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RunPlusMinus

# Introduction

The article here claims that the RunPlusMinus methodology produces the best single statistic for measuring the on-field performance of MLB players. Over the course of the 2018 season, play-by-play data was collected and analyzed for all 2430 MLB regular season games. This article contains:

• A concise summary of the RunPlusMinus methodology
• Evidence supporting the claim to be the best single statistic
• Charts showing the top 25 players in the AL, NL, and overall
• An example detailed report for the Angels

The year-end report of team performance can be found here.

# RunPlusMinus Methodology

Note: The material on Methodology is identical to that in the corresponding section of the report RunPlusMinus 2018 Team Performance Summary.

The RunPlusMinus statistic calculates a “better off” value for each player’s involvement in every event in a game. The result of each player’s actions makes his team better or worse off. These better off values can be accumulated to give a positive or negative total that measures how much each player’s performance is above or below average. The principles and methods used to calculate RunPlusMinus values satisfy the five CRAZI (see below) properties that are necessary — but not sufficient — to claim the title of best overall on-field performance statistic. These are:

• Comprehensive: must measure every player’s involvement in every play in every game
• Run-based: must be measured in runs (the only objective in a game is to score more runs than the opposing team)
• Additive: team performances must be the sum of player performances
• Zero-sum: Offense and defense values must be equal and opposite in every play
• Independent: player performance in each play must be independent of player performance values in preceding plays (This is the reason for using Expected Runs values)

The underlying formula that assigns a better-off value to the offense team in every play is:

RPM Value = runs scored + change in potential to score runs

Where the change in potential to score runs = (Expected Runs at the end of the play) minus (Expected Runs at the start of the play).

The RPM (better off) value of each player involved in a play is a fraction of his team’s RPM value. The fraction reflects the player’s degree of responsibility for the outcome of the play.

Because: 1) runs are scored in every completed game and 2) pitchers have the largest responsibility for defense, the raw RPM values for each player are biased by the role of the player in each play. This bias can be eliminated by using standard deviations and appropriate weights for each of the four performance components (batting, running, pitching, fielding). The result is the RPM Rating statistic that measures each player’s overall contribution to success by adding the four component ratings.

# Evidence Supporting the Claim of Best Baseball Statistic

Of the 117+ baseball statistics listed in Wikipedia, only the RPM statistic satisfies all five CRAZI criteria. (A comparison with OpenWAR can be found here).

Some examples. Most statistics, such as Batting Averages and ERAs are either offense or defense measures and are therefore not comprehensive or zero-sum. Many are not additive because they involve aggregate measures such as averages or use regression methods. (For example, a team’s batting average is not the sum of the players’ batting averages.) RBI values are not independent because they are affected by a player’s position in the lineup. Stats such as caught stealing are stated as fractions and are not run-based. The RPM Rating statistic however, satisfies all five necessary criteria.

## Question 1: Does the Game Winner Always Have a Positive RPM Value?

Yes. Team RPM totals at the end of a game are the sum of the RPM values in each play. The play value for each of the opposing teams can be positive or negative and the sum of the two team values is always zero. As you would expect, a team that wins by a large margin has large positive RPM total and a team that loses by one run has a small negative RPM value. The relationship between the winning run margin and the average RPM value of the winning team is shown in the chart below. The values are derived from all MLB regular season games in 2018.

The correlation coefficient is 99.9%. It is not 1 because there are variations in how the run difference was achieved. The “Max” line shows that for some run differences there were significant differences in the RPM winning margins. This can happen when for example, two games are won by a single run. If one of them had many double plays and the other had many 1–2–3 innings the RPM values of the winning teams will be different.

## Question 2: Do RPM Team Ratings Predict League Standings?

As the season progresses, how do league standings correspond to RPM totals? The chart below shows the relationship between team RPMs and games won in the 2018 MLB season. A chart containing the values of wins and RPM totals is included later in this article. The correlation between these values is 96%. It is not higher because league schedules are unbalanced. (Teams do not play each other the same number of times and therefore the strength of the opposing team is different for each team). Since the total RPM values of the two teams in each game is zero, if necessarily follows that the average of team RPMs over the course of the season is also zero.

## Question 3: How good are RPM Ratings in predicting game winners?

Predictions of game winners are based on:

1. Each team’s RPM game totals in the previous 28 days
2. The past performance of the probable starting pitchers
3. Which team has the home field

The accuracy of predictions for games in the 2018 season was 57%. Recognizing that the best teams only win approximately 66% of their games and that there are other probabilistic variables in every game, this is a very good result. In the 2019 season, we will provide daily forecasts of the winner in upcoming games.

# How are Rating Values Distributed?

One of the significant strengths of the RPM rating methodology is that it shows whether a given player’s total performance is above or below average compared to all other players. The average player Rating is zero. Players with Ratings greater than zero performed better than average. Since 1700+ players participated in the 2018 season, the Law of Large Numbers applies meaning one would expect a plot of player performance would have a bell-like shape. This is indeed the case as shown in the chart below.

A player’s total performance is the weighted sum of his four component (batting, running, pitching, fielding) ratings each of which also have an average of zero. This means that RPM ratings can be used to evaluate component performances as is shown in charts later in this article.

The graph shows that although the average rating is zero, there is a longer tail of higher ratings meaning that there were more players who had well-above-average rating than those who had well-below-average ratings. The long tail is balanced by a higher concentration of negative ratings near zero. This is not surprising since a large number of players played relatively few games and in general, those players had below average performances.

# Player Performances

The first 3 charts show the top 25 MLB players, the top 25 AL players and the top 25 NL players based on each player’s overall RPM Rating. The candidates are limited to players who participated in a minimum of 25 games.

