# The Hardball Times

## The opportunity of RBI

by Jason Mitchell
January 23, 2013

A well known criticism of runs batted in is that it measures opportunity as much as it does performance. Instead of discarding RBI as a helpful metric, however, maybe we should look at it from the other direction and account for each batter’s opportunity. Combining performance and opportunity in one metric can bring more validity to RBI.

Let’s define opportunity as the expected number of runs an average batter would drive in, given a specific base/out situation. We can then create a ratio from a batter's actual RBI (aRBI) to his expected RBI (eRBI) and compare one batter to another to show which performed better.

As far back as 1998, you can find other baseball minds looking into the same concept. Tom Ruane laid out a very good set of examples and explanations (see the link below under References). The concept requires finding out what the average outcomes of at-bats were in each season, such as a home run 3 percent of the time. Based on those outcomes, an expected RBI value is assigned to each of the 24 base out states, ranging from none to two outs, and from bases empty to bases loaded.

Next you isolate the number of at-bats a player encountered in each of these 24 base out states, and add in all of expected RBI values. Once a total expected RBI is calculated, you find the actual RBIs produced in the same situations, and divide by the eRBI to create a ratio.

This newly found ratio, which we’ll call actual/expected ratio (aeRatio), can be used in many different ways, but I will focus on three of the most important today. First, we will highlight the players who made the most of limited situations. Good hitters who suffer from the lack of teammate performance, poor lineup construction, or being walked in many high leverage appearances will all be recognized for their production despite these setbacks.

Second, hitters who have gaudy RBI totals despite their lesser relative performance will be exposed. While our eyes are drawn to triple-digit RBI totals, aeRatio can parse out the players whose opportunity played a more important role than performance.

Third, a ratio metric allows us to apply different hitters’ abilities into other hitters’ opportunities. When one team’s cleanup hitter is driving in 50 more runs than another team’s, we can now step into each player’s totals and see how much should be attributed to the individual player, how much to the team he plays for.

Using data from 2012, let’s look at a couple of leader boards. The list below displays the top 10 batters who drove in runs at the highest rates:

```Batter                    eRBI    aRBI   aeRatio
Edwin Encarnacion         60.4     107      1.77
Josh Hamilton             72.9     127      1.74
David Ortiz               35.8      60      1.68
Evan Longoria             32.6      53      1.63
Miguel Cabrera            86.3     138      1.60
Jose Bautista             40.0      63      1.58
Ryan Braun                70.7     111      1.57
Giancarlo Stanton         55.3      84      1.52
Alfonso Soriano           71.4     108      1.15
Garret Jones              57.3      85      1.48```

An aeRatio above 1 suggests that a player outperformed the average hitter in terms of driving in runs. It is a simple ratio, so a ratio of 1.5 is basically saying that a hitter is producing 1.5 aRBI for each full eRBI he encounters. An aeRatio below one works the opposite way, suggesting a hitter was worse than average and produced a fraction of an aRBI for every eRBI.

Atop our list is the Blue Jays’ newest breakout slugger, Edwin Encarnacion, who had far and away his best season at the plate. Despite his dominance last season, Encarnacion finished with only 107 aRBI, 30 fewer than Miguel Cabrera, but you can see that Cabrera had 26 more eRBI, which gave him a clear advantage for the RBI title.

A simple calculation suggests that Encarnacion would have had (1.771 * 86.25 =) 153 RBI if he had been presented with the same opportunities as Cabrera, while the 2012 Triple Crown winner would have only totaled (1.6 * 60.414 =) 97 RBI if he had been given Edwin’s opportunities. I am not suggesting that every single factor would remain the same if the two simply swapped uniforms, but I’m just supplying a method of equalizing players’ RBI totals from one team to another.

To identify the players who were put in the most fortunate situations, we will sort the list for highest eRBI totals.
```Batter                    eRBI    aRBI   aeRatio
Hunter Pence              94.3     103      1.09
Miguel Cabrera            86.3     138      1.60
Marco Scutaro             83.5      73      0.88
Hanley Ramirez            81.7      90      1.10
Starlin Castro            81.5      78      0.96
Matt Holliday             81.2     102      1.26
Billy Butler              80.0     106      1.33```

The aforementioned Cabrera is once again on our list. This would explain why he was able to lead the league: an abundance of eRBI paired with his high aeRatio. Ahead of Cabrera in eRBI is Hunter Pence. However Pence’s aRBI was a much lower 103, giving him an aeRatio of 1.093. The ratio still suggests that Pence was above average, but at a much slimmer margin than other members of the 100 RBI club.

Starlin Castro also had a career-high RBI total in 2012, but the list above shows that was a blatant product of opportunity. Castro led the league in at-bats last year, which allowed him to pile up over 81 eRBI on the season. His sub-1 aeRatio suggest that he was unable to knock in as many runs as the average hitter would have.

While driving in runs is still only half of the equation for scoring runs, the ability to isolate and compare that part of the equation can allow us to see who excels and who are the less impressive products of opportunity. A ratio format also eliminates the flaw of "counting" statistics which accentuate the values of players with more at-bats in general. RBI is one of the most traditional statistics baseball has, and is basically untouched by sabermetrics. My hope is to no longer ignore this part of the run scoring equation because of its limitations, but rather to identify those limitations and create methods of enhancing it.

References and Resources
For more information, please visit the aeRatio website for the aeRatio database from 1992-2012, as well as a glossary and introductory information on the process. All of the work was made possible with data from Retrosheet.

Tom Ruane’s work with expected RBI can be found here.

I greatly appreciate any feedback or suggestions, and can be reached at .(JavaScript must be enabled to view this email address)