When a game ends we know which team won. What we don't know is how each player contributed to the outcome we observed.
Coaches -- and perhaps some fans -- might want to think that teams win and lose entirely as a team. But that is not exactly right. Some players clearly seem to matter more than others.
In basketball -- as Sports Economics details -- we can convert the box score statistics into a measure of Win Produced. We can also do something similar -- as the discussion of Reggie Jackson in Sports Economics explains -- for hitters in baseball. And now we can do the same thing for hitters in softball.
According to Softball America, the top returning hitter in college softball is Amanda Lorenz of the University of Florida. Lorenz's stats are impressive in 2018. As Softball America notes, Lorenz posted the following numbers last year:
- Batting Average: 0.416
- On-Base-Percentage: 0.582
- Slugging Average: 0.753
- Home Runs: 11
Those stats are impressive. But as noted in Sports Economics, we can do more than just look at the some numbers. Once again, the numbers tracked for players can be translated into a measure of how many wins each player produced.
The process begins with measuring how many runs each player creates. Following the methodology laid forth by Asher Blass in the Review of Economics and Statistics in 1992, we begin by regressing how many runs a team scores per game on a collection of per-game team statistics. This was applied to college softball with data from 2012 to 2018. The results -- reported below --indicate that 94.49% of the variation in team runs is explained by the thirteen box score statistics listed.
Independent Variable | Coefficient | t-stat | p-value |
Constant Term | 1.25 | 8.37 | 0.00 |
Single | 0.55 | 48.33 | 0.00 |
Double | 0.88 | 30.44 | 0.00 |
Triple | 1.39 | 17.65 | 0.00 |
Home Runs | 1.46 | 57.79 | 0.00 |
Walks | 0.41 | 35.57 | 0.00 |
Hit-by-Pitch | 0.40 | 14.88 | 0.00 |
Stolen Bases | 0.21 | 11.93 | 0.00 |
Caught Stealing | -0.48 | -7.49 | 0.00 |
Sacrifice Flies | 0.81 | 9.34 | 0.00 |
Strike-outs | -0.19 | -19.05 | 0.00 |
Double-Plays | -0.46 | -7.10 | 0.00 |
Ground outs | -0.14 | -14.58 | 0.00 |
Fly outs | -0.22 | -23.64 | 0.00 |
R-squared | 0.9449 |
As both the t-statistic and p-values indicate, the estimated coefficients are all significant at the 99% level. These coefficients can also be used to measure how many runs Lorenz created in 2018. This involves multiplying Lorenz's production of each statistic by the corresponding coefficient. For example, Lorenz had 40 singles and the above analysis says each single is worth 0.55 runs. Therefore, Lorenz is worth 21.8 runs (or 40 * 0.55). If we do this for every statistic (as one sees in the following table) Lorenz's stats were worth 72.4 runs in 2018.
Variable | Amanda Lorenz production | Coefficient | Runs Created (production * coefficient) |
Single | 40 | 0.55 | 21.8 |
Double | 19 | 0.88 | 16.7 |
Triple | 4 | 1.39 | 5.5 |
Home Runs | 11 | 1.46 | 16.1 |
Walks | 70 | 0.41 | 28.4 |
Hit-by-Pitch | 2 | 0.40 | 0.8 |
Stolen Bases | 6 | 0.21 | 1.2 |
Caught Stealing | 1 | -0.48 | -0.5 |
Sacrifice Flies | 1 | 0.81 | 0.8 |
Strike-outs | 16 | -0.19 | -3.0 |
Double-Plays | 2 | -0.46 | -0.9 |
Ground outs | 40 | -0.14 | -5.6 |
Fly outs | 42 | -0.22 | -9.1 |
Total Runs Created | 72.4 |
To convert these 72.4 Runs Created into a measure of Wins Created, we follow these steps (also detailed for Major League Baseball players in Sports Economics):
- From 2012 to 2018, all softball hitters created 349,157.22 runs (following the methodology outlined above). These hitters also had 2,796,591 plate appearances. So, per plate appearance, an average hitter created 0.125 runs. Lorenz had 250 plate appearances in 2018. If she was average, she would have created 31.2 runs. In other words, Lorenz created 41.2 runs beyond average.
- A regression of team winning percentage on runs scored per game and runs surrendered per game indicates that each additional run scored is worth 0.076 additional wins. That means that Lorenz produced 3.114 wins beyond what an average hitter would have created (i.e. 0.076 * 41.2).
- If we assume hitters produced half of a team's wins (pitching and defense produce the remaining half), the average hitter from 2012 to 2018 produced 0.0096 wins per plate appearance. This means that an average player in Lorenz's plate appearances would have produced 2.409 wins (i.e. 0.0096*250).
- Putting steps #2 and #3 together, we see that Lorenz's hitting was worth 5.523 wins for the Florida Gators (i.e. 3.114 + 2.409).
The Gators won 56 games in 2018. The numbers indicate that Lorenz's hitting was worth nearly 10% of this total.
We can repeat this exercise for every hitter in softball from 2012 to 2018. Here are the top 10 hitters from the Power 5 Conferences (ACC, Big 12, Big 10, Pac 12, and SEC):
- Lauren Chamberlain (Oklahoma, 2013): 8.395
- Sierra Romero (Michigan, 2015): 7.485
- Kasey Cooper (Auburn, 2016): 7.460
- Sierra Romero (Michigan, 2014): 7.080
- Maddie O'Brien (Florida State, 2014): 7.023
- Katelyn Boyd (Arizona State, 2012): 7.022
- Emily Carosone (Auburn, 2015): 6.830
- Lauren Chamberlain (Oklahoma, 2015): 6.788
- Valerie Arioto (California, 2012): 6.628
- Sierre Romero (Michigan, 2016): 6.587
Sierra Romero shows up three times on this list and Lauren Chamberlain appears twice. Today this duo is starring for the USSSA Pride of the National Pro Fastpitch league (NPF). In 2018, USSSA Pride won the Cowles Cup and Romero and Chamberlain were a big part of that title team. Of course, they also had quite a bit of help (the Pride have many stars).
Part of that help came from the Pride's pitchers. In a future post we will discuss how to measure wins for pitchers in softball. And yes, it involves more than just observing who won the game.