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What Is a Run Worth?

I recently began thinking about how teams can know that they are efficiently spending their money, or where teams actually get the runs that they spend all their money on. With players signing massive contracts in the 2018-19 offseason, I began to wonder if any players were really worth that much money. The process begins with one big question: What is a run worth? I quickly realized that each team theoretically needs to manufacture the same number of runs as all the other teams do if they want a better chance to make the postseason. What is different from team to team is budget. This means that a run is worth a different monetary value to each team, and that each team would be willing to pay a different amount of money for the same number of runs. The problem is that to each player, a run costs the same amount, causing Billy Beane, played by Brad Pitt in the movie Moneyball, to claim that “It’s an unfair game”.

Figuring out what each team values their runs at would enable me to evaluate how efficient the signing of certain contracts was for each team and furthermore would allow me to figure out where the most value comes from in the payroll of a team. First, I had to figure out how to convert the basic statistics of a player into the number of runs that player actually contributed to the team. I eventually came across the Estimated Runs Produced statistic from the 1985 Bill James abstract. Below is the calculation.

ERP = (2 (TB + BB + HBP) + H + SB – (.605 (AB + CS + GDP – H))) .16

This is a stat created by Paul Johnson in order to obtain more accuracy than Runs Created, which he succeeded in doing. I then fired up R and ran some tests on team statistics to see how well it lined up with the actual number of runs that each team scored. I graphed ERP against Runs Scored first for every team dating back to the beginning of the 30-team era in MLB: Read the rest of this entry »


Created Statistic: Run Value

With so many complex statistics out there, I wondered if there was an easier way to project winning percentage or runs, a way that is simple yet more complex than Bill James’ classic Pythagorean Win Expectancy. To create a statistic like that, I would have to create one comprehensive stat for offense and one for pitching. Ultimately, I came up with the following and named them “Run Value” and “Pitching Run Value,” respectively.

RVAL = ( ( TB + BB – SO )/4) + RBI + HR  

PRVAL = ( ( ( H + BB – SO )/4 ) + HR) x FIP

These two metrics are used for teams. In the batting RVal formula, the higher the better. I tried to get down to the pure number of runs that a player or team produces by using the very relaxed definition of a run being four bases. In the pitching PRVal formula, the lower the better. I did something very similar to the batting stat by trying to get the pure run total. I then put the two stats into the win expectancy formula:

RVALWinExp = RVal^1.83 / ( RVal^1.83 + PRVal^1.83)

I then ran a program in R to see how closely this stat correlates to actual team win percentage for all teams from the 1998 season through the 2018 season. In addition, I tested to see how Bill James’ win expectancy formula correlates to team win percentage over the same period of time. The results are below. Read the rest of this entry »