What is the Best Tigers Line-up?

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 Bill James Handbook projections, I plugged OBP and SLG for the nine Tigers starters into the line-up analyzer.  The Handbook projections tend to be optimistic, but this is the time of the year to be optimistic.  Anyway, one possible line-up is shown in Table 1 below.  The line-up tool says that line-up would score 5.687 runs per game or 921 runs in 162 games.  That's a lot of runs, but that'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 Projected Line-up

Player 1:
Player 2:
Player 3:
Player 4:
Player 5:
Player 6:
Player 7:
Player 8:
Player 9:

The line-up tool considers every possible permutation of those nine batters and estimates that the best line-up would score 5.766 RPG or 934 runs, while the worst would score 5.502 RPG or 891 runs.  That is a difference of 43 runs which is not huge, but not insignificant either - between four and five wins.

Table 2 shows that four of the five best line-ups have Prince Fielder leading off!  In fact, eight of the top ten have Fielder at number one and all of the top thirty have either Fielder or Alex Avila.  Remember though that this only looks at hitting and does not consider speed of which Fielder and Avila have none.  More interesting to me is Cabrera in the two hole in all of the top thirty line-ups.  That actually makes some sense, but I'd probably want someone with at least a little speed (as well as the ability to get on base) in front of him.

You also might notice that all of the long list of "best" line-ups have Omar Infante batting ninth preceded by Andy Dirks, Torii Hunter and Jhonny Peralta in some order.  That also looks good to me, although we already know that Hunter will hit second in Jim Leyland's line-up.   

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

5.766	Fielder	Cabrera	Jackson	Avila	Martinez	Peralta	Hunter	Dirks	Infante
5.766	Avila	Cabrera	Jackson	Fielder	Martinez	Peralta	Hunter	Dirks	Infante
5.766	Fielder	Cabrera	Jackson	Martinez	Avila	Peralta	Hunter	Dirks	Infante
5.765	Fielder	Cabrera	Martinez	Avila	Jackson	Peralta	Hunter	Dirks	Infante
5.765	Fielder	Cabrera	Jackson	Avila	Martinez	Hunter	Peralta	Dirks	Infante

Table 3 looks at the worst line-ups.  Right away, you see the first problem - that Cabrera is batting ninth  which would obviously never happen.  As bad as those line-ups are, they would still produce less than 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

5.502	Peralta	Infante	Jackson	Dirks	Hunter	Martinez	Fielder	Avila	Cabrera
5.502	Dirks	Infante	Jackson	Peralta	Hunter	Martinez	Fielder	Avila	Cabrera
5.502	Peralta	Infante	Jackson	Hunter	Dirks	Martinez	Fielder	Avila	Cabrera
5.503	Peralta	Infante	Jackson	Dirks	Hunter	Fielder	Martinez	Avila	Cabrera
5.503	Dirks	Infante	Jackson	Peralta	Hunter	Fielder	Martinez	Avila	Cabrera

It's doubtful than any manager would ever have Fielder or Avila bat leadoff, but suppose we have Jackson lead off followed by Cabrera, an idea that appeals to me.  The bottom four will be Dirks, Hunter, Infante and Peralta in some order.  Fielder, Martinez and Avila will bat 3-4-5 in some order.  I played around with various combinations and came up with the line-up in Table 4.  This one would score and estimated 930 runs, 9 more runs or one win better than the Table 1 line-up.  That's probably not worth the uproar caused by having Cabrera batting second, but I like it in theory. 

Table 4:  One More Line-up

Player 1:
Player 2:
Player 3:
Player 4:
Player 5:
Player 6:
Player 7:
Player 8:
Player 9: