Those of you who follow me on Twitter know that I am somewhat obsessed with how teams (managers) construct their lineups. With few exceptions, managers tend to do two things when it comes to setting their daily lineups: One, they follow more or less the traditional model of lineup construction, which is to put your best overall offensive player third, a slugger fourth, and scrappy, speedy players in the one and/or two holes. Two, monkey with lineups based on things like starting pitcher handedness (relevant), hot and cold streaks, and batter/pitcher matchups, the latter two generally being not so relevant. For example, in 2012, the average team used 122 different lineups.

If you have read The Book (co-authored by Yours Truly, Tom Tango and Andy Dolphin), you may remember that the optimal lineup differs from the traditional one. According to The Book, a team’s 3 best hitters should bat 1,2, and 4, and the 4th and 5th best hitters 3 and 5. The 1 and 2 batters should be more walk prone than the 4 and 5 hitters. Slots 6 through 9 should feature the remaining hitters in more or less descending order of quality. As we know, managers violate or in some cases butcher this structure by batting poor, sometimes awful hitters, in the 1 and 2 holes, and usually slotting their best overall hitter third. They also sometimes bat a slow, but good offensive player, often a catcher, down in the order.

In addition to these guidelines, The Book suggests placing good base stealers in front of low walk, and high singles and doubles hitters. That often means the 6 hole rather than the traditional 1 and 2 holes in which managers like to put their speedy, base stealing players. Also, because the 3 hole faces a disproportionate number of GDP opportunities, putting a good hitter who hits into a lot of DP, like a Miguel Cabrera, into the third slot can be quite costly. Surprisingly, a good spot for a GDP-prone hitter is leadoff, where a hitter encounters relatively few GDP opportunities.

Of course, other than L/R considerations (and perhaps G/F pitcher/batter matchups for extreme players) and when substituting one player for another, optimal lineups should rarely if ever change. The notion that a team has to use 152 different lineups (like TB did in 2012) in 162 games, is silly at best, and a waste of a manager’s time and sub-optimal behavior at worst.

Contrary to the beliefs of some sabermetric naysayers, most good baseball analysts and sabermetricians are not unaware of or insensitive to the notion that some players may be more or less happy or comfortable in one lineup slot or another. In fact, the general rule should be that player preference trumps a “computer generated” optimal lineup slot. That is not to say that it is impossible to change or influence a player’s preferences.

For those of you who are thinking, “Batting order doesn’t really matter, as long as it is somewhat reasonable,” you are right and you are wrong. It depends on what you mean by “matter.” It is likely that in most cases the difference between a prevailing, traditional order and an optimal one, not-withstanding any effect from player preferences, is on the order of less than 1 win (10 or 11 runs) per season; however, teams pay on the free agent market over 5 million dollars for a player win, so maybe those 10 runs do “matter.” We also occasionally find that the difference between an actual and optimal lineup is 2 wins or more. In any case, as the old sabermetric saying goes, “Why do something wrong, when you can do it right?” In other words, in order to give up even a few runs per season, there has to be some relevant countervailing and advantageous argument, otherwise you are simply throwing away potential runs, wins, and dollars.

Probably the worst lineup offense that managers commit is putting a scrappy, speedy, bunt-happy, bat-control, but poor overall offensive player in the two hole. Remember that The Book (the real Book) says that the second slot in the lineup should be reserved for one of your two best hitters, not one of your worst. Yet teams like the Reds, Braves, and the Indians, among others, consistently put awful hitting, scrappy players in the two-hole. The consequence, of course, is that there are fewer base runners for the third and fourth hitters to drive in, and you give an awful hitter many more PA per season and per game. This might surprise some people, but the #2 hitter will get over 100 more PA than the #8 hitter, per 150 games. For a bad hitter, that means more outs for the team with less production. It is debatable what else a poor, but scrappy hitter batting second brings to the table to offset those extra empty 100 PA.

