This offseason, there’s been much made of the supposed lack of right-handed power hitters. Some teams are feeling their lineups leaning a little too heavily to the port side and are thinking that they need to either re-condition one of them to hit from the right side or trade for someone (Hello Justin Upton!). The tactical aspect of it is fairly obvious. Teams don’t like stacking left-handed hitters in their lineup, because it makes them vulnerable later in the game to a LOOGY coming in and being able to have a platoon advantage against a couple hitters in a row without having to worry about facing a righty somewhere in the middle there.

Should they worry about that? The platoon advantage is real and is well known, but left-handed pitchers do not reduce left-handed hitters to nothingness, just slightly-less-than-ness. Everything else equal, a team would rather have a righty to stick between two lefties, but of course, everything else is not always equal. At some point, it’s not worth grabbing just some random righty off the shelf just to say you have one. What if the lefty is an order of magnitude better than the righty?

How much of a difference does there have to be between a lefty and a righty before we can stop worrying about the platoon effect and learn to love the bombs?

**Warning! Gory Mathematical Details Ahead!**

This is a tougher nut to crack than one might imagine. Consider for a moment that a team that has three lefties in a row, they have an advantage against a right-handed starter, and right-handers made 73 percent of starts in 2014. Plus, a manager has the advantage of knowing who the starter is in advance, and if he sees fit he can alter his lineup to compensate.

The real problem comes later in the game when the opposing manager can bring out a left-handed reliever. (The same can be said for a team with a right-handed alley of hitters, but the RHB-RHP platoon effect isn’t quite as severe.) It’s easy to say that this will only affect one or two at-bats per game, but of course, the problem is that some of those at-bats will be in high leverage situations, so we have to adjust for that.

Let’s start with some calculations. I built a lineup simulator and fed it a lineup of nine clones of the average *American League* hitter from 2014. For the initiated, this a Monte Carlo-style Markov model. For the non-initiated, it models a baseball game in the same way that a board game with a lot of dice rolls would. It knows about things like double plays and stolen bases and tagging up on fly balls. No, this is not a perfect representation of baseball. It assumes that the batting team is always facing a league-average pitcher and doesn’t assume any sort of situational effects, but it’s a good starting place to get at what we’re aiming for.

I ran 100,000 nine inning games with our nine average clones and it reported that this lineup should score 4.201 runs per nine innings. The actual average AL team in 2014 actually scored 4.181 runs *per game* and 4.198 runs per nine innings (Remember that not all games go nine innings). So far, the simulator looks good.

Next, I replaced the top three hitters in the lineup with the aggregate line of a left-handed AL hitter facing a left-handed pitcher from 2014. By placing these three lefties at the top of the order, we assure that these three “diminished” hitters will get to bat more often. If we want to see what the effect is, let’s make it as big as we can. Now, in the late innings, when matchup relievers are more likely to be used, we don’t know where the lineup will “start.” When the starter leaves, it might be the no. 5 hitter due up. We don’t know. So, I’ll just put those three guys at the top. In the simulator, they scored 3.989 runs per nine inning game. You can read that as “If our fictional team had to play constantly with three average lefties at the top of their lineup and the opposing team could *always* matchup against them, we’re expect them to score 3.989 runs per game.” Recall, that’s roughly 0.21 runs per game, which over the course of a season would net out to 34 runs lost, but of course, no one is actually doing this.

Now, let’s take our lineup with three lefties at the top and swap out the middle one for a righty (in the two-hole). Our right-handed hitter will be the composite of all 2014 American League hitters facing a lefty. Again, spots 4-9 consist of the same overall league average profile. That lineup, over 100,000 nine-inning games scored 4.105 runs per game. Adding a righty between the two lefties increases a lineup’s potency by .116 runs per game, although again remember that this is a magical fantasy land where the opposing team is always matching up in those top three spots. Still, that pro-rates out to 18.8 runs over 162 games to give some idea of the magnitude.

But again, this is not an issue that teams will have to deal with every day. On a day when a lefty starter is going, the team will probably naturally separate the three lefties (unless the other six guys are just awful). On a day when a righty is starting, having three lefties in a row is a nice thing. But on average, the starter usually departs after the sixth inning, and if a team has three lefties stacked, they might end up facing the other team’s LOOGY. Worse, in the seventh or either inning, they could very well be doing so in high leverage situations. Those are the situations that everyone worries about.

From 2009-2013, the batting team entered the seventh inning either tied or down by a run or two roughly a third of the time. We know that these are the score differentials (from the batter’s side) that have the highest leverage, because the two most important runs in a baseball game are the run that ties the game and the run that un-ties the game. Teams encounter these sorts of high leverage situations in about a third of their games. If we extend it to situations in the seventh inning in which the game is within 2 runs either way, it’s roughly half of games for an average team.

