The Ideal Roster Construction Part 2

I recently wrote a piece that looked at how value distribution affected a team's success. (I recommend you read that fanpost before continuing this one.) As it turned out, more top-heavy teams centered around a few stars performed far worse than more balanced teams. The article led to many follow up questions, one being whether batting or pitching-heavy teams won more games. I felt like this would be something interesting to research and write about, plus I still had all of my data from the original post.

I began by taking each team's (since 2012 and excluding 2017) raw WAR total for each of four categories: position players, all pitchers, starters, and relievers. From there I looked at each "type" of WAR and its impact on the team's success. To measure this I used a metric called r^2 value, which I previously described like this:

The coefficient of determination (referred to as r^2) is a statistic that measures how good of a fit your regression model is. Look at it this way: an r^2 value of 1 indicates that the independent variable completely explains the dependent variable data while an r^2 value of 0 indicates the exact opposite.

Simply put a higher r^2 value means that there is a greater correlation between the data.

Category r^2 value (actual W-L) r^2 value (pythagorean W-L)
Position Player WAR 0.585 0.675
Total Pitcher WAR 0.377 0.342
Starting Pitcher WAR 0.318 0.311
Relief Pitcher WAR 0.152 0.109

A few takeaways from this table:

  • It's no shock that position player WAR held the highest R^2 value (after all, they control the entire offensive half of the game and all non-pitching aspects of the defensive half), but note the r^2 value for pythagorean W-L (win-loss record based on run differential). Position player WAR explained 67.5% of a team's run differential, nearly twice as much as total pitcher WAR, a surprisingly high ratio.
  • Speaking of ratios, the ratios between starter r^2 value and reliever r^2 are 2.1:1 and 2.9:1, respectively. The ratio regarding innings pitched is only 1.9:1, suggesting that starting rotations have a disproportionally high impact on success compared to bullpens.
  • One more note on relievers: they were considerably more indicative of actual win-loss success compared to pythagorean success. My theory on this? Bullpens are obviously more important in closer games. The idea behind pythagorean win-loss is that a team that wins by five runs is more talented than a team that wins by one. A run differential-based system will punish teams who consistently rely on close finishes–generally teams with better bullpens–whereas actual win-loss record doesn't care how much you win or lose by.
It was clear that position player WAR had the greatest impact on success, so I decided to break down position player WAR into the three metrics that FanGraphs uses to calculate fWAR: wOBA for hitting value, Def (defensive runs above average) for defensive value, and BsR for base running value.
Category r^2 value (actual W-L) r^2 value (pythagorean W-L)
wOBA 0.268 0.367
Def 0.084 0.082
BsR 0.028 0.038

What stands out here is how little fielding–and especially base running–correlate with winning ballgames, which should make us Cardinals fans feel a little better. Should.
However, I still hadn't fully answered the question that I entered this process with. I had looked at total position player and pitcher WAR totals, but not those WAR totals as a percentage of the team's entire value. That's when I decided to find what percentage of each team's WAR came from position players, all pitchers, starters, and relievers.
Category r^2 value (actual W-L) r^2 value (pythagorean W-L)
Position Player WAR% 0.048 0.074
Total Pitcher WAR% 0.048 0.074
Starting Pitcher WAR% 0.073 0.085
Relief Pitcher WAR% 0.01927 0.002239

This is my calculator's way of saying "I have no clue". No category had more than an 8.5% tie-in with either form of win-loss record, and the percentage of value resting in the bullpen had virtually no correlation whatsoever.

While this table pretty much shattered the possibility of any major conclusion, I could still see whether batting-centric or pitching-centric teams tended to perform better. I graphed each team's WAR percentages relative to their outcome that season, created a linear trendline for each graph, and then looked at the trendline's slope. This is just a super-duper nerdy way of saying I found out whether having more value in your lineup or pitching staff is better. All you need to know is that a positive slope means teams with a greater percentage of its WAR in that category won more often and a negative slope means the exact opposite.

Category Trendline Slope (actual W-L) Trendline Slope (pythagorean W-L)
Position Player WAR% 0.426 0.133
Total Pitcher WAR% -0.426 -0.133
Starting Pitcher WAR% -0.441 -0.169
Relief Pitcher WAR% 0.015 -0.041

The position player and total pitcher slopes are inverses because any value that doesn't come from your position players must come from your pitchers and vice-versa. The bottom line is that this table shows that teams with a greater investment in their offense win more than those with a greater investment in their pitching. It also tell us that there isn't any relationship of substance between proportional bullpen value and success.

I ranked each team since 2012 based on their win percentages and assembled this table, which confirmed the sentiments of the table above:

Team Ranking W-L% Position Player WAR% Total Pitcher WAR% Starting Pitcher WAR% Relief Pitcher WAR%
MLB Average 50.00% 56.09% 43.91% 34.62% 9.29%
1-30 58.91% 59.96% 40.04% 30.95% 9.09%
31-60 54.51% 57.64% 42.36% 33.28% 9.08%
61-90 50.41% 55.96% 44.04% 34.33% 9.71%
91-120 45.75% 53.11% 46.89% 37.05% 9.84%
120-150 40.43% 54.08% 45.92% 37.45% 8.46%
Cardinals 56.92% 56.73% 43.27% 35.06% 8.21%

None of these numbers rule overwhelmingly one way or the other, but there is a trend between more stock in your position players and more wins.

Thank you for reading. As always you can follow me on Twitter @Tyler_Opinion.

Go Cards!