The other mistake (among many) that managers make in constructing what they (presumably) think is an optimal order is using current season statistics, and often spurious ones like BA and RBI, rather than projections. I would venture to guess that you can count on one hand, at best, the number of managers that actually look at credible projections when making decisions about likely future performance, especially 4 or 5 months into the season. Unless a manager has a time machine, what a player has done so far during the season has nothing to do with how he is likely to do in the upcoming game, other than how those current season stats inform an estimate of future performance. While it is true that there is obviously a strong correlation between 4 or 5 months past performance and future performance, there are many instances where a hitter is projected as a good hitter but has had an awful season thus far, and vice versa. If you have read my previous article on projections, you will know that projections trump seasonal performance at any point in the season (good projections include current season performance to-date – of course). So, for example, if a manager sees that a hitter has a .280 wOBA for the first 4 months of the season, despite a .330 projection, and bats him 8th, he would be making a mistake, since we expect him to bat like a .330 hitter and not a .280 hitter, and in fact he does, according to an analysis of historical player seasons (again, see my article on projections).

Let’s recap the mistakes that managers typically make in constructing what they think are the best possible lineups. Again, we will ignore player preferences and other “psychological factors” not because they are unimportant, but because we don’t know when a manager might slot a player in a position that even he doesn’t think is optimal in deference to that player. The fact that managers constantly monkey with lineups anyway suggests that player preferences are not that much of a factor. Additionally, more often than not I think, we hear players say things like, “My job is to hit as well as I can wherever the manager puts me in the lineup.” Again, that is not to say that some players don’t have certain preferences and that managers shouldn’t give some, if not complete, deference to them, especially with veteran players. In other words, an analyst advising a team or manager should suggest an optimal lineup taking into consideration player preferences. No credible analyst is going to say (or at least they shouldn’t), “I don’t care where Jeter is comfortable hitting or where he wants to hit, he should bat 8th!”

Managers typically follow the traditonal batting order philosophy which is to bat your best hitter 3rd, your slugger 4th, and fast, scrappy, good-bat handlers 1 or 2, whether they are good overall hitters or not. This is not nearly the same as an optimal batting order, based on extensive computer and mathematical research, which suggest that your best hitter should bat 2 or 4, and that you need to put your worst hitters at the bottom of the order in order to limit the number of PA they get per game and per season. Probably the biggest and most pervasive mistake that managers make is slotting terrible hitters at the top, especially in the 2-hole. Managers also put too many base stealers in front of power hitters and hitters who are prone to the GDP in the 3 hole.

Finally, managers pay too much attention (they should pay none) to short term and seasonal performance as well as specific batter/pitcher past results when constructing their batting orders. In general, your batting order versus lefty and righty starting pitchers should rarely change, other than when substituting/resting players, or occasionally when player projections significantly change, in order to suit certain ballparks or weather conditions, or extreme ground ball or fly ball opposing pitchers (and perhaps according to the opposing team’s defense). Other than L/R platoon considerations (and avoiding batting consecutive lefties if possible), most of these other considerations (G/F, park, etc.) are marginal at best.

With that as a background and primer on batting orders, here is what I did: I looked at all 30 teams’ lineups as of a few days ago. No preference was made for whether the opposing pitcher was right or left-handed or whether full-time starters or substitutes were in the lineup on that particular day. Basically these were middle of August random lineups for all 30 teams.

The first thing I did was to compare a team’s projected runs scored based on adding up each player’s projected linear weights in runs per PA and then weighting each lineup slot by its average number of PA per game, to the number of runs scored using a game simulator and those same projections. For example, if the leadoff batter had a linear weights projection of -.01 runs per PA, we would multiply that by 4.8 since the average number of PA per game for a leadoff hitter is 4.8. I would do that for every player in the lineup in order to get a total linear weights for the team. In the NL, I assumed an average hitting pitcher for every team. I also added in every player’s base running (not base stealing) projected linear weights, using the UBR (Ultimate Base Running) stat you see on Fangraphs. The projections I used were my own. They are likely to be similar to those you see on Fangraphs, The Hardball Times, or BP, but in some cases they may be different.

