percentage (WPCT) as a function of its relative share of league payroll (equivalently, the ratio of their payroll to the league average). In this section, we develop a series of metrics designed to measure the intensity of a team’s sabermetric practice. That is, we will attempt to quantify the extent to which the on-field performance of a team reflects sabermetric thinking.
    In what follows, we develop relatively simple metrics that we hope will capture some element of sabermetric practice on the part of front offices. Generally, our approach to building metrics that measure sabermetric intensity is to examine the ratio of a saber-savvy metric to a more traditional performance metric. In this respect, we are not advocating for any of these particular metrics, but merely suggesting that they might be popular amongeither traditionalists or sabermetricians. In practice, this process involves several steps:
    1. Apply ballpark corrections to performance data
    2. Compute the ratio of each statistic to the league average in that year
    3. Compute the ratio of the sabermetric statistic to the traditional statistic
    In the resulting metrics, a higher score reflects more saber-intensity, i.e., better performance in the sabermetric statistics relative to the traditional statistic.
Step 1: Ballpark Corrections
    First, we have to adjust our raw performance data for ballpark conditions. We have chosen to do this using the ballpark factors provided by Sean Lahman 4 (appropriately scaled). These park factors reflect inflation in
runs
that are attributable to a specific park. For example, the batting and pitching
run
park factors (BPF and PPF, respectively) for Fenway Park in 2004 were 1.06 and 1.05, respectively. This suggests that Fenway Park inflated run scoring by about 5 to 6 percent, relative to a league average park. Simply dividing each statistic by this number would result in statistics that were correlated to the park factor. In contrast, the notion of correcting for ballpark is to
remove
the component of a statistic