Component rankings are specific to each of the 3 groups. For example, Batter rankings in the AL chart are based on batting ratings of AL players.

Player salaries are those published by Spotrac. The Performance Based team and league salaries are calculated by partitioning either the total payroll of the team or of the MLB respectively according to each player’s RPM Rating.

The rightmost two columns show how much the player was overpaid or underpaid based on the difference between his actual salary and his performance-justified league salary.

## Top 25 MLB Players

The table below shows the 25 players with the highest RPM Ratings. Comments follow the chart.

Comments: There are 14 AL players and 11 NL players in the top 25. The average rank of AL and NL players is very close to 12 and 13 respectively. Part of this difference is explained by the fact that in 2018, the spread between the best and worst teams in the two leagues was much different. In the NL, the difference between Cubs and Marlins was 32 wins whereas in the AL the difference between the Red Sox and Orioles was 61 wins. This means that the NL was generally more competitive than the AL which made it harder to win games within the NL versus winning intra-league games in the AL. This in turn made it easier for the top players in the AL to score well and that is reflected in the player rankings. (See the AL and NL charts which follow to get league-specific rankings.)

Why are there only 4 pitchers in the top 25? First, a caveat. Each component rating is normalized meaning that the average rating for each of the four components is zero. Since runs are always scored, normalization removes the bias against defensive players — pitchers in particular. Notwithstanding the normalization, NL starting pitchers are forced to bat and their batting performance is generally much below average. AL pitchers on the other hand have relatively few plate appearances and are not penalized for non-batting. (The participation level of each player in each level is taken into account during the normalization calculations.) This reduces the overall rating of NL pitchers. In other words, the DH rule negatively affects the total RPM values of NL pitchers even when their pitching skills match those in the AL

The generally poor rankings of running and fielding simply reflect the relatively low importance — and hence lower weights — of these components relative to batting and pitching. (Batters and pitchers are involved in the majority of plays.) Keep in mind that offense and defense are weighted equally.

The totals of the over-payments and under-payments are 112.million and 73.5 million respectively. The over-payment of 112.1 million simply shows that teams tend to pay more than is justified by the on-field performances of their best players. The underpaid players clearly have good arguments for getting salary increases.

## Top 25 AL Players

The chart below shows the 25 players in the AL with the highest RPM Ratings. The component rankings are limited to those 25 players. The Performance Based Team salary is calculated by splitting the team payroll according to each player’s Rating. The Over/Under salary values are the differences between the actual salary and the performance-based MLB salary. For example, Mike Trout was the highest paid AL player in the top 25 and he was overpaid by 22.9 million based on his on-field performance relative to all other MLB players. The small difference in the Over/Under totals indicates that on average, the top 25 players were fairly paid. The Astros got the best bang-for-the-buck by underpaying Bregman 10.2 million for his outstanding performance.

Finally, note that 6 pitchers made the top 25 in spite of making essentially no contribution from their hitting.

Top 25 NL Players

The chart below shows the top 25 NL players and has only 3 pitchers in the top 25. As explained in the comments following the chart of the top 25 MLB players, this results from: 1) the below average results of their (forced) plate appearances, and 2) the Rating is a weighted average of the ratings of all 4 components. In spite of this handicap, deGrom was the best overall NL pitcher, Scherzer was second and Nola was third. Scherzer was also the most overpaid NL player in the top 25 and Story was the most underpaid. The difference of almost 40 million between the over-payments and under-payments testifies either to the determination of some NL clubs to get the players they want or to having misjudged the value of particular players.

# Detailed Team Reports

A sample of a detailed team report (for the Angels) is shown below. To prevent players with very low participation levels from unfairly affecting rating values:

• players must have participated in at least 10 games
• players who had fewer than 10 plate appearances do not have a Batting rating
• pitchers who faced fewer than 10 batters do not have a pitching rating

Ranking within each team is based on the overall RPM Rating. This is a weighted average of the Batting, Running, Pitching and Fielding ratings.

The Angels report is shown below. This shows that Mike Trout was the team’s best on-field performer with a rating of 341.2 caused primarily by his batting prowess in 69 plate appearances. His salary of 34 million was 11.1 million more than his on-field performance justified. The Angels had an outstanding cohort of pitchers whose contribution ranked them in 4th, 5th & 6th and 8th through 14th place of the 43 players. Pujols was the most overpaid player and Heaney was the least underpaid player, yet they are only one rank apart and both near the bottom of the list.

The Angels report and the detailed performances for other teams can be found here.

# Conclusions

• The RunPlusMinus statistic measures how much a player makes his team better off by his participation in a play. Over 588 thousand participation records were used in the analysis of 2018 MLB games.
• Analysis of detailed game data for all 2018 MLB regular season games provides strong supporting evidence that the RunPlusMinus statistic is an excellent measure of player and team on-field performances
• Player RunPlusMinus ratings have a bell curve shape and have an average rating of zero. This means offense-oriented and defense-oriented players can be compared fairly using the RPM ratings
• Charts have been provided to show the top 25 players in the MLB and in each of the AL and NL
• Links to detailed player performance charts for each team have been provided.

RunPlusMinus player ratings can be used to:

• Rank overall player performance,
• Rank performances in each of batting, running, pitching and fielding
• Calculate performance-justified salaries

If you have any questions, comments, requests or complaints, please feel free to add them in the comments below or to email us at info@runplusminus.com

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## Ivan Lukianchuk

Entrepreneur, Metalhead, Computer Scientist. Currently CTO @RunPlusMinus — The best baseball stat. Principal Consultant at Strattenburg.