In order to calculate runs per game in a simulated fashion, I ran a simple game simulator which uses each player’s projected singles, doubles, triples, HR, UIBB+HP, ROE, G/F ratio, GDP propensity, and base running ability. No bunts, steals or any in-game strategies (such as IBB) were used in the simulation. The way the base running works is this: Every player is assigned a base running rating from 1-5, based on their base running projections in runs above/below average (typically from -5 to +5 per season). In the simulator, every time a base running opportunity is encountered, like how many bases to advance on a single or double, or whether to score from third on a fly ball, it checks the rating of the appropriate base runner and makes an adjustment. For example, on an outfield single with a runner on first, if the runner is rated as a “1” (slow and/or poor runner), he advances to third just 18% of the time, whereas if he is a “5”, he advances 2 bases 41% of the time. The same thing is done with a ground ball and a runner on first (whether he is safe at second and the play goes to first), a ground ball, runner on second, advances on hits, tagging up on fly balls, and advancing on potential wild pitches, passed balls, and errors in the middle of a play (not ROE).

Keep in mind that a lineup does 2 things. One, it gives players at the top more PA than players at the bottom, which is a pretty straightforward thing. Because of that, it should be obvious that you want your best hitters batting near the top and your worst near the bottom. But, if that were the only thing that lineups “do,” then you would simply arrange the lineup in a descending order of quality. The second way that a lineup creates runs is by each player interacting with other players, especially those near them in the order. This is very tricky and complex. Although a computer analysis can give us rules of thumb for optimal lineup construction, as we do in The Book, it is also very player dependent, in terms of each player’s exact offensive profile (again, ignoring things like player preferences or abilities of players to optimize their approach to each lineup slot). As well, if you move one player from one slot to another, you have to move at least one other player. When moving players around in order to create an optimal lineup, things can get very messy. As we discuss in The Book, in general, you want on base guys in front of power hitters and vice versa, good base stealers in front of singles hitters with low walk totals, high GDP guys in the one hole or at the bottom of the order, etc. Basically, constructing an optimal batting order is impossible for a human being to do. If any manager thinks he can, he is either lying or fooling himself. Again, that is not to say that a computer can necessarily do a better job. As with most things in MLB, the proper combination of “scouting and stats” is usually what the doctor ordered.

In any case, adding up each player’s batting and base running projected linear weights, after controlling for the number of PA per game in each batting slot, is one way to project how many runs a lineup will score per game. Running a simulation using the same projections is another way which also captures to some extent the complex interactions among the players’ offensive profiles. Presumably, if you just stack hitters from best to worst, the “adding up the linear weights” method will result in the maximum runs per game, while the simulation should result in a runs per game quite a bit less, and certainly less than with an optimal lineup construction.

I was curious as to the extent that the actual lineups I looked at optimized these interactions. In order to do that, I compared one method to the other. For example, for a given lineup, the total linear weights prorated by number of PA per game might be -30 per 150 games. That is a below average offensive lineup by 30/150 or .2 runs per game. If the lineup simulator resulted in actual runs scored of -20 per 150 games, presumably there were advantageous interactions among the players that added another 10 runs. Perhaps the lineup avoided a high GDP player in the 3-hole or perhaps they had high on base guys in front of power hitters. Again, this has nothing to do with order per se. If a lineup has poor hitters batting first and/or second, against the advice given in The Book, both the linear weights and the simulation methods would bear the brunt of that poor construction. In fact, if those poor hitters were excellent base runners and it is advisable to have good base runners at the top of the order (and I don’t know that it is), then presumably the simulation should reflect that and perhaps create added value (more runs per game) as compared to the linear weights method of projecting runs per game.

The second thing I did was to try and use a basic model for optimizing each lineup, using the prescriptions in The Book. I then re-ran the simulation and re-calculated the total linear weights to see which teams could benefit the most from a re-working of their lineup, at least based on the lineups I chose for this analysis. This is probably the more interesting query. For the simulations, I ran 100,000 games per team, which is actually not a whole lot of games in terms of minimizing the random noise in the resultant average runs per game. One standard error in runs per 150 games is around 1.31. So take these results with a grain or two of salt.

In the NL, here are the top 3 and bottom 3 teams in terms of additional or fewer runs that a lineup simulation produced, as compared to simply adding up each player’s projected batting and base running runs, adjusting for the league average number of PA per game for each lineup slot.

