What is the Tigers Best Line-up?

 Where should Miguel Cabrera bat in the Tigers line-up?
(Photo credit: Hardball Talk)

Every fan has his own idea of the ideal line-up.  Traditionalists tend to like to have a speedster lead off, a bat-control guy hit second, the best hitter third and the best slugger (who is not also the best hitter) bat fourth.  Some just want the numbers one and two hitters to get on base a lot and don't care as much about speed. Others follow The Book by Tom Tango, Mitchel Lichtman and Andrew Dolphins which claims that the best hitter should not bat third, bat rather first, second or fourth.  Still others toy with the idea of having the best hitter on the team lead off, the second best hitter bat second, etc. with the reasoning that the best hitters should get the most at bats.   

One thing I like to do before every season is check out the line-up tool at Baseball Musings.  Developed by analysts Cyril Morong, Ken Arneson and Ryan Armbrust, it estimates the number of runs a line-up would score based on every batter's on-base percentage (OBP) and slugging average (SLG).  Since getting on base (OBP) and advancing runners with hits (SLG) are the two most important elements of run scoring, their method makes some sense.

However, the line-up algorithm also has limitations.  Perhaps most importantly, it does not consider the speed of base runners.  It also does not address psychological factors such as batters feeling comfortable in certain spots.  What it does do is try to determine the best line-ups based purely on hitting which is a good place to start.

Using the Steamer projections, I plugged OBP and SLG for the nine Tigers starters into the line-up analyzer.  One possible line-up is shown in Table 1 below.  The line-up tool says that line-up would score 5.050 runs per game or 818 runs in 162 games.  If that sounds like a lot of runs, it's because we are assuming that all nine players are going to play 162 games which, of course, won't happen.  That's OK though.  The goal is just to compare different line-ups.

Table 1: Tigers Possible Line-up


The line-up tool considers every possible permutation of those nine batters and estimates that the best line-up would score 5.117 RPG or 829 runs, while the worst would score 4.856 RPG or 787 runs.  That is a difference of 42 runs which is not huge, but not insignificant either - an estimated four wins.

Table 2 shows that the top five line-ups have the same players in the top five spots of the order - Miguel Cabrera, Torii Hunter, Austin Jackson, Ian Kinsler and Victor Martinez.  That is not surprising and manager Brad Ausmus will likely also have the same batters atop the order.  What is interesting is that Cabrera is second in each optimal line-up.  In fact, the thirty most productive line-ups have Cabrera batting second.   In theory, this makers sense because Cabrera would maximize his plate appearances, but still have many opportunuities to knock in runs batting second. 


Table 2: The Five Top Run-Producing Line-ups 

Runs per Game	1	2	3	4	5	6	7	8	9
5.117	Jackson	Cabrera	Hunter	Martinez	Kinsler	Dirks	Avila	Castellanos	Iglesias
5.117	Jackson	Cabrera	Hunter	Martinez	Kinsler	Castellanos	Avila	Dirks	Iglesias
5.117	Jackson	Cabrera	Kinsler	Martinez	Hunter	Dirks	Avila	Castellanos	Iglesias
5.116	Jackson	Cabrera	Kinsler	Martinez	Hunter	Castellanos	Avila	Dirks	Iglesias
5.116	Martinez	Cabrera	Hunter	Jackson	Kinsler	Dirks	Avila	Castellanos	Iglesia

Table 3 looks at the worst line-ups.  Right away, you see a big problem - that Cabrera is batting ninth.  I think we can all agree that this would not be a good idea. As bad as those line-ups are, they would still produce only 5% fewer runs than the best line-ups.  We want those five percent though, so those line-ups are out.


Table 3: The Five Lowest Run-Producing Line-ups

Runs per Game	1	2	3	4	5	6	7	8	9
4.856	Castellanos	Iglesias	Kinsler	Dirks	Avila	Martinez	Hunter	Jackson	Cabrera
4.856	Castellanos	Iglesias	Avila	Dirks	Kinsler	Martinez	Hunter	Jackson	Cabrera
4.856	Castellanos	Iglesias	Jackson	Dirks	Kinsler	Martinez	Hunter	Avila	Cabrera
4.857	Castellanos	Iglesias	Avila	Dirks	Hunter	Martinez	Kinsler	Jackson	Cabrera
4.857	Castellanos	Iglesias	Kinsler	Dirks	Jackson	Martinez	Hunter	Avila	Cabrera

Getting back to the best line-ups, The Book would agree that Cabrera, as best hitter, should not bat third, but rather first, second or fourth. The second best hitter - Martinez - should also bat in one of those spots. The line-up optimizer cooperates by putting Martinez clean up in the top four line-ups.  It wouldn't make much sense to have either of those lead-footed runners batting lead off, so second and fourth seems to be the way to go.  The next best hitter is either Jackson or Kinsler, so either one of them could leadoff.  So, I think any of the top four line-ups seems reasonable.