Tangotiger Blog

Monday, January 01, 2024

Explaining how the worst-sequenced batting lineup will only cost you 0.25 runs per game

Suppose you have the best-sequenced batting lineup, with the following batters and their wOBA

1. 0.400
2. 0.370
3. 0.350
4. 0.340
5. 0.330
6. 0.320
7. 0.310
8. 0.300
9. 0.290

The number of plate appearances (PA) each batter has is 1/9th as much as the next batter. So, we have these number of PA per game:

1. 5.000 0.400
2. 4.889 0.370
3. 4.778 0.350
4. 4.667 0.340
5. 4.556 0.330
6. 4.444 0.320
7. 4.333 0.310
8. 4.222 0.300
9. 4.111 0.290

Now, let's swap the first batter and the last batter. What happens? Well, instead of 5 PA going to the .400 wOBA batter, 5 PA will go to the .290 wOBA batter. That's a drop of .110 wOBA, or .110/1.2 = .092 runs, per PA. For 5 PA, that's a drop of .458 runs. However, our .400 wOBA batter will now increase the 9th place by .092 runs per PA, albeit for only 4.111 PA. So, that's .377 more runs for that slot. The swap of the 1st and 9th batters will give us a total net runs value of .081 runs.

Do the same for the 2nd/8th batters, and we have a net change of .039 runs. The 3rd/7th .015 runs, and 4th/6th is .004 runs. That gives us a total of 0.14 runs of change, based purely on the shifting of talent. A little bit more than that as the number of total PA will be less. The synergy of that change will be less than 0.14 runs. And so, the expectation will be a change of 0.2 runs, maybe 0.25 runs per game.

Tuesday, September 08, 2015

Multi-Lineup Index

?Bill James has a Multi-Position Index.  I don't know what he actually calls it, but let's go with that.  We can apply that concept for anything, including batting lineup.  I've got a request out over at his site, so you can see how it works.  Bill put out an idea as to what to do with it.  Let's see the aspiring saberists roll up their sleeves.

Saturday, June 06, 2015

Where to bat Trout?

?Jeff Fletcher looks into it. I like the quote from Mike Scioscia:

“You have to find two guys that are going to present themselves or a combination of guys that are everyday table-setters for it to make sense,” Scioscia said. “From the first hole down to third hole you are taking 40-50 at-bats away from him during the year. If they are more productive at-bats, great. If they are not, then you are moving away from your optimum offense.”

Sunday, April 05, 2015

Votto #2, @DatDudeBP #7

?Whoah, it's actually happening.  Maybe Mike Trout started something big.

Sunday, January 04, 2015

Was Mattingly only one switch away from an optimal batting lineup?

?So Xeifrank presents a fascinating set of optimal lineups.  His most optimal had Kemp at leadoff, but his second best, at just 0.0003 runs per game worse than optimal has Kemp at 7th.  So what Xei does is present the 25 most optimal lineups, and shows how frequent each player occupies each slot. 

Gordon?  Most popular spot is leadoff among the most optimal lineups, even if he's in the second slot in the most optimal lineup.  His second most popular spot is 7th.  Basically, any reasonably-optimal slot will put him 1st, 2nd, or 7th.  Mattingly put him 1st.

And on it goes.  Puig was put 2nd by Mattingly the most.  His most reasonable slots were 5th and 2nd.

The ONLY thing Mattingly did wrong was put Ramirez 5th instead of 3rd or 4th, and putting Kemp 4th when his best slot was... basically any spot EXCEPT 4th.  Simply swapping Ramirez and Kemp would have been reasonable (and gained him 3 runs per 162 G in the process).  That would have been the 21st best lineup, and 5 runs per 162 games below perfect.

I love what Xei did here with his "frequency" table.  It's really the model here, as it shows how much range there is in lineup building, and gives the manager reasonable options without being forced the single most strict optimal lineup.

Great job Xei!

Tuesday, December 30, 2014

Difference between the best and worst possible lineup order?

