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Introducing: aRBI+

It’s becoming commonly accepted that RBI has its flaws and is not a great statistic for player comparisons. It fails to account for the fact that not every player has a similar number of opportunities to accrue RBI. Even more problematic, it doesn’t account for the fact that not all RBI are created equal – it’s not the same to hit a man home from third with a one-out sac fly as it is to hit a clutch, two-out, RBI-double in the 12th inning with your team down a run and the runner starting at first base.

For many fans and analysts alike, we want to be able to compare players based on their ability to create runs for their teams. After all, that’s the entire objective of baseball. However, due to the inherent simplicity of RBI, it’s difficult to rely on RBI as a tool for accurate comparisons. That is where aRBI+ comes into play.


WHAT IS aRBI+

In short, aRBI+ is a metric that I have developed to use as a tool in evaluating a player’s ability to create runs for his team. It uses a player’s rate of RBI per plate appearance (RBI/PA) from various splits that can be used to determine the difficulty of those RBI and the total number of opportunities that a player had to drive in a run.

Using this set of split statistics (will be expanded on later), aRBI+ compares those splits to the expected rate of a league-average player, and puts the result into a number that is relative to a league-average of 100 – meaning a score of 100 is perfectly league-average, while each point above/below 100 is a one percent disparity from league-average. For example, a player with an aRBI+ of 140 is about 40% better at producing RBI for his team than an average MLB hitter. On the contrary, a player with an aRBI+ of 85 would be considered 15% worse at generating RBI than a league-average hitter. As with other “+” stats, there is a general scale of what scores constitute tiers of aRBI+:

Table 1: aRBI+ Tier Classification

Other advanced statistics that look at run production don’t necessarily focus only on a player’s ability to drive in a runner to the plate (these would be more overarching statistics), or fail to adjust for the player’s total opportunities and difficulty of accomplishing those RBI compared to the league-average. Below are other statistics that may be mistaken as similar or that this may be derivative of:

  • wRC+ – While wRC+ and other forms of Runs Created and weighted-Runs Created are often very good statistics, they are based on the outcome of the play for the hitter, and mostly ignore whether or not the player drives home any runs on that play. wRC and wRC+, specifically, are heavily based on the batter’s wOBA (weighted On Base Average). Because of the heavy use of wOBA, wRC+ is a far-more overarching statistic that better measures a player’s total offensive contribution.
  • Offensive Runs Above Average (OFF) and weighted Runs Above Average (wRAA)- OFF and wRAA, much like wRC+, use wOBA as a heavy factor, in addition to using a player’s base-running ability as a factor. Base-running plays no factor in aRBI+.
  • RE24 – This is probably the most similar statistic that currently exists to aRBI+, but only in the sense of what it’s trying to accomplish. RE24 looks at the scenario the batter is facing at the beginning of the play (number of outs, and runners on base), and what the scenario is at the end of the play, then finds the difference in the two. The difference is, effectively, the run contribution of that plate appearance. This is a very effective statistic, but still accounts for base-running in some scenarios, as well as failing to provide a context for how a player’s RE24 compares to a league-average player.

The most important thing to keep in mind is that a high-performing player in aRBI+ is not necessarily a good overall hitter — and a low-performing player is not necessarily a bad hitter. This metric is not an overall measurement of a player’s offensive ability (like the stats listed above). Rather, it is a measurement to be able to effectively compare players’ abilities to drive in runners compared to the abilities of their peers. Two prime examples of this are below:

Lorenzo Cain, CF, MIL
2018: 620 PA, 38 RBI, .812 OPS, .359 wOBA, 124 wRC+, 29.53 RE24, 75.9 aRBI+
Obviously, Cain had a fantastic season in 2018, and he was rewarded with a seventh-place finish in the NL MVP voting. He posted the second-highest OPS of his career, and has not finished a season of 250+ PA with that high of a wOBA or wRC+ since his first stint with the Brewers — in Double-A. However, despite the accolades, Cain failed to produce RBI in nearly every scenario last year. Out of each split measurement tracked, the only one where Cain possessed a higher RBI/PA rate than league-average was with a runner on third, and no other baserunners — a split that would not be highly weighted in this statistic since just 2.64% of all MLB plate appearances came in the scenario last season.

