# Expected RBI Totals: The Top 267 xRBI Totals for 2013

While there is almost zero skill when it comes to the amount of RBI a player produces, through the creation of an expected RBI metric I have found a way to look at whether or not a player has gotten lucky or unfortunate when it comes to their actual RBI total.

I hope I don’t need to do this for most of our readers, because it’s 2014 and you’re reading about baseball on a far off corner of Internet, so you obviously are more informed than the average fan who consumes ESPN as their main source of baseball information, but lets talk about why RBI, as a stat, and why it is not valuable when you look at a players’ talent. The amount of RBI a player produces are almost—we’ll get into the almost a little later—entirely dependent on the lineup a player plays in. If a player doesn’t have teammates that can get on base in front of them in the lineup, there aren’t very many opportunities for RBIs; that’s the long and short. Really, RBI tell more about the lineup a player plays in than the player himself.

Intuitively, this makes sense.  The more runners there are on base, the more chances the batter will have for RBI, and the more RBI the batter will accumulate. When I said, “The amount of RBI a player produces are almost…entirely dependent on the lineup a player plays in”, lets be a little more precise. My research took the last three years of data (2010 to 2013) and looked at all players that had 180 runners on base (ROB) during their at bats over the course of a season. Over the three seasons, which should be enough data—it was a pain in the ass to obtain the data that I did find—ROB correlated with RBI by a correlation coefficient of .794 (r2 = .63169), which is a very strong positive relationship.

But hey, that doesn’t mean that you can be a lousy hitter get a lot of RBI. That would be like if you threw a hobo in the Playboy Mansion and expected him to get a lot of tail; all the opportunity in the world can’t mask the smell of Pall Malls, grain alcohol and a lifetime of deflected introspection; trust me, I worked at a liquor store for three years in college, and I know.  In the same sample of players from 2010 to 2013 as used above, the correlation between wOBA—what we’ll use here to define a player’s ability at the plate—and RBI is .6555. So there is a relationship between a player’s ability and their RBI total, but nowhere near as strong as the relationship between their RBI total and their opportunity—ROB.

However, when we combine a player’s opportunity—ROB—with their talent—wOBA—we should get a good idea of what to expect for a hitter’s RBI total. Here is the formula for the expected RBI totals based on the correlations between ROB and wOBA, and RBI: xRBI =- 85.0997 + 262.7424 * wOBA + 0.1918 * ROB.

When you combine wOBA and ROB into this formula you end up with a correlation coefficient of .878 and an r2 of .771. Wooooo (Ric Flair voice)!!!!!  With the addition of wOBA to ROB we increase our r2, from .63 with just ROB, by fourteen percent.

Photo by: Keith Allison

Let’s think about why Chris Davis xRBI is so much lower than his 2013 actual RBI total.

Davis had 396 runners on base while he batted in 2013, which is 140 ROB less than Prince Fielder who led the league with 536 ROB; Davis’ opportunity was limited.

Davis’ RBI total was considerably higher than what his opportunity would suggest his RBI total should be, and one of the reasons that he outperformed his xRBI total by so much was because of the amount of home runs he hit. Davis, or any batter, doesn’t need a runner on base to get an RBI when he hits a home run. But beyond home runs there is another reason why Davis and other batters outperform their xRBI totals: luck.

Hitting with runners on base is not a skill. A batter has the same probability, regardless of the base/out state, of a hit. Lets forget pitcher handedness and Davis’ platoon splits at the moment. With a runner on second base and two outs Chris Davis will get a hit .272 (27%) of the time—I averaged his Steamer and Oliver projections for 2014 together. Davis, and Alfonso Soriano for that matter, who was the only player to outperform his xRBI by more than Davis in 2013, was lucky and happened to have runners on base the majority of the 28.6%—Davis’ 2013 batting average—of the time he got a hit in 2013.

To put Davis’ 2013 136 RBI season into perspective, in the last five seasons there have been eight players to record 130 or more RBI in a season. Of those eight players, only two—Ryan Howard (2008-9) and Miguel Cabrera (2012-13)—were able to duplicate the performance the following year.

While the combination of ROB and wOBA has allowed us come up with a reliable xRBI, the next step, to increase the reliability of xRBI and account for players who produce a large amount of their RBI from home runs (i.e. Davis), is to include a power component in xRBI: HR/FB ratio.

Devin Jordan is obsessed with statistical analysis, non-fiction literature, and electronic music. If you enjoyed reading him, follow him on Twitter @devinjjordan.

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Guest
Sam Horwich-Scholefield

super interesting analysis here. I think theres a conception that just because some of these traditional stats like RBI or pitcher wins are not great measures of skill that there is no reason to try and predict them. If you work in a front office, sure, but for us internet nerds I think that these descriptive statistics like RBI, wins, and average can be worth examining and breaking down. also, they can help you win your league

Guest
Joseph Randall

Where did you find the RunnersOnBase information?