?According to Xeifrank's simulator, it's 2 wins (or about 20 runs).  Remember, absolute best to absolute worst.  Since no one is going to construct anything close to the absolute worst lineup, our comparison point is really absolute best to random / pick out of a hat, which would therefore be about a 10 run difference.  And, we shouldn't really be close to constructing a lineup that looks like it might have been picked at random.  So, the difference between the absolute best lineup and anything better than a random lineup is going to be about 7-8 runs or so.

If you remember from a few days ago, swapping players between lineup slots gives you a 2 or 3 run gain.  So, that's pretty much where we are, you might need to swap two or three pairs of players, and that'll give you something like a 7 or 8 run gain.  Over 162 games.  That's 0.05 runs per game.  That's what the thousands of words we've spent on optimization is giving us, about 0.05 runs per game.

Friday, December 26, 2014

Effect of an imbalanced batting lineup

Pizza gives us some good data to work with.  The net effect is that you can gain 2 runs in terms of transferring talent so that you get some imbalance, but it is overall equal (per PA). ? Could we have predicted that?

Let's see.  Pizza said he transferred (the equivalent of) 30 wOBA points to the leadoff hitter from the 9th place hitter (or around .025 runs per PA).  We know that there's a gap of 144 PA between the leadoff hitter and the 9th place hitter.  With the leaoff hitter getting .025 runs per PA for those 144 extra PA, we have what we need for our calculations: .025 x 144 = 3.6 runs.  Whoah.  Pizza is showing only 2.1 runs.  That means that there's alot of deleveraged PA at work here.

Let's see the next one, as he repeats the same in transferring talent from the 8th place hitter to the 2nd place hitter (which is 108 PA).  So, .025 x 108 is 2.7 runs.  And Pizza is showing the marginal change as 2.6 runs.  Pretty good match.

If we look at the 3rd place / 7th place swap (72 PA), that's 1.8 runs, compared to Pizza's simulator of 2.1 runs.  Close.

Finally, the 4th / 6th place swap (36 PA), that's 0.9 runs compared to Pizza's 1.1 runs.  Close again.  Overall, I get a change of 9 runs, and Pizza is showing 8.  For a sniff test, that's fine.

Saturday, August 23, 2014

Batting Order Primer

?MGL gives us a primer on the batting order.  And then does a random check of each team's batting order.

The obvious one is what we expect: the teams that are most at odds with the "simple optimal" order is that teams put below average hitters in the 2-hole.

But he also notes that just using the "simple optimal" order is not much different, overall, than what teams are doing right now!  That is, you can't just use a simple algorithm, and think you'll improve anything, since you may be right just as often as you are wrong.  You have to give each team a very personalized touch, and on top of that, you need to run simulations because there are many interactive effects that simple rules just can't capture well enough.

Saturday, April 12, 2014

Gabe Kapler, saberist

Sunday, March 23, 2014

Is this the right team to put Trout as #2?

?As most of you know, your best hitter should hit somewhere in the 1, 2, or 4 spots (most of the time).  It may occasionally work out that you want your best hitter #3, but it all depends on the kind of hitters your team has.

If you have three great hitters, you simply put the guy with the most walks / fewest HR as leadoff, the guy with most HR / fewest walks as cleanup, and the other guy as #2.  But according to Steamer Forecasts, the Angels don't have three great hitters to play with.  Their best hitter is both the highest in OBP and the highest in SLG.  Their second best hitter is 2nd on the team in OBP and 2nd on the team in SLG. 

To make things harder, Oliver Forecasts don't correspond very well with Steamer.  Neither does ZiPS.  So, it's really hard to put everyone somewhere, when we can't agree on how well each hitter is.

I wouldn't be surprised that depending on which forecasts you use, you could have Trout as leadoff or #2 or #4.  Pujols could be #3 or #4.  The rest might change wildly depending on which forecast, and lefty-righty.

As MGL is fond of saying: when it's this close, nothing is so obvious that you can figure out the right answer, without running thousands of simulations.

Who out there wants to use each of these forecasts, and figure out the optimal orders?

