Lineup optimization is a topic that is on the minds of many managers, gms, and coaches at any level of baseball (and really any sport). In baseball, lineup optimization can be reduced to a statistical science, thanks to the ridiculous amount of data provided by 30 teams playing 162 games every year. I would like to take some time to explain a few of the findings found by some researchers through the example of one of my favorite video games of all time, Ken Griffey Jr. Presents Major League Baseball for SNES.

START

All data on lineup optimization is taken from The Book, by Tom Tango, Mitchell Lichtman, and Andrew Dolphin. Today, we'll be looking at the lineup of my favorite team, the Milwaukee Brewers. One of the quirks of Ken Griffey Jr. Presents Major League Baseball is the use of fake names for all the players. This is because of the fact that Nintendo did not acquire the MLBPA license for this game, and thus could not use any names (other than that of Griffey Jr.'s). This will be interesting, because after the lineup is optimized, I will go back and replace the fake names with the real ones and we can compare stats using lineup optimization tools on the web. Rosters are from the 1993 season. Also, note that the Brewers are still in the AL at this time, and so they still use the DH. Let's take a look at the current lineup.

FORMAT: NAME AVG/HR/RBI "BAT/POW/SPD/DEF" Bat = Contact rating,

Pow = power, SPD = speed, DEF = defense (basically arm)

RF J. DRAKE .310/9/48 9/4/10/8 CF

S. TEMPLAR .258/8/51 7/4/7/9 3B

N. SOLO .274/7/79 8/4/5/6

LF J. STEED .267/30/97 7/9/5/6

DH E. PEEL .249/13/60 5/7/4/3

1B K. GALE .264/19/70 6/7/5/5

CA J. BOND .257/7/40 6/4/4/7

SS J. ROCKFORD.244/3/30 5/4/9/8

2B P. MARLOWE .238/2/36 5/4/5/6

BENCH

CA G. IRONSIDE.198/4/25 4/6/5/5

IF S. SLADE .228/5/36 4/4/5/8

IF T. PRISONER.269/11/57 7/7/4/6

IF P. COLUMBO .269/1/33 7/3/5/5

OF R. STEEL .183/6/29 3/8/4/6

IF P. MAGNUM .319/0/1 7/2/6/8

So that's what we have to work with here. Clearly not a whole lot, only one 20+ HR hitter, only 4 10+. Not a whole lot of team speed either, with only two players with above an "8" rating in speed (basically the cutoff needed to beat out any infield hit against a half decent defense). Now that we have our team, we need to think about what we want in our batting order. Here are some points that we should consider

1. The best hitters should bat the most times.

2. The best hitters should bat the most often with men on base.

3. The worst hitters should bat the least times.

That's the simple way to look at it. Point 2 is often why the best hitter is placed in the #3 order in the lineup. However, statistical analysis of MLB over multiple seasons show that this does not give the most leverage to the best hitter. This sounds odd, because you would expect that the #3 hitter would often expect to have runners on base in front of him and the ability to drive them in. However, when you realize that even the league leaders in OBP are rarely above .450 and almost never above .500 (except for one Barry Bonds), the chances are actually very high that the #3 hitter will bat with nobody on base and 2 outs in the first inning, a very low leverage situation. This is why it is better to have the best hitter in the #4 spot, where they are either batting with runners on base in front of them or leading off an inning, another relatively high leverage situation.According to The Book, in order to maximize leverage for a lineup

Your three best hitters should bat somewhere in the #1, #2, and #4 slots. Your fourth- and fifth-best hitters should occupy the #3 and #5 slots. The #1 and #2 slots will have players with more walks than those in the #4 and #5 slots. From slot #6 through #9, put the players in descending order of quality

OK, so now we have to decide how we will measure hitter quality. Simply using BAT + POW + (SPD/5) would give a simple measurement (since speed is relatively indeterminate in a hitters contribution but should not be ignored) would work well, but through personal experience in this game I know that a BAT 5 POW 5 player would be much better than a BAT 9 POW 1 player. This makes sense in the real world of baseball given that players like Adam Dunn and Jack Cust are far more productive than guys like, say, David Eckstein who are known as "contact" hitters but can barely hit the ball out of the infield. However, in this game there is a bit of relation of contact to power, so we can't let POW completely outweigh BAT. I suggest BAT + 1.33POW + .2SPD + .5DEF Defense is also quite important, especially in a video game in which the players are much smaller than they are in real life relative to the field and thus have to cover much more ground. So using this equation, we get the following ranks:

