# The RBI Is Dead, All Hail tRBI+

## TPOP unveils our own created stat to measure run production efficiency

I have a few baseball pet peeves, but chief among them is the over-reliance on the RBI stat to determine if a player is good or not. “I think Alvarez needs to get 100 RBI this year for us to be good,” you hear in Spring Training. “Walker needs to drive in more runs before I would consider signing him long-term,” you may hear on talk radio.

The problem with both of these statements is that a player has little control over his RBI total, aside from the prospect of driving himself in with a home run. A player’s RBI total depends primarily on two things:

- Are his teammates getting on base ahead of him?
- What spot in the batting order is the player hitting?

When Pedro Alvarez has a mental hang-up about hitting 4th in the order and primarily has batted 6th and 7th this year, that’s going to lead to fewer opportunities for not only RBI’s, but also plate appearances in general. To say nothing of his platooning, of course.

To that end, I’m proposing a new stat that evaluates a player based on the opportunities presented to him and how he drove runs in compared to the league average. I’d like to call this stat True Proportion of Production RBI’s, or TPOP RBI for short. But let’s shorten it further to **tRBI+** for now. The next section will get into the nuts and bolts behind the proposed stat, so if you are numbers-averse, feel free to progress down to “tRBI+ for Pirate Starters” section.

### METHODOLOGY

How well did Player X do in terms of driving in runners during his at-bats, related to his peers? That’s what we’re trying to prove here. I’ll get wonky at first, but then run the numbers with a real-life Pirate.

The way I’m starting this is by dividing a player’s plate appearances with men on base (PA MOB) by his total plate appearances (PA) to get his PA MOB%. This will help level the playing field in the end with regards to how many RBI opportunities a leadoff hitter gets versus a cleanup hitter versus a #8 hitter.

Then take the player’s batting average with men on base (AVG MOB), *not batting average with runners in scoring position,* and multiply that by his PA MOB. This is a somewhat crude attempt to capture a total RBI chances stat. The plate appearances, in lieu of at-bats, will grab bases loaded walks and sac flies that result in RBI’s.

To get the base level tRBI, we need to factor in solo home runs, too. So far, all of our work has dealt with situations with men on base, but that would leave out some key run production for players. To work around that, we’ll add in solo home runs to both the numerator (by using total RBI’s) and denominator below. This is what the tRBI formula looks like:

**tRBI = [Total RBI [(PA MOB x AVG MOB) + Solo HR]] PA MOB%**

Let’s take a look at this stat in action with Pedro Alvarez, with all stats after the September 1st games.

tRBI = [67 [(184 x .263) + 19]] .446 = 2.229

In a vacuum, this doesn’t really tell us a lot. That’s where the tRBI+ will come in. The “+” of the stat refers to how a player does versus the league-wide average tRBI. So now let’s get a league tRBI number:

tRBI (league) = [15,816 [(63,777 x .264) + 2321]] .428 = 1.929

**tRBI+ = Player’s tRBI League tRBI**

For Alvarez, this equates to 2.233/1.926 = 1.156. This indicates that Alvarez is driving in batters above league average by 15.6%. As a noted Alvarez dissenter, this was surprising to me, but heartening at the same time. He’s a much maligned figure, but he does produce runs. It’s just that by being in the #6 spot, he doesn’t get as many opportunities. All of this just makes it that much more frustrating that he’s unable to handle the rigors of the cleanup spot.

### tRBI+ FOR PIRATE STARTERS

Shown below are the stats and tRBI+ figures for all the Pirates’ typical starters, as of the evening of September 1st.

Player |
PA |
PA MOB |
%PA MOB |
AVG |
HR |
SOLO HR |
RBI |
tRBI |
tRBI+ |

Polanco | 522 | 179 | 0.343 | 0.292 | 7 | 6 | 41 | 2.051 | 1.063 |

Marte | 508 | 254 | 0.5 | 0.263 | 15 | 8 | 63 | 1.684 | 0.873 |

McCutchen | 550 | 232 | 0.422 | 0.335 | 20 | 6 | 85 | 2.406 | 1.247 |

Kang | 413 | 180 | 0.436 | 0.313 | 13 | 10 | 49 | 1.694 | 0.878 |

Walker | 502 | 218 | 0.434 | 0.273 | 13 | 7 | 55 | 1.905 | 0.988 |

Alvarez | 413 | 184 | 0.446 | 0.263 | 22 | 19 | 67 | 2.229 | 1.156 |

Cervelli | 402 | 169 | 0.42 | 0.301 | 6 | 4 | 37 | 1.606 | 0.833 |

Harrison | 350 | 124 | 0.354 | 0.271 | 4 | 3 | 23 | 1.775 | 0.92 |

There’s a lot to unpack from this table. It’s not really a surprise that McCutchen is good at run production, considering he’s good at just about everything related to the game of baseball. It’s also not a surprise to me that Walker is right around league average. I’ve mentioned for a while now that Walker is like that one piece in a finely tuned Swiss watch that allows everything else to rotate smoothly around it.