Top 3

Team Linear Weights Lineup Simulation Gain per 150 games ARI -97 -86 11 COL -23 -13 10 PIT 10 17 6

Here are those lineups:

ARI

Inciarte

Pennington

Peralta

Trumbo

Hill

Pacheco

Marte

Gosewisch

COL

Blackmon

Stubbs

Morneau

Arenado

Dickerson

Rosario

Culberson

Lemahieu

PIT

Harrison

Polanco

Martin

Walker

Marte

Snider

Davis

Alvarez

Bottom 3

Team Linear Weights Lineup Simulation Gain per 150 games LAD 43 28 -15 SFN 35 27 -7 WAS 42 35 -7

LAD

Gordon

Puig

Gonzalez

Kemp

Crawford

Uribe

Ellis

Rojas

SFN

Pagan

Pence

Posey

Sandoval

Morse

Duvall

Panik

Crawford

WAS

Span

Rendon

Werth

Laroche

Ramos

Harper

Cabrera

Espinosa

In “optimizing” each of the 30 lineups, I used some simple criteria. I put the top two overall hitters in the 2 and 4 holes. Whichever of the two had the greatest SLG batted 4th. The next two best hitters batted 1 and 3, with the highest SLG in the 3 hole. From 5 through 8 or 8, I simply slotted them in descending order of quality.

Here is a comparison of the simple “optimal” lineup to the lineups that the teams actually used. Remember, I am using the same personnel and changing only the batting orders.

Before giving you the numbers, the first thing that jumped out at me was how little most of the numbers changed. Conventional, and even most sabermetric, thought is that any one reasonable lineup is usually just about as good as any other, give or take a few runs. As well, a good lineup must strike a balance between putting better hitters at the top of the lineup, and those who are good base runners but poor overall hitters.

The average absolute difference between the runs per game generated by the simulator from the actual and the “optimal” lineup was 3.1 runs per 150 games per team. Again, keep in mind that much of that is noise since I am running only 100,000 games per team, which generates a standard error of something like 1.3 runs per 150 games.

The kicker, however, is that the “optimal” lineups, on the average, only slightly outperformed the actual ones, by only 2/3 of a run per team. Essentially there was no difference between the lineups chosen by the managers and ones that were “optimized” according to the simple rules explained above. Keep in mind that a real optimization – one that tried every possible batting order configuration and chose the best one – would likely generate better results.

That being said, here are the teams whose actual lineups out-performed and were out-performed by the “optimal” ones:

Most sub-optimal lineups

Team Actual Lineup Simulation Results (Runs per 150) “Optimal” Lineup Simulation Results Gain per 150 games STL 62 74 12 ATL 31 37 6 CLE -33 -27 6 MIA 7 12 5

Here are those lineups. The numbers after each player’s name represents their projected batting runs per 630 PA (around 150 games). Keep in mind that these lineups faced either RH or LH starting pitchers. When I run my simulations, I am using overall projections for each player which do not take into consideration the handedness of the batter or any opposing pitcher.

Cardinals

Name Projected Batting runs Carpenter 30 Wong -11 Holliday 26 Adams 14 Peralta 7 Pierz -10 Jay 17 Robinson -18

Here, even though we have plenty of good bats in this lineup, Matheny prefers to slot one of the worst in the two hole. Many managers just can’t resist doing so, and I’m not really sure why, other than it seems to be a tradition without a good reason. Perhaps it harkens back to the day when managers would often sac bunt or hit and run after the leadoff hitter reached base with no outs. It is also a mystery why Jay bats 7th. He is even having a very good year at the plate, so it’s not like his seasonal performance belies his projection.

What if we swap Wong and Jay? That generates 69 runs above average per 150 games, which is 7 runs better than with Wong batting second, and 5 runs worse than my original “optimal” lineup. Let’s try another “manual” optimization. We’ll put Jay lead off, followed by Carp, Adams, Holliday, Peralta, Wong, Pierz, and Robinson. That lineup produces 76 runs above average, 14 runs better than the actual one, and better than my computer generated simple “optimal” one. So for the Cardinals, we’ve added 1.5 wins per season just by shuffling around their lineup, and especially by removing a poor hitter from the number 2 slot and moving up a good hitter in Jay (and who also happens to be an excellent base runner).

