The Optimal Tiger Lineup

On Friday, Lee aggregated various projections for Tiger players to find the average projection. On Saturday, David Pinto web enabled a script written by Ken Arneson based on work by Cyril Morong that optimizes lineups. On Sunday, I do the easiest part of all and stick Lee’s numbers into David’s tool.

First some lineups, and then some explanation. I first put in what would probably be the most common assortment of players the Tigers would use. I’m guessing this would be Rodriguez/Inge/Guillen/Polanco/Shelton/Monroe/Granderson/Ordonez/Young. Various combinations of those players would average 5.330 runs per game. Here are the best and worst variations on that lineup

Best – 5.448

  1. Guillen
  2. Shelton
  3. Granderson
  4. Young
  5. Ordonez
  6. Monroe
  7. Pudge
  8. Inge
  9. Polanco

Worst – 5.213

  1. Monroe
  2. Inge
  3. Granderson
  4. Polanco
  5. Pudge
  6. Guillen
  7. Ordonez
  8. Shelton
  9. Young

Both of those look pretty screwy, but still are pretty high powered. One thing that you may notice is that the #3 hitter is the same in the best and worst lineups. This goes against the conventional wisdom that the best hitter hits third. If this were the case, you’d think the #3 hitter would be significant, but that doesn’t appear to be the case. In fact, Dan Scotto has been experiementing with these models quite extensively and found some interesting trends. The high OBP players get put at 1, 2, and 9 with 9 being kind of like a second lead off hitter. The clean-up spot goes to the biggest slugger and the number 8 spot goes to the worst hitter.

In case you were wondering, I put together a more conventional lineup that balances left/right handed batters, takes into account old school paradigms (centerfielder=leadoff), and balances egos. The lineup of Granderson/Polanco/Guillen/Ordonez/Shelton/Young/Pudge/Monroe/Inge has an expected run value of 5.384 per game

Now because there are some position battles and platoon options I tried a couple variations. First I substituted Nook Logan for Curtis Granderson. That lineup averaged 5.117 runs per game with the best and worst cases being 5.269 and 4.966 respectively. You can see the results of the various permutations here. Now the model doesn’t take stolen bases into account, so Nook’s ability to “make things happen” isn’t accounted for in the model.

Finally, I ran one more version. This one had Granderson in center and Dmitri Young at third base (with Pena DH’ing). That lineup averaged 5.443 runs per game with 5.549 and 5.348 at the extremes.


First, and not surprisingly, it appears that the components of the lineup are just as important as the order. Subsituting a weak hitter for a strong hitter seemed to produce a shift of about .2 runs. The difference between an optimized lineup, and an unoptimized lineup is about .2 to .3 runs.

Second, lineup optimization would only probably gain a team (at least this Tiger team) no more than two wins a season. With a swing of only .25 from best to worst lineups, and assuming that Jim Leyland doesn’t march the worst possible line up out there the difference is probably much smaller. If one assumes an improvement of .1 runs a game, thats only 16 runs over the course of the season.

Third, it is too bad that we will never see these lineups as experiments. I can’t imagine many managers who would bat Polanco 9th more than once. On a related note, having a set lineup is such a rarity between platoons, injuries, and off days I don’t know how much you’d be able to tell.

Fourth, the baseball blog-o-sphere is wonderful. All these other people do substantial work, so I can just plug and play.

Go ahead and play around with the line-up optimizer and let me know what you find. See how many more runs the Tigers could have theoretically scored in 1984. Or what would be the optimal all time Tiger lineup. It’s fun stuff.
detroit tigers, batting order, baseball, sabermetrics


  1. Robert

    February 26, 2006 at 3:41 pm

    Where did you come up with your OBP and SLG numbers for each player? Just quickly glancing, they aren’t last year’s numbers and they aren’t career numbers.

    Did you just find some projections for 2006 and use those? At first glance, the numbers for Inge are worse than either his 2004 or 2005 season.

  2. billfer

    February 26, 2006 at 4:21 pm

    The numbers are the averaging of 3 different projection systems (ZiPS, PECOTA, Bill James) that Lee compiled over at his blog.

  3. tiger337

    February 26, 2006 at 5:01 pm

    Bill, This is really interesting stuff. I’m sure I’ll make good use of David’s program. Of course it mostly shows that line-ups, in theory, don’t matter too much. I remember reading once how Dave Johnson, who was a mathematician as well as a 2B, used optimization to put together some lineups when he was a manager. He tried it once as a player too but he handed his optimized line-up with himself batting clean up to Earl Weaver and Weaver tore it up.


  4. zimm

    February 26, 2006 at 8:53 pm

    i’m amazed at how little the best and worst varied from the mean. i’m not sure if i should take this as meaning that the order of the lineup is not as significant as i once thought or that the Tigers have a lot of players who produce similar results, making it less important for their order vs other teams. or maybe i’m undervaluing the effect of having 30 more/less runs per season.

  5. Jeff M

    February 26, 2006 at 9:39 pm

    Thanks Billfer. Definitely an interesting post. I suppose I’d like to see two different lineups to account for handedness, but other than that, this is informative

  6. Joe

    February 27, 2006 at 10:11 am

    Zimm, I believe the standard sabermetric point of view is that the order isn’t very important. I guess my central hope in creating a batting order would be to shield guys with platoon problems from situational relievers by surrounding them with guys of the opposite hand. So if you’ve got Inge in the order, he might see more lefties if he were surrounded by Granderson and Pena, Pena might benefit from being surrounded by Inge and Shelton, etc. Of course, this effect probably doesn’t even add up to two or three more hits over an entire season, so it’s probably not very important either.

  7. zimm

    February 28, 2006 at 11:36 am

    Thanks for the feedback Joe.

    Call me crazy, but if Granderson wins the CF job as expected and hits leadoff as Leyland wants from the CF, I would like to see Inge bat leadoff against lefties with Granderson dropped towards the bottom of the order. My thinking is that (with the exception of exceptional talents) young players should be put into positions where they have a good chance to succeed, and shielded from positions where they are more likely to fail. I think Granderson will be able to handle the defensive dutes of CF on an everyday basis and will probably do an adequate job hitting leadoff against righties. but I think asking him to hit leadoff against lefties is asking a little much. Since Inge is particularly strong against lefties, why not let him leadoff against them and put Granderson in a less stressful position. That, and some spot starts by Logan (assuming he wins a job) against lefties would make sense to me…

  8. Edman85

    March 20, 2006 at 9:21 pm

    Zimm, I’ll do the Marlins using PECOTA projections and get back to you on the similar results front.


    Willingham C
    Jacobs 1B
    Uggla 2B
    Ramirez SS
    Cabrera 3B
    Agulia LF
    Owens CF
    Hermida RF
    Willis P

  9. Edman85

    March 20, 2006 at 9:30 pm

    4.810 is the best lineup, and 4.352 is the worst, leaving a .458 difference for the Marlins, showing that variation between players does have a slight effect on the difference.

  10. Edman85

    March 20, 2006 at 9:30 pm