What is surprising is that Marte and Kang are significantly below league average (nearly 13% below for both of them). Marte has men on base exactly half the time he is at bat, so the numbers say that his RBI’s should be higher. Perhaps his high hit-by-pitch count is affecting this stat, as it is only advancing runners one base and not driving them in. He does have a lower batting average with men on base than without, which isn’t helping matters either. Kang is a tougher nut to crack. He has plenty of runners available to him and his batting average with men on base is excellent. For Kang it appears as if he isn’t getting the extra base hits in these situations to drive in multiple runs and pad his RBI totals.

You can also see how tRBI+ compensates for Polanco batting leadoff and shows that when presented with the opportunity, Polanco is an above-average run producer.

### APPLICATION TO OTHER MLB RUN-PRODUCERS

For comparison sake, here’s the tRBI+ for the top five RBI guys in MLB. Each of these guys are typically in the #3 to #5 slots of their respective batting orders.

Player | PA | PA MOB | %PA MOB | AVG | HR | SOLO HR | RBI | tRBI | tRBI+ |

J. Donaldson | 582 | 248 | 0.426 | 0.348 | 36 | 24 | 108 | 2.298 | 1.191 |

N. Arenado | 533 | 245 | 0.46 | 0.335 | 32 | 13 | 98 | 2.241 | 1.162 |

P.Goldschmidt | 587 | 289 | 0.492 | 0.31 | 27 | 11 | 97 | 1.96 | 1.016 |

C. Davis | 538 | 236 | 0.439 | 0.26 | 36 | 18 | 94 | 2.698 | 1.399 |

E. Encarnacion | 509 | 227 | 0.446 | 0.321 | 30 | 14 | 92 | 2.375 | 1.231 |

Not all RBI’s are created equal. Goldschmidt has had a plethora of men on base, nearly 50%, with a very good batting average with men on base, but he “only” has a tRBI+ 1.6% greater than league average. Conversely, we see that Chris Davis takes full advantage of having men on base. Even with a so-so .260 batting average in these situations, Davis has produced 94 total RBI on the season and is a stunning 39.9% higher than league average by our tRBI+ stat.

***

In years past, baseball has been viewed as a game of compiling numbers. Just get the bulk totals of RBI’s and HR’s and it will all sort itself out in the end. But with tRBI+, we can start to see how efficiently a player achieves those RBI’s. A possible application for this stat could be when it comes to splitting hairs in MVP votes, as the true “value” can be teased out further now. However it is ultimately used, I just hope the conversation shifts away from focusing on a player’s total RBI, much like the conversation is slowly drifting away from a pitcher’s total of wins.

I propose this: runner advancement percentage (RAP), Ie, number of runners-bases advanced per opportunity. It goes like this:

If a batter comes up w/ the bases empty, his total runner-base advancement opportunity is four, as he can potentially advance a runner (in this case, himself) four bases (with a home run). If he would triple, for that AB his percentage would be .750.

Where it gets interesting is w/ men on base: each runner adds potential runner advancement bases for the batter, depending on what base they’re on. Thus, a runner on third could be advanced one base; a runner on second two bases; a runner on first, three.

So w/ the bases loaded, the total runner base advancement potential is 1 (runner on 3rd) plus 2 (runner on 2nd) plus 3 (runner on 1st) plus 4 (batter himself) for a total runner base advancement potential of 10. A grand slam would produce the max, or 10 runner bases advanced; a single scoring two runs leaving runners on 1st and 2nd, for example, would yield an advancement number of 5 (runner on 3rd, one base advanced; runner on 2nd, two bases advanced; runner on 1st and the batter, one base each) for a percentage for that AB of .500 (5/10).

Of course, over the season the stats would accumulate, like any over; and the ABs w runners on would automatically be properly weighted to show success (or failure) based on opportunity.

I really like this idea, David. I’m just trying to think how it can be tracked in any other way than “live”. Meaning, how could someone who is not watching…say…the SEA-TEX game at that moment, calculate the RAP? Go through the game logs? I do like it, but I’m trying to figure out the logistics.

Both ideas (Kevin’s and David’s) seem to provide a measurement that refines the situational impact of a baseball event. Have long forgotten my stats, but these seem promising…Luv the sight BTW!

Thanks for reading, Harry. Spread the word about TPOP!

I’m not an expert, but I’m confused by this part of the calculation:

“Then take the player ?s batting average with men on base (AVG MOB), not batting average with runners in scoring position, and multiply that by his PA MOB. This is a somewhat crude attempt to capture a total RBI chances stat. The plate appearances, in lieu of at-bats, will grab bases loaded walks and sac flies that result in RBI ?s.”

Using Plate Appearances instead of At-Bats will incorporate walks, sac flies, HBPs, etc., but multiplying by batting average doesn’t that take credit away from RBIs on non-hits? Unless you don’t want to give credit to the hitter for sac flies, etc.

There’s no real good “off the shelf” stat to capture what I wanted to, so I had to do the AVG MOB by PA MOB to try to get the walks and sac flies. I know it’s not perfect, but there isn’t really a “batting average with men on base based on plate appearances” number, unfortunately.

You might be interested in RE24 runs scored/prevented.

definition: http://www.fangraphs.com/library/misc/re24/

2015 leaderboard: http://www.fangraphs.com/leaders.aspx?pos=all&stats=bat&lg=all&qual=y&type=3&season=2015&month=0&season1=2015&ind=0&team=0&rost=0&age=0&filter=&players=0&sort=6,d