Optimizing Batting Orders Across MLB

Of the many topics discussed in The Book is lineup optimization; essentially, the degree to which teams can extract extra runs throughout a season through better lineup construction.

The general consensus seems to be teams don’t do a great job at optimizing lineups. But the gains from proper optimization aren’t that great, anyway.

That being said, I was curious whether there’s evidence for league-wide changes in the ways players are deployed throughout lineups. Given the statistical research in the past few decades, is the league any more in line with setting lineups with the expressed idea of simply avoid outs?

Back in 2009, Sky Kalkman wrote a great piece at Beyond the Box Score about how teams should optimize their lineups based on The Book’s findings. Sky summed it up nicely at the end, with regard to on-base percentage (OBP):

Another way to look at things is to order the batting slots by the leveraged value of the out. In plain English (sort of), we want to know how costly making an out is by each lineup position, based on the base-out situations they most often find themselves in, and then weighted by how often each lineup spot comes to the plate. Here’s how the lineup spots rank in the importance of avoiding outs:

#1, #4, #2, #5, #3, #6, #7, #8, #9

OBP isn’t the only way you organize your lineup — you need to take into account the ability to hit for extra-bases — but generally speaking, optimizing a team’s lineup is about which positions should be occupied by hitters with a the highest penchant for avoiding outs.

To depict this visually, I created a heat map of the optimized batting order Sky cited and then showed the actual rank of each batting order position aggregated by year. Darker green correlates with the highest rank; dark red correlates with the lowest rank:

In 1995, the OBP for the leadoff spot ranked third among all nine batting positions. Three-hole hitters earned the highest OBP, while two-hole hitters came in sixth.

The pattern that jumps out is how consistently managers placed their best one or two hitters — in terms of OBP — in the third spot in the order. Sky suggests that a team’s fifth-best OBP hitter should hit third, but in reality, this is never the case. League-wide, three hitters are overwhelmingly the highest OBP hitters. The three-spot has an average of 1.2, followed by clean-up hitters at 1.9, lead-off hitters at 3.5 and five-hole hitters at 3.9. The difference between what Sky suggest the OBP rank for three-hole hitters should be and what we actual observe by far the largest of any position (3.8). In reality, the biggest issues are found with the top three spots in the order, as the difference between the optimal rank and the average rank is below .5 in spots four through nine. This shouldn’t be surprising.

No. 4 hitters experienced a few odd years, specifically from 1990 to 1993. During that time, those hitters’ OBP rank varied between third and fourth. Outside that, though, they varied between first and second. Five-hole hitters jumped around quite a bit, despite the fact that their average rank was basically the same as Sky’s recommendation. That being said, No. 5 hitters’ OBP generally ranked third, fourth or fifth in every year except for 1998 and 2007 — when the position ranked sixth. Basically, the range of their variation was pretty narrow.

The biggest issues are in the top two spots. Leadoff hitters have never ranked above second in OBP and they only did that five times (the last was in 1993). There was a string of four years where leadoff hitters ranked second (from 1990 to 1993), which coincidentally, was the same four-year stretch in which the clean-up spot ranked outside the top two. Since 1993, the leadoff spot has put up an average rank of 3.7 in OBP — basically, the league is still significantly devaluing out avoidance at the top of the order.

The No. 2 spot has varied considerably from The Book and from Sky’s analysis. Theoretically, you want the two-hole to be the third best at avoiding outs. In practice, they’ve been about the fifth best and have varied between third and sixth since 1974. As with the leadoff spot, it seems to have only gotten worse. No. 2 hitters haven’t ranked better than fourth since 1992; the average rank is fifth. This includes being the sixth-best (or fourth-worst) spot in 2012′s batting orders when it came to avoiding outs.

At an aggregate level, the league hasn’t learned much. The best hitters at avoiding outs are primarily hitting third, while lesser on-base hitters occupy the first and second spots. If we looked at this by team, I’m sure we’d see greater variation. Perhaps some teams recognize the advantage (however slim) of placing greater value on out-avoidance at the top of the order? Still, the league-wide data make clear that those teams are in the minority.




