"Doing the Math" to Set Your Lineups

[MARCPELLETIER]

Just found this. A mathematicien put his science to work. His finding is that the best optimal line-up should have the best hitter #2, the second best #3...and the worst player should #7. WHo`s willing to try? :P

[quote:c7b2ced141]
Man wielding pen and paper knocks baseball tradition clean out of the park. (Mathematics).(Bruce Bukiet of the New Jersey Institute of Technology in Newark)(Brief Article). Klarreich, Erica.

Full Text: COPYRIGHT 2002 For more science news and comments see http://www.newscientist.com.

BASEBALL teams would play better if they did away with the traditional batting line-up beloved of coaches and aficionados. Putting the best batter second, rather than the customary fourth, can substantially improve team performance, a mathematical analysis suggests. Surprisingly, the weakest hitter shouldn't bat last.

Baseball managers have known for years that not all batting orders are created equal. If there are already players on base, a strong hitter has a better chance of getting them back to home base to score several runs -- "a dean-up" in baseball parlance. For that reason, managers tend to put the strongest players together in the line-up.

But it's a subtler decision whether the two best hitters should bat second and third, or third and fourth, for instance. In all there are more than 360,000 possible ways to line up the nine players. To find the best line-up, mathematician Bruce Bukiet of the New Jersey Institute of Technology in Newark took data from the 1989 US baseball season and used it to calculate the likely number of runs each potential line-up would earn. The difference between a team's best and worst batting order could change the outcome of as many as 10 games in a season, he found.

For the majority of National League teams that season, the optimal line-up would have been to use the best batter in the second spot. "Managers traditionally put the team slugger in the fourth spot, on the rationale that several players might get on base before he comes to bat, and he can clean up."

But it's more important to get the top hitter batting earlier, so he may get more chances to bat over the course of a game, Bukiet reported last week at the annual meeting of the Society for Industrial and Applied Mathematics, in Philadelphia, Pennsylvania.

The study also found that the worst batter, usually the pitcher, should bat seventh or eighth, not last, where he is almost always placed. "The pitcher should be far away from the slugger in the line-up," says Bukiet. That lessens the chance that he'll be the clean-up hitter responsible for getting the strongest batter back to home base.
[/quote:c7b2ced141]

[MARCPELLETIER]

Bleacher, usually, I take 0.3* (OPS vs lhp) + 0.7*(OPS vs rhp).

To the question: can I take Total base as a slugging measure? The answer is: yes, if you want to keep it simple. But have in mind that you will undervalue players who walk a lot.

A simple thing you can do to avoid this bias is to give a value for the "slugging" provided by walks. I usually use a value around 0.5.

So I suggest: on-base + total base + 0.5*(walk+hbp) + stadium adjustment (as rightly pointed out by dr.glenn!!!) + clutch/2 (so easy to do)

(this way, a walk will be worth 1.5, a single will be worth 2, a double will be worth 3....)

[MARCPELLETIER]

I just want to come back to my mathematician. While the optimal line-up he found out had the best hitter at the #2 spot, less than 0.33 run per season was lost by moving the best hitter to #3. In another article, he set up a list of golden rules you should follow to have a highly optimal line-up:

Place the best batter (by scoring index) second, third, or fourth.
Place the second best batter in the first five positions.
Place the third and fourth best batters in the first six slots.
Place the fifth best batter first, second, fifth, sixth or seventh.
The sixth best batter should bat in any position except eighth or ninth.
Place the seventh best batter either first or sixth through ninth.
The eighth and ninth best batters should bat in the last three positions.
Either the second or third best batter must be placed immediately before or immediately after the best batter.
The worst batter must be placed four through six positions after the best batter.
The second worst batter must be placed four through seven positions after the best batter.


Now, try to use these rules by putting speed at #1, by avoiding gbA at #2, and by using clutch at #4, #5 and #6, and you should be fine!!!

[MIKERANSICK]

Baseball is becoming too bogged down in numbers and formulas, when you need to call Alan Greenspan to interprete Scott Rolen vs. D-Train matchup.