In these high leverage situations, it would be *really really really *advantageous for the batting team to score. As a game wears on, a team actually gains more win probability by going from tied to up by one than they do from going from one run up to 538 runs up. One run can make a big difference. But how can we model a team’s chances of scoring a run (or two) in this particular inning. Thankfully, that heavy lifting has been done by Tom Tango and his Tango distribution. It asks for the number of runs per game that a team scores (or runs per inning) and then gives discrete probabilities that a team will score no runs, one run, two runs, etc.

Since we have runs-per-nine-inning estimates for our conditions, let’s see what the distribution thinks about our team’s chances.

Condition |
Runs per Game |
Prob of 0 runs in an inning |
Prob of 1 run in an inning |
Prob of 2 runs in an inning |
Prob of 3+ runs in an inning |
Prob of 0 runs in 7 |

Baseline |
4.201 |
73.6% |
14.9% |
6.5% |
5.0% |
39.9% |

Left-Right-Left |
4.105 |
74.1% |
14.7% |
6.4% |
4.8% |
40.7% |

Left-Left-Left |
3.989 |
74.6% |
14.5% |
6.2% |
4.7% |
41.6% |

Worst Case |
3.500 |
77.0% |
13.6% |
5.6% |
3.8% |
45.7% |

I added an extra row. Worst Case (which I arbitrarily set at 3.5 runs per game) is meant to show a worst-case scenario. The numbers I generated above assumed an average platoon split for the players involved. Maybe a team has three guys who have really big platoon splits. Maybe you could make the case that because a team only has to use one LOOGY, rather than going left-right-left on three consecutive batters, they are able to neutralize a lefty further down in the lineup later on. This row is for those of you who believe that the penalty that I’m assigning to the left-left-left category to be not big enough.

We see that the difference between our left-right-left and our left-left-left lineup in being able to muster even one run over the course of the last three innings (assuming that the opponents are always able to muster a matchup against the lefties, yet still leave the lefty out there to face the righty), is not even one percent of the time (but let’s just call it 1 percent). Let’s also assume for the sake of simplicity that it’s all on the offense here as our team has a stellar bullpen who keeps the other team quiet for the last three innings.

We’re going to use the home team for the following exercise. Using the visitor team numbers changes things a bit, but not much.

Team enters 7 |
Percentage of games this happens (09-13) |
Scoring 1 run within 3 innings increases win expectancy by |
Difference between how often LRL and LLL do this |
Scoring 2 runs |
Difference between how often LRL and LLL do this |
Scoring 3+ runs |
Difference between how often LRL and LLL do this |
Penalty in win expectancy for LLL (per 162 games) |

Down 2 |
9.8% |
— |
— |
0.26 |
0.3% |
0.78 |
0.3% |
.05 |

Down 1 |
11.7% |
0.12 |
0.5% |
0.64 |
0.3% |
0.64 |
0.3% |
.08 |

Tied |
11.8% |
0.39 |
0.5% |
0.39 |
0.3% |
0.39 |
0.3% |
.08 |

Up 1 |
11.4% |
0.18 |
0.5% |
0.18 |
0.3% |
0.18 |
0.3% |
.04 |

Up 2 |
8.7% |
0.09 |
0.5% |
0.09 |
0.3% |
0.09 |
0.3% |
.01 |

Win expectancy numbers came from here. We see that the effect of having three lefties in a row is worth something on the order of a quarter of a win in terms of win probability, due to the fact that the other team could use a LOOGY to gain a platoon advantage. If you take the worst case scenario above, the penalty is 1.24 wins.

Remember, that we are making some heavy assumptions, which always favor making the effect appear bigger than it will be. These include that a manager would not pinch-hit for one of the lefties, that the bullpen won’t blow it, that the opposing team always has a reasonable LOOGY available, that the visiting team would not issue a tactical intentional walk to the middle-righty (if the walk means little, why not get that lefty-lefty matchup), and that the other team would always play matchups, even in the ninth when most teams would send out their (likely right-handed) closer to face whoever is coming up, even if it’s the three lefties.

**Hard to Port!**

If your favorite team is considering two players, one of whom is better, and one of whom promotes lineup “balance” whom should you call into the sports yakker and recommend that they sign? (Remember: Teams listen very very very closely to sports talk stations and take the calls to heart when making personnel decisions.*) The answer is that there is a small penalty to be paid for lineup imbalance. There will be a few games where the other manager deploys his lefty reliever against you and maybe one where it costs you. However, when you do the #GoryMath, you see that the penalty is only a quarter of a win over a season, and that number is propped up with some major assumptions that just aren’t going to hold.

The moral of the story is that if you have a player who is clearly better than the other (and it’s not hard to make up a quarter of a win), don’t be afraid to yell “Hard to port!” (or starboard). The quality of the players in a lineup are much more important than what side of the plate they hit from. Lineup balance is nice, but it’s much less important than just acquiring talented players.

** – No, not really.*

#### Thank you for reading

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Overall, really interesting stuff. It makes sense if you think about it - the guy who is just flat better is going to be better in all those situations where it's not obvious (2nd AB against an average RH SP, etc) so even if it seems painful to have them neutralized once in a while, that's really just selective memory.