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Bill works as a consultant by day. In his free time, he writes for The Hardball Times, speaks about baseball research and analytics, consults for a Major League Baseball team and appears on MLB Network's Clubhouse Confidential. Along with Jeff Zimmerman, he won the 2013 SABR Analytics Research Award for Contemporary Analysis. Follow him on Tumblr or Twitter @BillPetti.

77 Responses to “Optimizing Batting Orders Across MLB”

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  1. sam says:

    Could be interesting to see a .slg chart next to the OBP one

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  2. TKDC says:

    But isn’t it true that unless you do something really stupid, like bat Jason Heyward 7th, the lineup order doesn’t make much difference at all?

    How many wins would the Braves gain by batting Heyward 2nd instead of 3rd?

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    • Craftcj says:

      I wish doing “something really stupid” was only hypothetical for my favorite team; instead, Reds fans were treated to watching a .254 OBP from the lead off spot last year.

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      • Baltar says:

        I’ll bet the #2 spot was even worse. Dusty sucks.

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      • Bip says:

        The Dodgers are just as bad, with a .583 OPS out of their leadoff spot last year – worse that any of the 2-8 spots by 80 points. All because Dee Gordon is fast and therefore Mattingly can’t imagine where else to put him.

        I wonder if the fact you pointed out has anything to do with the Red’s being 6th in OPS and 9th in runs scored last year. I would be more confident of that pattern if the Dodgers, similarly clueless with regard to lineup construction, weren’t 13th in both OPS and runs.

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      • Calvin says:

        Dusty really sucks, but he also got unlucky. Brandon Phillips, in his time in leadoff, hit .202/.254/.298 in 120something PAs which is just awful. In other spots, .301/.336/.463, which is just fine. Some of his other leadoff and 2-hole choices were just as bad on paper as they turned out in practice though.

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    • merizobeach says:

      “unless you do something really stupid”

      Like Bengie Molina batting cleanup. How many wins would the Giants gain by batting Posey 4th instead of Molina? Right, 2xWS.

      Gets me thinking: Wins Above Replacement is a relative measurement like Celsius or Fahrenheit, with zero in the middle of the scale…

      WAM (Wins Above Molina) would be a more absolute measurement like degrees Kelvin. Posey posts a very high WAM.

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    • Synovia says:

      Some of the optimizations have seen swings as big as 50 runs.

      Thats $25M+ of value.

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  3. JCA says:

    I’d be curious to see if the line ups are optimized for slugging rather than OBP. The line up optimizer sites weigh both OBP and SLG that I have seen. If there were a way to strip out the OBP component from the optimizing formula so you could just optimize by SLG, you might see the best sluggers stacked at 3, 4, and 5, and that might be how managers are lining up their orders.

    By the way, I think this might work better with SLG than ISO. I think using SLG captures average, which I think plays in to managers thinking.

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    • mikec says:

      That doesn’t get us anywhere. Managers have been prioritizing SLG at 3,4,5 forever. It’s not a “might be.” More specifically, this has been standard tradition: 3 best overall hitter, 4 most power, 5 big power and maybe not so much average.
      But some of the good studies I’ve seen in the past on lineup optimzation conclude that the best overall hitter, power included, actually should hit 2nd. That he’d create more runs, and it’d be a positive tradeoff of his scoring more runs and knocking in fewer, and he’d get more PA’s. I’d definitely try it in AL, and I’d lean toward it in NL if I had decent-hitting pitchers. I also might do the LaRussa thing and bat bad-hitting pitcher 8th. On the broad level of this topic, I don’t believe going by OBP–or SLG–alone helps us. And what doesn’t help hurts. Lineup optimization should take in every aspect of offensive production as well as the pluses, minuses of things like PA’s per individual.

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  4. dcs says:

    The real problem is that different abilities tend to occur together in the real world. A high OBA hitter also tends to have a high SLG. This makes The Book’s lineup system much more difficult to implement with real players.

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    • Bip says:

      I think the correlation between the two makes it easier. It is more important to avoid outs in situations with a higher opportunity for run scoring. With none on and two outs, any runner who gets on is likely to be wasted, so if you have to make out, do it there. On the other hand, with men on first and second and none out, getting on base increasing run scoring more dramatically. It is the nature of baseball that it is better to get 4 hits in one inning and go 1-2-3 in the next three than to get only one hit in 4 consecutive innings. Therefore you want your high OBP guys to come up with men on base, which is also when you want your high SLG guys to come up.

      It is only when you have an odd assortment of high-OBP low-SLG guys and their opposites that lineup construction presents a particular challenge.

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  5. A Braves Fan says:

    Isn’t the data for the importance of out avoidance based on the results from unoptimized lineups? For example, if managers followed the suggestions and put their best on base guy at the top of the lineup and the 3rd best second, would that not make the outs fir the third spot more valuable?

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    • Baltar says:

      Yes, you are correct. #3 rates relatively low in importance because most managers put mediocre batters in #1 and even worse in #2 (see Reds above).
      If a team actually put high OBP’s in the first two spots, #3 would be very important.

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      • Bip says:

        The problem with the three spot, however, is that in the 1st inning, if the 1 and 2 guys get out, which will always be a likely outcome, then the 3 guy comes up with none on and 2 out, which is least valuable situation in which to get on base. If the 4 guy comes up in the first inning, however, it can only be with men on base. If the 1st inning is 1-2-3, then the 4 guy leads off the 2nd inning. So look at it this way:

        Possibilities for 3-spot batter (1st at bat):
        -men on and < 2 out (in which case the 4 hitter will likely come up with men on)
        -none on and 2 out

        Possibilities for 4-spot batter (1st at bat):
        -men on and any number of outs
        -leads off inning.

        Leading off any inning is always more important than none on and 2 out. Also, the cost of failing with 1 out is not too different than the cost of failing with two outs, therefore for any base-out situation, it isn't particularly worse to fail or better to succeed with the same base-situation and one more out. On the other hand, the benefit of success with 0 on 0 out is MUCH greater than for 0 on 2 out.

        So the first at bat for the 4 hitter with generally be much more important than for the 3 hitter. And I don't think any other at bat will varying among batting order positions nearly as much, i.e. after the first run through the lineup, you can't really distinguish the lineup spots according to the likely base-out situation.

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  6. PL says:

    I still don’t understand why teams don’t just stack the lineup from best OPS to worst. Getting your best hitter the most plate appearances always makes the most sense, qualities like speed be damned. Sure, having a guy who can hit HRs in front of guys who don’t get on base very well is going to cost runs, but those are still runs. A way to address that is to perhaps go #1-3 OPS then have the #7-9 be the best OBP’s of who’s left, however, runs are runs.

    When you have a guy with a 650 OPS who’s leading off because just because he steals bases, youre still giving a guy with a 650 OPS the most PA’s, that just sounds fundamentally nonsensical.

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    • Cidron says:

      reasons..

      1. Tradition – thats the way its been done for ages. who is gonna go against all that tradition.
      2. Speed guys=leadoff – easiest way to steal a base? have nobody clogging the basepaths ahead of you.
      3. Sluggers=cleanup – more people on base=more runs crossing when slugger hits a homer
      4. Risk – Who is going to be the one manager to set the MLB world on its ear and actually do this lineup change? nobody.
      5. Old Stats – avg, rbi, hr. There are alot of traditionalists out there employed by mlb teams that are not fully aware of the “new stats” such as ops and others.

      The above five, and more are reasons that these ideas are not implemented. And, it might have to “break in” via a college coach (or at a much lower level, A or Rookie league.. I just dont see it at or above AA)

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    • mikec says:

      Not based on the best studies I’ve read. You propose OPS descending order from 1 down. But what I’ve gathered is, there’s more benefit to an in-prime Albert Pujols hitting 2nd, not 1st. The highest OBP besides Pujols at 1. Of course, this also takes Pujols out of his conventionalist spots at 3 or 4. At 2, he’s not directly following the pitcher. He’s got a high possibility of a base-runner via No. 1. He gets almost as many PA’s as he would at 1, and more than at 3, 4. We give up a few more chances for 3-run homer, but not 2-R HR’s. Makes up for that with more runs scored. Also, I’ve never read any study that looks at going by OPS for 1-3, and switching to OBP thereafter. It’s fine to present an opinion or a theory, but one needs to present data to demonstrate a provable benefit.