RF J. DRAKE 16.32 20.32

CF S. TEMPLAR 13.72 18.22

3B N. SOLO 14.32 17.32

LF J. STEED 19.97 22.97

DH E. PEEL 15.11 16.61

1B K. GALE 16.31 18.81

CA J. BOND 12.12 15.62

SS J. ROCKFORD12.12 16.12

2B P. MARLOWE 11.32 14.32

BENCH

CA G. IRONSIDE12.98 15.48

IF S. SLADE 10.32 14.32

IF T. PRISONER17.11 20.11

IF P. COLUMBO 11.99 14.49

OF R. STEEL 14.44 17.44

IF P. MAGNUM 10.86 14.86

Now, let's make a lineup. In the first column is pure hitting value. In the second column, defensive value is included. Because defense is regardless of position in this game, we are free to take simply the top 9 overall values. This gives us the following 9:

LF J. STEED 19.97 22.97

RF J. DRAKE 16.32 20.32

IF T. PRISONER17.11 20.11

1B K. GALE 16.31 18.81

CF S. TEMPLAR 13.72 18.22

OF R. STEEL 14.44 17.44

3B N. SOLO 14.32 17.32

DH E. PEEL 15.11 16.61

SS J. ROCKFORD12.12 16.12

First, we need our top 3 batters. They are Steed (19.97), Prisoner (16.32), and Drake (16.32). In order to decide who goes at 1, 2, and 4, let's look at the value of the HR at each position. The average run value of the HR at the 1, 2, and 4 spot respectively is 1.291, 1.349, and 1.436. Therefore, power among these 3 hitters should increase. That means that Drake will leadoff (4 POW), Prisoner will bat 2nd (7 POW), and Steed will cleanup (9 POW). Now we need the next two best hitters. They are Gale and Peel. Because these two hitters have equal POW numbers, the better BAT player will go in the 5 spot because the average run value of the single, double, and triple are slightly higher. So Gale will bat 5 (6 BAT) and Peel will bat 3 (5 BAT). After that, we merely go in descending order. So #6 is Steel, 7 is Solo, 8 is Templar, and 9 is Rockford. Here is the lineup, along with the real person they correspond to along with their OPS+ for the 93 season.

1. J. DRAKE = Darryl Hamilton 109

2. T. PRISONER = Kevin Seitzer 119

3. E. PEEL = Kevin Reimer 87

4. J. STEED = Greg Vaughn 128

5. K. GALE = John Jaha 103

6. R. STEEL = Tom Brunansky 58

7. N. SOLO = B.J. Surhoff 91

8. S. TEMPLAR = Robin Yount 90

9. J. ROCKFORD = Pat Listach 73

It would appear that I weighted POW slightly high, but this still worked pretty well overall. Since Brunansky appears to be an outlier, let's replace him with the next highest total value on the list, which would be J. BOND, or Dave Nilsson, who had a 93 OPS+, but has the lowest offensive value by the game formula, so he'll bat 9th and everybody under him will move up. So our final lineup is:

1. J. DRAKE = Darryl Hamilton 109

2. T. PRISONER = Kevin Seitzer 119

3. E. PEEL = Kevin Reimer 87

4. J. STEED = Greg Vaughn 128

5. K. GALE = John Jaha 103

6. N. SOLO = B.J. Surhoff 91

7. S. TEMPLAR = Robin Yount 90

8. J. ROCKFORD = Pat Listach 73

9. J. BOND = Dave Nilsson 93

Finally, let's take a look at the expected runs/game for both the original lineup and the final lineup, using the lineup analysis tool at http://www.baseballmusings.com/cgi-bin/LineupAnalysis.py

Original lineup: 4.436 runs/game

Final lineup: 4.632 runs/game

So we've added .196 runs/game, which over the course of a 162 game season, adds 31.752 runs. At 10 runs/win, that adds a total of 3 wins to our total! That could very well be the difference between making or missing the playoffs, and in a market where an additional win is worth about 4.5 MM/yr, that's 13.5 MM!

Now wasn't that fun?