Lourdes Gurriel Jr, SS, TOR
2018: 263 PA, 35 RBI, .755 OPS, .322 wOBA, 103 wRC+, 1.82 RE24, 147.8 aRBI+
Gurriel was a relative “average joe” by Major League standards in 2018: his wRC+ is right near 100 (league-average), his OPS+ (OPS adjusted to league-average and park factor) was 108 — again, right near the league-average score of 100. By nearly all measurements listed above, Gurriel was basically a typical “league average” player. However, he rates highly in aRBI+ due to his high rate of RBI last season, despite actually having fewer runners on base than the average player would see in that same number of plate appearances. He was able to capitalize on high-value RBI opportunities by hitting nine solo home runs in 159 PA with the bases empty. This is significant because, as expected, it’s much harder to score yourself on your own hit than a runner already on base.


HOW DOES aRBI+ WORK?

As mentioned above, aRBI+ uses a player’s RBI/PA in different splits and compares it to league average, then uses those factors to compile a single number. This single number (aRBI+) represents the player’s ability to drive in runs compared to that of a league-average player. The different factors considered for the aRBI+ calculation are below, with the league-wide average of RBI/PA for each possible scenario in that split:

Note: All statistics and research presented was over the course of the 2018 MLB season and were gathered from baseball-reference.com

  • Outs in the inning: as seen below, it’s easier to hit RBI with one out in the inning than any other due to the fact that runners have had time to get in scoring position as well as the batter having an out to work with, opening the option for a sacrifice.
Table 2: RBI/PA by Outs in the Inning
  • Inning of the game: Run production throughout the game is not linear, if we are to search for a true comparison, players should be rewarded and penalized accordingly with their production throughout the game accordingly.
-Table 3: RBI/PA by Inning
  • Batting order position: Clearly, players don’t produce the same number of runs at the beginning and end of the lineup as they do in the middle, in large part because of the players that are batting around them. Hitters in the eighth, ninth, and first positions generally have fewer opportunities than players in the other lineup positions, and due to this, RBI from players in batting in those positions are weighted slightly heavier to assist in balancing opportunity.
Table 4: RBI/PA by Batting Order Position
  • Score of the game: As a game grows further apart, more runs begin to be scored as teams tend to grab rallies when their bats are already hot. This trend has increased in recent years, thanks to the trend of teams using position players on the mound in blowouts. This also allows for a certain level of “clutch factor” to be calculated into the formula since players with a high RBI rate when their team is losing are rewarded for their high-value RBI to get the team back into the game.
Table 5: RBI/PA by Score
  • Position of runners: This is obviously the most important part of the equation. Where baserunners are at the beginning of the play, more than any of the other factors, tells us both the difficulty of the player’s RBI total, as well as whether or not they had more opportunities for RBI. Players that have a higher percentage of their plate appearances coming with runners on the bases will more likely than not continually produce more and more RBI than players that don’t. The “difficulty” portion of these splits is based that driving home a runner from first or home, is significantly more challenging and far more rare than driving home a runner from scoring position.
Table 6: RBI/PA by Runners

Using these factors and adjusting the player’s total plate appearances so that each player had equal opportunity in each split, we are also able to more-effectively compare the true value of each RBI that a player is responsible for, as well as adjust for the total number of opportunities granted to a player over the course of the season.


WHAT DOES aRBI+ LOOK LIKE IN THE MLB?

Now that you know what it is, and how it works, let’s look at how aRBI+ worked over the course of the 2018 MLB season. Keep in mind while looking at how certain players did that this is not an overall measurement of a player’s offensive ability – simply their ability to get a runner across the plate.

One significant aspect that is different from other “+” statistics in aRBI+ is  the average rating of hitters that have at least 250 plate appearances over the course of the season. As you’ll notice, it seems like there are many more players that are well-above the league-average mark of 100. This is because the vast majority of RBI accounted for in the MLB are credited to the players that reach 250 PA – 85.6% of all RBI recorded in 2018 were by a player with at least 250 PA, while only accounting for 81.3% of all plate appearances. While 4.3 percent doesn’t sound like much, over a stretch of 185,139 plate appearances, this makes for a sizable margin — one that is corrected by the other 677 players who made at least one plate appearance last season. So, while the average for the players with 250+ PA of many “+” statistics is generally around 103, the average among the 313 players in this study is roughly 108.