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  7. MSom13 says:

    So as a for instance, based on ‘The Book’, the Cardinals lineup last year would have looked like (provided everyone healthy):

    1: Matt Holliday
    2: David Freese
    3: Jon Jay
    4: Allen Craig
    5: Yadier Molina
    6: Carlos Beltran
    7: Rafael Furcal
    8: Dan Descalso

    Interesting… and so radically against baseball tradition that people would be calling for managers heads as soon as this lineup was announced. Too bad, because Jon Jay reaching 100+ RBI’s would be hilarious.

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  8. BABIP says:

    If it really mattered, teams like the Cubs and A’s would be making their lineups like this…being that their FO’s are more statistically inclined. What you do see are teams who look for speed from a leadoff guy and others who look for a good approach and on base ability.

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    • Bip says:

      The manager makes the lineup, however, and I’m guessing the managers are generally less statistically savvy than the FO guys.

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  9. Eminor3rd says:

    Ignoring SLG in this makes this exercise, IMO, useless. I don’t think we’ve learned much of anything here. The Book doesn’t ignore SLG, so why shouldn’t we take it that far, at least?

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  10. JeffMathisCera says:

    Doesn’t Sky suggest that a team’s 2nd best hitter should hit third, not their 5th?

    Also I’d like to see this with OPS because as you say OBP doesn’t account for XBH. Well OPS does, and it still weighs OBP.

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    • Bryan Grosnick says:

      No, he doesn’t.

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      • JeffMathisCera says:

        An excerpt used from Sky, “Here’s how the lineup spots rank in the importance of avoiding outs:

        #1, #4, #2, #5, #3, #6, #7, #8, #9″

        …later on…

        “Sky suggests that a team’s fifth-best OBP hitter should hit third”

        If the only way this analysis is done is by using OBP, then aren’t these contradictory, or wrong? Am I missing something?

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      • Bryan Grosnick says:

        I think there’s some confusion. The two quotes actually say the same thing.

        The first one says that #1 spot in the order is the most important for avoiding outs, followed by the #4 spot, and so on. According to that list, the #3 spot is fifth-most-important, therefore should be occupied by the fifth-best player at getting on base.

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      • 23553 says:

        @Jeff It’s not contradictory, the way you read it is that, for example, because #3 is the 5th in the list, it is the 5th most important spot.

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    • Gareth says:

      Sky is saying that the #3 spot is the fifth-most important in avoiding outs. Thus, the 5th best OBP hitter should be in the #3 spot.

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  11. Skin Blues says:

    The data you’re using – the leveraged importance of not making an out – is predicated on the best hitters being in the 3 spot. Basically, it’s a circular argument. The reason the #4 spot is so important is largely because in practice, the highest OBP is always in the #3 spot. This is the kind of thing that requires simulation rather than using linear weights from historical data. I believe Xeifrank has done work with simulation and lineup optimization, but I can’t find it right now. I believe it was from the Barry Bonds era. From what I remember, as long as you generally order the lineup from best-to-worst OBP then the difference made by tinkering is negligible over the course of a season.

    One consideration is also the fact that the 4 hitter can never spend his first plate appearance of a game with 2 outs and nobody on base – a decidedly low-leverage situation in which to put your best hitter – and something that happens the majority of the time to the #3 hitter. But that is not the only consideration. It may very well be that the #3 hitter should be the 5th best/worst hitter in the lineup, but the data provided just doesn’t fully support that.

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    • Doug Lampert says:

      Not really, I’m pretty sure people have run analysis including feedback effects from changing which hitter is where, up to calculating the expected runs for every permutation of the lineup using the expected states from the lineup being tested, and in the cases I’ve seen they still get back that the importance is something like 1, 4, 2, 5, 3, 6, 7, 8, 9, in that order.

      And such analysis also comes back “doesn’t much matter”. So I suspect managers who are aware of it just shrug and go with the assumption that a fast lead-off guy helps the batters behind him get hits when he’s on base and that this and going right-left-right are more important than theoretical linup optimization.

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    • Baltar says:

      Correct and very well presented.

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    • Xeifrank says:

      Lots of lineup simulation stuff here. There will be much more to come in the next few days.
      vr, Xeifrank

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  12. Eric says:

    Why the reliance on OBP, or SLG as other commenters are making, when we have a statistic that accurately weights each of the potential offensive outcomes with their value: wOBA. This statistic seems superior to both OBP and SLG in this case, as it takes both into account with the proper value of the different potential outcomes. Would like to see this exercise re-run using wOBA.

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  13. jjbooth74 says:

    It would also be curious to see this broken out by team. There may be less reliability in sample size, but it’s hard to say “the league” hasn’t learned when really it’s “Dusty Baker and Buck Showalter haven’t learned”. I would like to see, for example – how do the Rays compare to the Reds? Or, how have the Rays evolved over time? Is there a clear delineation before and after Joe Maddon? This could also be a contributing factor towards measuring manager wins.

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    • Cidron says:

      or, put another way. How much success would the rays have over the last five years with Dusty at the helm, vs the Reds with Maddon? Interesting.

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      • mikec says:

        Minimal. Because every study on lineups says whatever the lineup doesn’t make a big difference. But….minimal is not nothing. In baseball, it’s all about the so-called little things and operating a little smarter than the next guy. And then those little things start adding up. Dusty Baker is an idiot. He is the posterboy for traditionalist lineups with speedy, little outmakers at 1, 2 that create a net negative for team’s runs scored. We know intuitively that it’s really stupid, and it’s proven to be really stupid. It’s bad because it’s an unnecessary negative. But, again, the effect is minimal rather than ruinous.

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    • Bip says:

      The Ray’s lineup spots, ordered by descending OBP, followed by the suggested order:

      #3, #7, #5, #8, #1, #6, #4, #2, #9
      #1, #4, #2, #5, #3, #6, #7, #8, #9

      So no, not particularly well put together. Every spot is at least 4 places away from where it should be except the 5, 6, and 9 spots.

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  14. JoeS says:

    I’ve always thought teams should bat their best player first. Why wouldn’t you want your best player to get the most possible PA?

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    • Baltar says:

      Your argument is good, as far as it goes. The answer is that since the #9 (especially in the NL) and #8 batters are usually the poorest on the team, leaving the #1 batter to come up with bases empty a lot (and, of course, always on the first PA).
      Puttting the best guy first might work well if the team can put high OBP, low SLG batters in 8-9.

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    • Cidron says:

      Define “best” from the managers point of view. Is it the guy who hits 40 homers, 100 rbi, but a .225 avg — or the guy with a .330 avg, but only 10hr, and 25 rbi? (using ‘old school’ stats as alot of managers are comfortable with them, and will use them)

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  15. DominicanRepublican says:

    One thing to consider is that advanced front officees know that there’s only a very slight advantage to optimizing your lineup in most cases and they’re willing to give up a few runs each season to keep interest in each game high (i.e. scoring in the first inning or getting your stud guy a guaranteed plate appearance in the first inning every single game).

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    • Synovia says:

      Do you really think these things “keep interest in the game high”?

      I’m not sure I’ve met anyone who would give a crap.

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    • Calvin says:

      Somebody (Tango?) said that the gains are so small that they just let the managers do the order to keep them happy. Maybe that’s even worth it as long as they don’t have somebody like Dusty going full retard and batting black holes 1 and 2 most of the time.

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  16. Cheese says:

    Imagine leading a game off with Barry Bonds

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    • Baltar says:

      In his prime, that would have been a stunning success. I actually modeled it once based on actual results, with best of the other batters 2nd, next best 3, etc.
      However, he’s an exception because of all those BB’s.

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  17. Aaron (UK) says:

    There’s a nice little tool available at baseballmusings.com: http://bit.ly/SNkbgt

    The example provided (of the Nats, using BJ projections) suggests that they happened upon something close to optimal last year (Werth leading off) and, now that they’ve acquired a “classic lead-off man” in Span they’re going to regress. The difference between this tool’s optimal lineup and what they will probably do is 0.145 runs per game – 2-3 wins per season.

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  18. Brian says:

    These have all been argued to death, but the one thing I never hear discussed is … why do managers insist on putting a guy best able to advance himself across the bases (SB guy) in front of the hitter most likely to drive him in regardless of what base he is on?

