## Runs and Batting Order

In my most recent article, I estimated that a typical power hitter should lose 7.6 RBI over the course of a season if he bats second in the order compared to if he bats fourth. From a narrow perspective, that’s bad news for fantasy owners. But typical fantasy formats deal with more than just RBI, and runs scored in particular seem to have an inverse relationship with RBI where, as a hitter moves toward the front of the order, his runs should increase to offset some or all of his RBI loss. The question is which influence is bigger.

I wanted to make a balanced evaluation of that question, so I started with the same model player as before. That means the hypothetical player skews more toward a power hitter than a typical leadoff hitter, but I will be making his speed the major league average by design. This batter hits a single 18.0 percent of the time, a double 5.0 percent of the time, a triple 0.5 percent of the time, a home run 5.0 percent of the time, and I’ve also added that he walks 8.0 percent of the time, a consideration that I did not need for the RBI research. Based on 2017 performances, the model player looks most similar to Andrew McCutchen.

Those reach-base percentages provide a starting place for run estimates, but then things get a lot more complicated. With the RBI research, everything was at-bat-specific. With runs research, you have to consider everything that could happen once a batter reaches base, and that could span multiple batters across an entire half-inning. Rather than tumble down a rabbit hole trying to estimate the likely quality of batters in various situations when a given runner is on base, I settled on a couple of considerations and let everything be assumed to be average.

The first consideration is the number of outs. Whether a runner is on first base, second base, or third base, he is more likely to score if there are fewer outs. That one’s obvious, but I found it less obvious how many outs tended to precede the plate appearances of batters in various lineup positions.

Bat Order | 0 Outs | 1 Out | 2 Outs |
---|---|---|---|

1 | 46.9% | 26.1% | 27.1% |

2 | 33.0% | 40.3% | 26.6% |

3 | 27.9% | 34.9% | 37.2% |

4 | 34.1% | 30.3% | 35.7% |

5 | 34.6% | 33.4% | 32.0% |

6 | 32.3% | 34.3% | 33.4% |

7 | 32.4% | 33.2% | 34.4% |

8 | 33.0% | 33.0% | 34.0% |

9 | 32.4% | 33.5% | 34.1% |

This is all about the first inning. Because the leadoff hitter gets a guaranteed plate appearance with no outs to start the game, his frequency is skewed toward 0 outs. He sees that 46.9 percent of the time. Then, since leadoff hitters make outs more often than they reach base, the No. 2 hitter skews toward 1-out situations, which he sees 40.3 percent of the time. None of the first three hitters is more likely to reach base than not, but since they collectively have three shots at it, the No. 4 hitter skews a bit toward 2-out situations. Beyond that, the frequency moves toward an equal balance of 0-out, 1-out, and 2-out situations for the final five spots in the order.

Once we have an estimate of how often the model batter reaches each of the various bases and an estimate of the expected out state once he reaches them, we only need to know how often he can be expected to score from each base-out state. Again, I made these estimates based on the overall MLB trends in recent seasons. I’m not making any consideration for the likely quality of the batter based on the runner’s lineup position.

From Base | 0 Outs | 1 Out | 2 Outs |
---|---|---|---|

1B | 34.1% | 22.9% | 11.1% |

2B | 53.6% | 36.1% | 19.2% |

3B | 74.7% | 57.7% | 24.1% |

From there, it’s just a matter of chaining. I start with an estimate of the batter’s total plate appearances in each lineup position, which just adds walks to the at-bat estimates I made in that previous article. Then, I multiply those plate appearances by his percent chance to reach each of the bases times his expected ratio of 0 outs, 1 out, and 2 outs times the baserunner score rates from each base-out state.

To demonstrate, the first piece of that equation for the model batter would be 691 plate appearances from the leadoff spot times a 26.0 percent chance to reach first base—which combines his 18.0 percent single rate with his 8.0 percent walk rate—times a 46.9 percent chance for there to be 0 outs times a 34.1 percent chance to score from first with 0 outs, which equals 28.7 runs. That plus the 10.7 runs from leadoff, one-out reaches of first base and the 5.4 runs from leadoff, two-out reaches of first base rounds to equal the 44.9 expected runs I listed under *From 1B* in the first line of the following table. The table does the same calculation for every state for every lineup position.

Bat Order | PA | From 1B | From 2B | From 3B | From HR | Total |
---|---|---|---|---|---|---|

1 | 691 | 44.9 | 13.7 | 2.0 | 30.0 | 90.6 |

2 | 691 | 42.1 | 12.9 | 1.9 | 30.0 | 86.9 |

3 | 670 | 37.7 | 11.6 | 1.7 | 30.0 | 81.0 |

4 | 652 | 38.2 | 11.8 | 1.7 | 30.0 | 81.6 |

5 | 631 | 37.7 | 11.6 | 1.7 | 30.0 | 81.0 |

6 | 615 | 36.1 | 11.1 | 1.6 | 30.0 | 78.8 |

7 | 601 | 35.1 | 10.8 | 1.6 | 30.0 | 77.5 |

8 | 584 | 34.3 | 10.5 | 1.5 | 30.0 | 76.4 |

9 | 563 | 32.9 | 10.1 | 1.5 | 30.0 | 74.5 |

As expected, runs peak in the leadoff spot and then decline through the rest of the order. However, notice there is a plateau in the three, four, and five holes where the No. 4 hitter actually sees a fractional run more than the No. 3 hitter. Meanwhile, when you combine estimated runs with my previously estimated RBI, you can see that the No. 4 spot is clearly the place to be.

Bat Order | PA | Runs | RBI | Total |
---|---|---|---|---|

1 | 691 | 90.6 | 77.1 | 167.7 |

2 | 691 | 86.9 | 82.9 | 169.8 |

3 | 670 | 81.0 | 87.3 | 168.3 |

4 | 652 | 81.6 | 90.5 | 172.1 |

5 | 631 | 81.0 | 85.0 | 166.0 |

6 | 615 | 78.8 | 79.5 | 158.3 |

7 | 601 | 77.5 | 78.4 | 155.9 |

8 | 584 | 76.4 | 76.4 | 152.8 |

9 | 563 | 74.5 | 75.7 | 150.2 |

The model hitter sees 2.3 extra runs plus RBI over anywhere else in the lineup. However, also note that the fantasy concerns I had for a power hitter hitting second were mostly unwarranted. Yes, he will lose out on some RBI, but runs scored nearly makes up that loss if runs and RBI are equally weighted, as they are in traditional roto formats. The No. 2 hitter even sees more runs plus RBI than the No. 3 hitter. So there is no need to sweat the Marlins’ and Cubs’ decision to bat Giancarlo Stanton and Kris Bryant. They’ll still get you stats, just maybe not in the ratios you originally envisioned.

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Scott Spratt is a fantasy sports writer for FanGraphs and Pro Football Focus. He is a Sloan Sports Conference Research Paper Competition and FSWA award winner. Feel free to ask him questions on Twitter – @Scott_Spratt

Thanks for churning this out. It looks like you would want most of your hitters in the 1 through 5 spots in the batting order for runs and RBIs . . .

Yep. As with the RBI Article it’s intuitive but very nice to see the numbers in black and white. Good stuff :)

Trying to use that “2nd lead off hitter” who bats ninth is just a loser of plan, is what it comes down to.