Thursday, February 06, 2014

Batting #2

?Some interesting data here.  I like to use the "300 PA" cutoff in whatever study I do.  I never used it the way it was presented in this article, which is simply to count the number of players who had at least 300 PA in a particular batting slot (which in this case is #2).  The author notes that only 14 hitters qualified, which.... seems low.  But, having never tracked it before, I don't know what I should have expected.

Can someone show it for each of the 9 batting slots (though obviously, this will knock out the NL teams for the #9 slot)?  And maybe do it for all the Retro years?

Thursday, October 17, 2013

Shifting the lineup one slot

Bravo Jim Leyland!  What I like about what he did was that he kept the players adjacent to each other, so that they didn't experience any "shock".  If Fielder is used to seeing Cabrera on base, well, he still gets to see him.  Cabrera is used to Torii?  Well, he still will be.  By shifting everyone one slot, you are simply choosing a different starting spot (Torii instead of Austin). 

Indeed, had Leyland put Austin 9th, it would have been as if nothing really changed.  Leyland would have maintained the same rotation order, and simply started as if Jackson made the out in the previous 0th inning.?

In any case, the relationship of how much we talk about batting orders to the impact batting orders have: that's got to be pretty disproportionate.  More important than the actual order is the IDENTITY of the starting nine.  90% of the talk should be on that, then 9% on the players' ego as to where they'd like to hit, and then 1% on how to structure those nine.  Ultimately, no matter how well you can squeeze out 2 or 5 or 10 runs in organization of the batters, it pales in comparison to the players buying into it, and that pales in comparison to selecting the right players for the starting lineup.

The way I see it, it's like Google Maps.  Instead of trial and error as the best way to get from Newark Airport to JFK, you let the Google Maps optimizer decide it for you.  You can tell Google Maps that you might be afraid of tunnels or bridges or ferries, or that you need to avoid a certain stretch of highway.  Then, after all those preferences are set, then you simply let the optimizer tell you the best arrangement given YOUR constraints.

And if Google Maps gives you back a bad result?  Well, you didn't give it all the constraints in the first place.  Either that, or Google Maps didn't consider the traffic situation at 9AM (or how Fielder might react without Cabrera ahead of  him).

Wednesday, August 21, 2013

Number 2 hitter

It's interesting that for all the talk of the number 2 hitter (some managers put great hitters here, and others put terrible), things don't seem to change overall.  If you look at the OPS+ at the league level by batting order (which you can find easily enough on BR.com), it's disappointingly unchanging.

However, that's the mean.  I'd like to know if the spread is changing, either at the team level, or at the player level (at least among players with at least 300 PA in that slot).  If the spread is getting larger, but the mean remains constant, that means that managers are putting both much better and much worse hitters than ever.  That is, there is even more confusion.  If the spread is getting tighter, that means they are more in agreement that you simply want an average hitter there.

The true answer is that you need an above average hitter in that slot, and I'm not sure if we'll get there by increasing the standard deviation (that is, stable group of bad hitters, and a better class of good hitters, to increase both mean and SD), or by increasing the mean with a stable SD.  I THINK we'd see a few leaders among managers, and so, we should see an increase in both SD and mean.

I'd love to see the aspiring saberists look at this historically to see what we get.?

Monday, July 15, 2013

More opportunities to hit a HR

One of the "unfair" things about baseball is that the batting order makes it so that each lineup slot gets an average of 18 fewer plate appearances than the previous slot, per 162 games. (*)  Schoenfield asks:

One thing working against Davis, however, is that Buck Showalter continues to hit Davis fifth in the order, choosing to bat Adam Jones cleanup between lefties Nick Markakis and Davis. That will cost Davis plate appearances over the season -- an estimated 30 over the entire year, if he was hitting third instead of fifth -- and those 30 missing PAs could be the difference between 59 and 62. With Matt Wieters not having a great year behind him, Davis may also start receiving more walks (although July has produced his lowest walk rate of the season, so pitchers haven't been pitching around him).