    I would think that the best hitter should bat 3rd or 2nd, with the high-OBP guys in front of him, regardless of speed. Then, if you have a legitimate speedster with OBP problems, you bat him ahead of a batter with no power. Then the speedster can steal second and score on a single, or steal third and score on a sac fly.

    It has less to do with OBP-optimization and more to do with the individual talents of the players (can you imagine a buy like Bourn batting ahead of the pitcher? He’d be on third base every time)

    Also, the comment by Skin Blues above is right on the money.

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    • Baltar says:

      Your comment is also right on the money. I’d love to see a statistical analysis of that idea.

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    • Bip says:

      The Dodgers were totally backwards in this regard last year, batting Dee Gordon (.228/.281/.281, 32 SB) 1st and AJ Ellis (.270/.373/.414, 0 SB) 8th all year. I think it would have been perfect to switch them.

      First of all, putting a much higher OBP guy first just means more runners on base all season. Secondly, Whenever Gordon does get on, he’ll be getting on with the heart of the lineup and the highest OBP guys coming up, and he’ll be in position to score because he’s stolen or the pitcher has sacrificed him. Also, the pitcher has no power, so on the off-chance he gets a hit, it’s best to have a speed guy on base. The 6 and 7 guys are also probably low-OBP so Gordon is less likely to be blocked on the bases. Ellis has low power relative to his OBP so having a speedy guy on in front of him helps too.

      It just made too much sense for Don Mattingly to do it.

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    • octelium says:

      Agreed, put your speed guy 7th or 8th let him steal or be sacrificed over and ready to score when you #1 hitter is up.

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  19. Brian L says:

    Speed hasn’t been mentioned enough. Its clearly the #1 reason a lot if not most current leadoff guys are batting leadoff. In theory speed/bsr could be a pretty important factor – I’m remembering one of Dave’s articles justifying Trout over Cabrera for MVP, and how he quantified how many more runs Trout created over Cabrera by going 1st to 3rd and 2nd to home. As as a side note, both had about .395 OBPs.

    The fact that the OBP-based lineup construction analysis shows negligible advantage in some of the lineup changes we’re talking about makes me think using that method is overlooking some pretty important pieces, even if OBP is still the most important factor.

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    • Bip says:

      Yes, I think speed probably has a noticeable effect on lineup construction relative to the effect of lineup construction on run scoring. It may have a small overall effect, but as long as we’re talking about lineup construction (something with a small overall effect on run scoring) we should probably be thorough.

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    • Kc says:

      This. If base running is important than it should be factored in. #4 hitters still hit more singles and doubles than they do triples and HR’s. So having someone on base ahead of them who can score on any/all of the #4′s hits would be better than a slow poke who only scores on triples or HR’s.

      OBP is probably most important factor but BSR has to have an impact.

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  20. @notrizzo says:

    This doesn’t take into account the pitcher, a slugger in the middle of the order will get “pitched around” far more often than a leadoff hitter. Thus a player with good OBP skills batting leadoff might not actually get on base as often as a power bat player batting 5th with significantly less OBP “skill”

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  21. Dr. Dave says:

    I looked at something similar back in the late ’90s, using linear programming and base/out data provided by Tom Ruane. What I was looking for was the relative value of batting average (for a given OBP — didn’t have wOBA then) in each of the lineup positions. As noted above by others the problem with using this to design lineups is that the mix of base-out situations each lineup slot will see changes as soon as you construct your lineup in a novel way.

    For what it’s worth, in a traditional lineup, you want the highest contribution from batting average in the #3 slot, other things being equal. I don’t remember the run value differences or the rest of the rankings.

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  22. I looked into this a little while ago using a lineup simulator; the basic answer is:

    (a) Lineups are complicated
    (b) Lineups don’t matter very much
    (c) To the extent that they do matter one of the most important things is to make sure you don’t hit into double plays, because that’s actually something a lineup has control over.

    http://measuringshadowsblog.blogspot.com/2012/08/checking-in-on-giants-lineup.html

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  23. KM says:

    I would think that one should take OBP and OPS into account, weighting them differently based on a player’s role in the lineup. A couple high OBP guys followed by a high OPS guy, something along those lines.