[The Biomechanical Man]

marcus wilby said:[quote:1d889192d3]can I take Total base as a slugging measure? The answer is: yes, if you want to keep it simple. But have in mind that you will undervalue players who walk a lot. [/quote:1d889192d3]

Luckyman, I'm confused. I thought in baseball that Slugging = total bases from hits (not counting walks) divided by at-bats (not counting walks). Therefore,
[list:1d889192d3][*:1d889192d3]Slugging of a Strat card = TB of card / 108 (3 x 36 dice rolls)
[*:1d889192d3]On Base Pct on a Strat card = OB of card / 108
[*:1d889192d3]On Base Plus Slugging of card = TB/108 + OB/108 = (OB+TB)/108[/list:u:1d889192d3]

[LMBombers]

Interesting theory about hitting your best hitter #2. The San Francisco Giants are going to try that out this year by hitting Bonds #2 according to reports. Howver I don't think they are going to hit their pitcher #7!

[APS1]

Quite interesting...many talk about "Clutch"...what is the mathmatical way of determining "Clutch" :wink: ... I always lookes at # of AB, RBI's etc

[1crazycanuk]

I try not to worry too much about clutch. There is like an infinitely small chance that the clutch factor will come up in the game. If a guy has a positive or negative clutch of "1", how often is that going to affect the outcome of a game? Not often enough to worry about...nor care.

[MARCPELLETIER]

Glenn,

no worry, it's a topic easily confused, and I have not been as clear as I should.

total base and slugging aren't the same thing.

Slugging is: total bases/out

so by definition, when you compute OPS, what you should really do is:

onbase/108 + total bases/(108-walks).

As you can see, the divider for on-base and slugging is not the same, just like in real life, where on-base is obtained by dividing (hits and walks) by (AB+walks) and slugging is obtained by dividing total bases by (AB) only.

If you use the last equation, you will be perfectly fine. However if you use:

on-base + total base

which is equivalent to:

on-base/108 + total base/108

the net result is that you will be undervaluing players who walk a lot. You will be calculating their slugging as if the walks on their cards are outs.

Because making division is dragging, and in a spirit to let things simple, what I do is adjusting for the bias against "walkers" by providing 0.5 for each walk:

on-base + total base + 0.5*walk.

[doug_tucker10]

ok explain the math behind these 3 players and their output...i love to tinker with statistics but can you really hold to a set mathematical formula with the online TSN SOM game? true you need to have some sort of logic running when youre building a team but the end results can defy explanation (working both ways. towards a good and bad result)

exhiibt A Alex Rodriguez
144 19 4 5 13 13 1 1 .215 .375 .283

exhibit B Barry Bonds
99 23 9 11 30 30 0 0 .424 .869 .557

exhibit C Aaron Rowand
152 31 10 10 31 8 3 0 .342 .618 .388

my home park is Shea... my original comparison was between Bonds and Rowand alone until i noticed Arod's clutch against righties is as bad as Rowands...they both have similar actual OBP non ballpark against rhp as well ive had Rowand batting 1st,2nd and 3rd all season...Bonds 2nd,3rd and 4th...Arod 2nd,5th and 6th. Huff,Damon and H Matsui are usually in the mix somewhere between these 3 players(against rhp). Damon and Huff arent doing much in production. against lhp most of the time i have Arod,Rowand and Bonds following each other consecutively in the batting order. My thiird best "slugger" against RHP has been Eric Valent all this and a very poor David Wells and Mike Timlin on my team and im tied for 1st after 36 games...ok im only 19-17 but for most part its been a successful over all in the early going...why? :D

btw, since ive left Johnny Damon to bat leadoff against RHP AND LHP my team has gone 6-3 (better than 13-14 which is what it is with Rowand at leadoff)... my team has had 2 seasons so far ...when hot they are 11-4. when cold 8-13.

for all his typical mind blowing offensive numbers it would seem that Barry Bonds overall production is at a level no greater than Aaron Rowand... maybe 36 games isnt a large enough sample...