Note: All players with at least 250 PA in 2018 were included in these calculations

Best and Worst Overall Players

Table 7: Highest and Lowest Players in aRBI+

Closest to League-Average

Table 8: Players Nearest Above/Below 100 in aRBI+

Top-5 by Position

Table 9: Top-Ranking Catchers and First-Basemen in aRBI+
Table 10: Top-Ranking Second- and Third-Basemen in aRBI+
Table 11: Top-Ranking Shortstops in aRBI+
Table 12: Top-Ranking Outfielders in aRBI+

PLAYER HIGHLIGHTS

As you may be able to tell from the tables above, many players wound up performing significantly different last year in aRBI+ than they may have in their other metrics. Here is a deeper dive into why some players performed to a certain level in aRBI+ compared to their other metrics:

Max Muncy, LAD
2018: 481 PA, 79 RBI, .973 OPS, 162 wRC+, 186.8 aRBI+
Muncy burst onto the scene in 2018, and proved that he was a more than sufficient hitter, and, as it turns out, was better than any other player at capitalizing on his RBI opportunities. Muncy was able to do this by performing well above league-average nearly across the board. Muncy was able to put up a staggering weight of solo home runs (2.894 times the league average) which certainly helped his cause significantly. Overall, Muncy’s most impressive numbers came in his splits for the alignment of runners, given that he was able to maintain extremely high RBI/PA rates in the situations that players face most often (bases empty, runners on first and/or second).

Tyler Austin, SFG
2018: 268 PA, 47 RBI, .767 OPS, 103 wRC+, 165.5 aRBI+
Austin’s was most likely not a name you’d expect to see on this list, especially considering how few RBI he had last year. However, Austin benefitted from a smaller sample size (268 PA, minimum was 250) that may have actually boosted his numbers beyond what they would normally be in a season with 500+ PA. Austin provided significant boosts to his score by hitting 13 RBI in his 61 PA with a runner on first, as well as putting up absurd RBI/PA rates while batting in the fifth spot (20 RBI in 73 PA, 2.260 times league-average) and in tied games (15 RBI in 52 PA, 2.905 times league-average).

Charlie Blackmon, COL
2018: 696 PA, 70 RBI, .860 OPS, 116 wRC+, 148.1 aRBI+
Blackmon was arguably the most interesting player to study by the numbers with this formula. He didn’t have any spectacularly-high RBI/PA rate in any splits, however he also was rarely given any support with runners on base. Last year, 468 of Blackmon’s 696 plate appearances (67.24%) came with no runners on base, and when they were, they still had a long way to run. More than any other player last season, Blackmon was facing a significantly harder challenge to earn an RBI.

Table 13: % of Plate Appearances with Runner at a Base

Chris Davis, BAL
2018: 522 PA, 49 RBI, .539 OPS, 46 wRC+, 100.9 aRBI+
While it may surprise you than Chris Davis was league-average in just about anything last year, he actually performed right along the league-average benchmark in aRBI+. He was able to do this by capitalizing on plate appearances with a runner at second, as well as those with runners at first and third. He also was able to tally high RBI rates in the eighth, ninth, and extras, where runs come at a premium and pitchers are often at their best. Like Blackmon, Davis was also hindered in his RBI total last year by receiving little-to-no help from his teammates and starting his plate appearances with less-than-ideal situations.

Mallex Smith, TBR
2018: 544 PA, 40 RBI, .773 OPS, 117 wRC+, 63.1 aRBI+
Smith put up a pretty solid offensive season last year with a 117 wRC+ at the major league level, to go along with a .339 wOBA and 3.4 fWAR. However, that didn’t translate into an ability to get his teammates to home plate. A significant detriment to his score was the fact that he was able to get only one solo home run last year in 326 PA with no runners on — in a situational split where players get a lot of plate appearances, this will strongly damage a player’s aRBI+ rating. In addition, Smith also failed to produce with no outs in the inning, runners at second and third, tie scores, and when his team was behind in the game — having a RBI/PA rate less than 50% of the league-average in each of those situations.


aRBI+ TEAM RANKINGS

The formula for aRBI+ can also be used and applied to full-team offenses — unfortunately, there is one significant problem to address, and even once solved, there remains an inherent flaw in the logic of the formula.

The problem to address is whether you should penalize National League teams for their pitcher’s plate appearances, which are indiscriminately detrimental to team-wide numbers. I don’t believe that a team’s offense should be penalized for that, so the formula adjusts for the disparity caused by pitchers on a league-average scale by forcing the average score of the NL and AL is each equivalent to 100. If you were wondering, there was a six percent disparity.

Even after adjusting for the difference caused by the DH rules, the major drawback that remains in the formula for aRBI+ — at least in team context — is the part of the equation that adjusts for opportunity. In effect, since the sample is over the entire team rather than one player, it effectively penalizes teams for getting runners into scoring position. Due to this, I wouldn’t recommend aRBI+ as an effective measurement of team success or failures.