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  24. Cidron says:

    Role seems fine the first time thru, but as the game progresses, we may see the “slugger” batting leadoff, and the lil utility guy with no bat hitting cleanup (in any given inning). Role in a lineup only survives generally one time thru. After that, who knows.

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  25. Tom says:

    How does lineup balance factor in?

    I’d think the drop off at the end of the lineup 8/9 hitters starts being a factor vs the extra AB’s a better hitter may get batting say 3rd vs 5th..

    If you have black holes at 8/9 then your #3 hitter probably should be your 5th best hitter. But if the dropoff is not that pronounced, is the first inning effect enough to compensate for the lost extra AB’s if you drop him down to 4th or 5th?

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  26. Bip says:

    I would think that after the first time through the lineup, there is no discernible pattern when looking at the distribution of base-out situations by lineup spot. In other words, I think it would be a safe assumption to say that over the course of the season, if you exclude the first at bat of each game, the average value of an at-bat would be the same for every lineup spot. In fact we can see this effect when we look at the lineup spots in order of importance:

    #1, #4, #2, #5, #3, #6, #7, #8, #9

    Notice how the 6-9 spots are simply ordered with regard to the number of at bats they are likely to see. I think this is because there is enough possible variation in the outcomes of the first 5 at bats to basically negate the possibility of the 6 and 7 spots seeing a significantly different distribution of base-out states over a season. In a previous post, I lay out the large difference between the base-out states that the 3rd and 4th hitters with see in their first at bat. Now, I’m appending that to say that the effect I describe applies only to the first run through the batting order, and maybe not even that far.

    Allowing this assumption makes the job of analyzing batting order with regard to something other than OBP much easier. First, we can weight the value of an at bat with a particular wOBA to calculate the pure value of putting a high wOBA high in the order. Next, we just have to factor in the effect of the situation on the value of the at-bat, and if my above assumption is valid, then all we have to do is find the average value of the first 5 or 6 at bats of the game and weight that value against the value of simply giving more at bats to better hitters. Presumably, the effect is great enough to justify giving the 2nd best hitter the 4th most plate appearances.

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    • Bip says:

      That is to say, when we know the exact base-out states a particular place in the batting order is likely to see the first time through, we can exactly find out the value of each type of hit, as well as the value of being able to advance bases from there, meaning we can find the value of SLG and speed at that spot in the lineup, and then we’ll know what to do with guys who may have odd skill sets.

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  27. Robert says:

    The Angels 2012 lineup by this method:
    Trout
    Ianetta
    Hunter
    Callaspo
    Pujols
    Kendrick
    Aybar
    Morales
    Trumbo

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  28. Dr. Chaleeko says:

    Also, a post-facto review of lineup construction of a single team won’t account for variation from true-OBP talent level. In the Angels example cited by Robert, Pujols might hit in a different spot based on his true talent, which is how managers would be making out a lineup since they don’t know a player’s end-of-season performance.

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  29. Anthony says:

    Great article! If I were an owner, I would employ statistical analysis whenever I could do it. I think teams are better off when they can utilize objective, quantifiable information, as opposed to intuition.

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    • mikec says:

      And they all do these days. It’s no longer a “sabermetric movement.” It’s fully incorporated into every big-league organization. Effectively blending with scouts’ necessary observations. The hybrid approach. It’s no longer optional, but mandatory. And it’s here, across the board. That doesn’t mean there won’t always be refinements. As an example, defensive stats still have a long ways to go. But we all should cease with our pleadings of five, 10 years ago for our teams to get on the stat wagon. They’re all totally on board. Some always will do it better than others, though. That applies to anything.

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  30. kallven says:

    When looking at OPS you have to take account of walks. the player occupying to 3rd and 4th spot are usually power hitter and will draw more walk from fear of them hurting you with and extra base hit. If those types of hitters were also base staling threats, its possible that unless the were the only option to bat 3rd they would be higher in the order. For example, even though Albert Pujols usually had the best average on the team, and there were other options for the 3 hole and clean-up (Holliday, Friese, Trout,), He has to be in that spot because he offers no speed along with getting on base.

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