I received some really interesting comments on my previous article on RBI luck, and that has steered me toward several new avenues of related research. Commenter Bill identified that several of the unlucky batters who had fewer RBI on home runs than I expected batted second in the order. Intuitively, it makes a lot of sense for batting order to influence a player’s opportunities for RBI, but that issue can be a bit difficult to disentangle from the quality of the offense he is a part of. Still, I think it is possible, and I’ve made an attempt to do so with a model that chains some league average rates to a hypothetical power hitter’s expected batting outcomes.

The easiest place to start is with baserunners. I mentioned in that last article that a batter can expect about 0.6 runners on base on average, which is a generalization calculated from historical seasons for all lineup positions. But when you calculate those averages based on the current run environment and split them by batting order, you can see how much of an impact that order has on a player’s opportunities to drive in runs.

Average Number of Baserunners by Lineup Spot, 2017 Bat Order Runners On 1B Runners On 2B Runners On 3B Runners On 1 0.232 0.160 0.084 0.477 2 0.310 0.175 0.085 0.569 3 0.340 0.198 0.102 0.639 4 0.356 0.220 0.116 0.692 5 0.339 0.209 0.112 0.660 6 0.330 0.199 0.100 0.629 7 0.336 0.201 0.102 0.639 8 0.327 0.204 0.104 0.635 9 0.336 0.209 0.112 0.656

We’re working with fractional runners here, but over the course of a full season—which I’ll approximate as 600 at-bats—the difference between the prime RBI spot in the order, 4th, and even 3rd in the order is 32 baserunners. For players like Giancarlo Stanton and Kris Bryant who frequently bat second, it is a loss of 74 baserunners over their potential in the No. 4 hole. That’s not to say it is worse for the team. Quite the opposite. This is just one of the places where the real world and fantasy have incompatible interests.

Those RBI opportunities mean different things to different batters. A runner on first base is a great RBI opportunity for Stanton since he hits so many home runs. He is less so for a batter like Mookie Betts, who generates the bulk of his RBI on singles and doubles. So I opted to create a hypothetical batter to represent what I consider to be a typical run producer. I gave this batter an 18.0 percent chance of hitting a single, a 5.0 percent chance of hitting a double, a 0.5 percent chance of hitting a triple, and a 5.0 percent chance of hitting a home run. Those rates mean the batter hits for an average of .285 and a slugging percent of .495. Over 600 at-bats, he would produce 108 singles, 30 doubles, 3 triples, and 30 home runs.

Next, I calculated the model batter’s expected RBI totals based on the typical distribution of baserunners he should see in various lineup spots and given the average score percentages of baserunners on singles, doubles, triples, and home runs. In other words, this batter will have perfectly average baserunners with perfectly average frequencies of baserunners.

Baserunner Score% by Result Type Result Type Runners On 1B Runners On 2B Runners On 3B Single 0.5% 53.6% 90.2% Double 39.2% 92.7% 92.9% Triple 95.9% 95.0% 95.5% Home Run 100.0% 100.0% 100.0%

Then, I just chained it all together. The batter would hit 108 singles multiplied by 0.232 runners on first base when he bats first in the lineup multiplied by the 0.005 chance that runner would score on a single equals 0.125 RBI. I did that for each of his batting outcomes for each of his expected baserunners in every lineup spot, assuming he had 600 at-bats regardless of his lineup spot. Here are the results:

Expected RBI by Lineup Spot, Model Batter, 600 At-Bats Bat Order Runners On 1B Runners On 2B Runners On 3B Batter Total 1 10.5 19.0 13.3 30.0 72.7 2 14.0 20.7 13.4 30.0 78.2 3 15.4 23.5 16.1 30.0 85.0 4 16.1 26.1 18.3 30.0 90.5 5 15.3 24.8 17.7 30.0 87.8 6 14.9 23.6 15.8 30.0 84.3 7 15.2 23.8 16.1 30.0 85.1 8 14.8 24.2 16.4 30.0 85.4 9 15.2 24.8 17.7 30.0 87.7

I was surprised to see that the RBI opportunities were fairly flat between the No. 3 spot and No. 9 spot. In that range, a hitter is losing no more than 6.2 RBI over his maximum potential hitting 4th. However, batting second really hurts a hitter’s RBI potential. There, he can expect to lose 12.3 RBI over the course of a season. The relative drop from 3rd to 2nd is more significant than even the drop from 2nd to 1st.

As an aside, I think the No. 9 hole has a higher total here because teams intentionally put runners on base for the pitcher in the NL. I didn’t bother to split the leagues out since it’s unrealistic for our model batter to be batting ninth in any case.

Those calculations omit one important piece of the puzzle, which is that a batter who hits first in the order can expect more at-bats over the course of a year than one who hits fourth. That increased volume of at-bats should help to offset his lesser RBI potential in each specific at-bat. To make that adjustment, I calculated the total number of plate appearances for each lineup spot in recent seasons and then adjusted it to the No. 4 hole, assigning it the expected 600 at-bats. Here are the adjusted at-bat and corresponding RBI totals:

Expected RBI by Lineup Spot, Model Batter Bat Order At-Bats Runners On 1B Runners On 2B Runners On 3B Batter Total 1 636 11.1 20.1 14.1 31.8 77.1 2 636 14.8 22.0 14.2 31.8 82.9 3 616 15.8 24.1 16.6 30.8 87.3 4 600 16.1 26.1 18.3 30.0 90.5 5 581 14.8 24.0 17.1 29.0 85.0 6 566 14.1 22.3 14.9 28.3 79.5 7 553 14.0 21.9 14.9 27.6 78.4 8 537 13.2 21.6 14.7 26.9 76.4 9 518 13.1 21.4 15.3 25.9 75.7

Relative to the fixed-600 at-bat calculations, the No. 2 hitter gains back 4.7 RBI, but he still falls short of his potential RBI in the No. 4 hole by 7.6 RBI. That’s a big deal, and it neatly explains many of the perceived shortfalls in RBI that No. 2 hitters had in my previous article. Meanwhile, the No. 5-9 spots in the order now see a much steeper decline in expected RBI as they lose upward of 82 at-bats over the course of the season.