Growing up a starting pitcher, I was always intrigued by the concept of inherited/bequeathed runners, and how the Starting Pitcher gets the credit for them.
Outside of an Inherited Runners' scored percentage, the value of those runs scored were given to the statistics of the pitcher who allowed them to get on base. For middle relievers (or relievers who enter the game with runners on-base), I attempted to quantify their value to better understand their impact over the course of the season.
Data
Shoutout to Baseball Savant, as I pulled all of my data from their website. I specifically tested the 2021 MLB season, but these results can be extended throughout the course of each eligible player’s career.
The data I decided to work with only involved a few statistics, such as Inherited Runners, Inherited Runners Scored, ERA (Innings and earned runs). The goal was to create an ERA counterpart for Middle Relief Pitchers. Here is the process I took:
Assumptions
ERA as a base for own run prevention
When starting my analysis, I wanted to create a statistic that relied on both a reliever’s ability to prevent inherited runners from scoring and his ability to prevent his own runs from scoring. For the sake of simplicity, I used a general ERA structure (Earned Runs per 9 innings), but any of its more advanced counterparts can be substituted in for a deeper analysis.
Inherited Runners Scored - Inherited Runners prevented = RS
Because a reliever having inherited runners is situational at best, a purely counting statistic felt wrong. At the same time, I was attempting to quantify value, so it makes sense that the more inherited runners a reliever has, the more he can prevent scoring, and the more value he provides.
So for example, Liam Hendriks had 30 inherited runners in 2021, to which only 3 of them scored, so he had an unseen value of 27 runs.
Eligibility
I made baseline eligibility requirements of having 20 innings pitched and 10 inherited runners in the 2021 season to weed out starters and in most cases, closers. I thought this was a fine threshold for one season of relief pitching, but I’m sure they can be adjusted accordingly.
Analysis
After much trial and error, I settled on a specific formula for what I will now call MrP (Middle Relief Performance). Considering that the reliever themselves did not allow their inherited runners on base, I could not weight each run saved (RS) equally to their earned runs. Instead, I settled for each of those runs being half of an earned run. I think that there can be more work done to see which weighting is best, but half was a good starting point. In most cases, the differences were marginal.
Here is the final formula that I worked with to analyze middle relief pitchers across 2021:
MrP = (Earned Runs + .5(Inherited Runs Scored - Inherited Runs Prevented))/Innings Pitched
Clearly here, the lower the MrP, the more value a pitcher provided in the bulk of his work.
After sifting through the data and finding pitchers who fit my specifically chosen eligibility requirements, 249 pitchers remained from the 2021 season. Here is the list of our top 10:
Name - Team - MrP
Casey Sadler - Mariners-.087
Aaron Loup - Mets-.027
Joe Mantiply - Diamondbacks - 0.00
Austin Warren - Angels- .025
Blake Treinen - Dodgers - .076
Jonathan Loaisiga - Yankees - .085
Jose Alvarez - Giants - .093
Ranger Suarez - Phillies - .094
Domingo Tapia - Royals - .105
David Bednar - Pirates - .108
*Austin Warren pitched just 20.1 innings in 2021, whereas the rest of this group pitched 30+ innings.
*Ranger Suarez started 12 games for the Phillies in 2021, but met the inherited runner threshold.
Observations
In most cases, the relievers here have a low amount of Earned Runs, but they also have a solid Inherited Runs Scored percentage. From this top 10, I see the possibility of a cumulative stat that shows whether or not relief pitchers are good at both preventing their runs and runs they are given.
I think the most interesting fact about this list is the relationship between ERA. Only 4 of these pitchers on the list for MrP are in the Top 10 for ERA among these 249 relief pitchers (Suarez, Sadler, Warren*, and Treinen). What this tells me is that the value of preventing inherited runners, although related to ERA, may provide more insight into the value of a relief pitcher.
One concern that I thought of regarding something like this is evident in the top 10 list. All 10 players come from different teams, and for the most part, there is a significant difference in MrP between most teammates. One explanation that I can think of is that teams already have their guy in situations where runners are on base. I plan on looking into this on a team-to-team basis.
Conclusion
There is a lot more that can be done on this front. My first order of business will be to find the best weighting for the RS statistic. From there, I believe that this statistic can evolve by adding a multitude of other variables, such as bequeathed runners when a reliever leaves the game. Finding hidden talent from relievers is something I have a lot of fun doing, especially when there is a primary emphasis on starters and closers, and not the middle guys in between.
Ultimately, my goal was to explore the hidden value of relief pitchers with their inherited runners, and this small project is definitely a good start. Even from the top 10 list, there are some names that I never expected to see. Over time, I plan on fine tuning this, but for now I think this is a solid introduction for what I had in mind.