A good example of the flaws in aRBI+ for a team last year is the Boston Red Sox. According to the formula, they would have finished 16th among MLB teams. However, the team’s aRBI+ rating was significantly damaged (more than any other team) by their excellent ability to get into scoring position. The same part of the formula used earlier to help determine that Charlie Blackmon had significantly fewer opportunities for RBI than his peers is actually now penalizing the Red Sox because the team was able to find their way to second base 11.8% more than league-average, and reached third base 22.3% more than league-average. In terms of offensive production, there are few teams in baseball history that can match the 2018 Red Sox who scored an absurd 5.41 runs per game, and to say that they “lacked an ability to drive in runs” would be simply wrong.


HOW aRBI+ SHOULD BE USED

As stated earlier, aRBI+ is not a metric intended to measure the full offensive capabilities of a single player. Rather, the purpose of the design of aRBI+, at least from a fan’s perspective, was to give a more useful meaning to RBI by giving it context and adjusting for the total opportunities that have a larger disparity between players as the season goes on. This statistic is a far-better tool for comparisons than RBI, and possibly RE24, because it no longer requires such a small margin in sample size for two players to be comparable. If you were to compare two players in RBI (or RE24) over the course of a season, and one player has 100 more plate appearances, it is certain that the player with more plate appearances will have more RBI, and the same player is far more likely to have the upper-hand in RE24 as well.

The other purposeful use for aRBI+ is more targeted at team management and setting lineups, as opposed to deciding what players are worthwhile acquisitions. Metrics like wRC+, OPS+, and OFF are far superior to this in evaluating the true talent of a player and predicting the player’s future performance — primarily because this is not a metric that is designed to evaluate a player’s entire contribution. What it can be used for, however, is deciding where certain players should be hitting in the lineup. Players with an aRBI+ above 130 (give or take) should be the players that are taking a majority of their plate appearances between the second and sixth spots in the lineup, where the vast majority of RBI opportunities take place. Placing a player with a high aRBI+ in the leadoff position would be a significant waste of his ability to drive in runs because – more often than not – he will be hitting with the bases empty (see Charlie Blackmon). Likewise, placing a low aRBI+ player in the third, fourth, and fifth spots would likely limit your team’s run production since more of their plate appearances would be in prime RBI opportunities, in which the player struggles to capitalize.


CONCLUSION

The next phase of this project will be focusing on expanding the data set outside of this group of players from last season. While the numbers are quite reassuring, there is never complete certainty in advanced metrics — there are always small intricacies to these statistics that cause things to result in error. However, as the pool of seasons and players who’ve been evaluated by a metric grows, so does that certainty. Along with further testing, the added benefit to finding the results of previous seasons is that we will be able to gain a further understanding of the predictability of aRBI+ to help understand how a player’s ability to generate RBI changes with age.

While the current formula of aRBI+ seems to be sufficient in accomplishing its goal, I will continue to research how other factors may change and potentially improve aRBI+.

The most significant of these potential additions — and most likely to become a permanent part of the formula — is the incorporation of Park Effect, which would adjust a player’s RBI for inflation or deflation of production caused by the natural phenomena caused by the ballparks in which the player took his plate appearances. Park Effect certainly makes a significant difference in run production, however, the reason this is not currently considered in the formula is largely due to the fact that this study was done over the span of just the 2018 season. To accurately determine how each ballpark effects RBI production, a much larger collection of data must be used. The other significant change I’ve considered is quantifying and adjusting for the ability of the pitchers a batter faces over the course of a season. Making adjustments based on pitchers faced may be a really big challenge due to the potential intricacies of quantifying each pitcher, however, it would allow the formula to weed out any outlier seasons where a hitter happened into an irregularly-high rate of really good or really bad pitchers.

There will likely be more content coming out in the coming weeks regarding aRBI+, in addition to open discussion on Twitter. If you have any questions about the statistic, or how a specific player performed, feel free to direct a tweet my way, and I will try to respond in a timely manner. In the coming weeks, I will be working to expand the data of aRBI+ scoring throughout the history of baseball, to explore what players through the history of our game were able to generate RBI better than anyone else.

Featured Photo: dodgerblue.com

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Mick Callahan

I'm a fifth year student in a five-year Electrical Engineering program at RIT in Rochester, NY. Originally from St. Louis, MO. Big Redbirds fan, and a fan of the game as a whole. If you're new to my articles, spoiler alert: I like math. Many of the things I write focus on breaking the game down to the mathematics that explain why and how baseball works the way it does. Yes, I'm a huge nerd.

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