Braves

Name Projected Batting runs Heyward 23 Gosselin -29 Freeman 24 J Upton 20 Johnson 9 Gattis -1 Simmons -16 BJ Upton -13

Our old friend Fredi Gonzalez finally moved BJ Upton from first to last (and correctly so, although he was about a year too late), he puts Heyward at lead off, which is pretty radical, yet he somehow bats one of the worst batters in all of baseball in the 2-hole, accumulating far too many outs at the top of the order. If we do nothing but move Gosselin down to 8th, where he belongs, we generate 35 runs, 4 more than with him batting second. Not a huge difference, but 1/2 win is a half a win. They all count and they all add up.

Indians

Name Projected Batting runs Kipnis 5 Aviles -19 Brantley 13 Santana 6 Gomes 8 Rayburn -9 Walters -13 Holt -21 Jose Ramirez -32

The theme here is obvious. When a team puts a terrible hitter in the two-hole, they lose runs, which is not surprising. If we merely move Aviles down to the 7 spot and move everyone up accordingly, the lineup produces -28 runs rather than -33 runs, a gain of 5 runs just by removing Aviles from the second slot.

Marlins

Name Projected Batting runs Yelich 15 Solano -21 Stanton 34 McGhee -8 Jones -10 Salty 0 Ozuna 4 Hechavarria -27

With the Fish, we have an awful batter in the two hole, a poor hitter in the 4 hole, and decent batters in the 6 and 7 hole. What if we just swap Solano for Ozuna, getting that putrid bat out of the 2 hole? Running another simulation results in 13 runs above average per 150 games, besting the actual lineup by 6 runs.

Just for the heck of it, let’s rework the entire lineup, putting Ozuna in the 2 hole, Salty in the 3 hole, Stanton in the 4 hole, then McGhee, Jones, Solano, and Hechy. Surpisingly, that only generates 12 runs above average per 150, better than their actual lineup, but slightly worse than just swapping Solano and Ozuna. The achilles heel for that lineup, as it is for several others, appears to be the poor hitter batting second.

Most optimal lineups

Team Actual Lineup Simulation Results (Runs per 150) “Optimal” Lineup Simulation Results Gain per 150 games LAA 160 153 -7 SEA 45 39 -6 DET 13 8 -5 TOR 86 82 -4

Finally, let’s take a look at the actual lineups that generate more runs per game than my simple “optimal” batting order.

Angels

Name Projected Batting runs Calhoun 20 Trout 59 Pujols 7 Hamilton 17 Kendrick 10 Freese 8 Aybar 0 Iannetta 2 Cowgill -7

Mariners

Name Projected Batting runs Jackson 11 Ackley -3 Cano 35 Morales 1 Seager 13 Zunino -14 Morrison -2 Chavez -24 Taylor -2

Tigers

Name Projected Batting runs Davis -2 Kinsler 6 Cabrera 50 V Martinez 17 Hunter 10 JD Martinez -4 Castellanos -20 Holaday -44 Suarez -23

Blue Jays

Name Projected Batting runs Reyes 11 Cabrera 15 Bautista 34 Encarnacion 20 Lind 6 Navarro -7 Rasmus -1 Valencia -9 Lawasaki -23

Looking at all these “optimal” lineups, the trend is pretty clear. Bat your best hitters at the top and your worst at the bottom, and do NOT put a scrappy, no-hit batter in the two hole! The average projected linear weights per 150 games for the number two hitter in our 4 best actual lineups is 19.25 runs. The average 2-hole hitter in our 4 worst lineups is -20 runs. That should tell you just about everything you need to know about lineups construction.

Note: According to The Book, batting your pitcher 8th in an NL lineup generates slightly more runs per game than batting him 9th, as most managers do. Tony LaRussa sometimes did this, especially with McGwire in the lineup. Other managers, like Maddon, occasionally do the same. There is some controversy over which option is optimal.

When I ran my simulations above, swapping the pitcher and the 8th hitter in the NL lineups. the resultant runs per game were around 2 runs worse (per 150) than with the traditional order. It probably depends on who the position player is at the bottom of the order and perhaps on the players at the top of the order as well.