If I remember right, Larussa moved McGwire to the 2-hole to try to maximize his plate appearances near the end of the season.  (Easy enough to confirm, for someone out there.)  If Davis' true talent level is somewhere between .06 and .07 HR / PA, and with 66 games to go, the difference between batting third and fifth is .222 x 66 x .065 = 1 HR.  Is it worth it to chase a statistical record, by slotting players as if you can just move them around, even if players may have a preference, thereby cancelling out the advantage of the extra PA?  And, aren't there any players on the team to worry over, besides this statistical (non-team) chase?  We're talking about upsetting whatever balance is supposed to exist among his players, in order to give one of his players one extra HR (at the cost of his other players something else).

(*) Math question: can someone tell me why the answer is always "average of 18", regardless of how m?any innings there are in a game?

Monday, July 08, 2013

Correcting the batter out of turn

Rob Neyer points to an interesting passage:

"Guess I might as well admit," said Richards, "I purposely had Adair bat out of turn. I was hoping the count would get to 3-and-0, and then I could send up Jones to get a walk. I didn't have another pitcher hot, so I didn't want to take out Jones."

This refers to this rule, where Baker bats out of turn (Abel should have been batting):

PLAY (1). Baker bats. With the count 2 balls and 1 strike, (a) the offensive team discovers the error or (b) the defensive team appeals. RULING: In either case, Abel replaces Baker, with the count on him 2 balls and 1 strike.

So, if the defense is paying attention, they should lob it in to Baker.  It's either a free strike, or Baker makes contact, and Abel is automatically out.

(By the way, why would the defense appeal mid-plate appearance?  And if you want to get really really mean: the pitcher could throw the ball directly AT the batter, getting the hit batter nullified by the out for batting out of turn!)

I therefore have this question, and hopefully someone out there flexes their Retrosheet muscles (1988-2012): what is the distribution of ball-strike counts in situations where a batter hits out of turn?  We should hope that the defense is alert enough that there are far more strikes than balls in those situations.  Does this actually happen?

Thursday, June 27, 2013

Batting your best hitters second

There's nothing new here.  I'm just linking to it because it's from my hometown and it's in French.?

Tuesday, May 21, 2013

Batting lineup styles

I really like the idea behind this research.  Comparing OBP to wOBA to try to figure out how much a player's game is geared toward OBP or SLG is a great way to do it.  Basically, if OBP matches wOBA, y?ou know that the player's game is well-balanced between getting on base and moving runners over.  If OBP is way above his wOBA, you know that player has a disproportionately high walks and/or low HR.  (That's because you get 0.7 for walks and 2.0 for HR.)  And naturally, if OBP is way below his own wOBA, you're looking at a high-HR low-walk player.

Anyway, the fun part is that he looks at how rosters are constructed, how many "extreme" players does each roster have, and in which way are they extreme.  Then he continues, trying to see what composition of roster does to expected runs scored.

All very fine work and ideas, and should certainly inspire others to put in their own two cents.

Thursday, April 25, 2013

Where to bat Ben Revere?

?Bill tries to figure out where to put Revere in the Phillies lineup.  He astutely notes that the best way to utilize Revere is in front of Young.  Xeifrank ran his simulator a while back, and he has Revere as ninth batter.  And who does he have batting right after Revere?  Why, leadoff hitter Michael Young!  I love it when the optimal solution can be traced back to a logical process.

Xei also notes this, which I find hard to believe, and maybe MGL can verify with his sim (though, he has a different forecast for players from ZiPS), which will obviously make a difference:

Against RHP using the simulator lineup over the default lineup garners the Phillies an extra 5.59 wins per 162 games.  Against the LHP it garners 5.31 more wins per 162 games.

Monday, April 08, 2013

Lineup construction

When I was in college, the first programming language I learned was Turbo Pascal (actually, I learned COBOL and Fortran before that, but neither were available for the PC).  You might consider Pascal a scaled-down version of C.  Anyway, considering that I love baseball, that I love everything about math, and that I'm learning this tool, the first large-scale project I wrote on my own was a baseball simulator. The best way to learn a tool is to apply it to something you love.  I used to run pools in college, and I'd do some pretty nifty things with Lotus 1-2-3.?

Anyway, I just wanted to know the impact of different batting orders, whether to clump hitters or not, whether my softball team with a wide range in hitting talent can be better leveraged.  I still have that program, and I wrote it almost 25 years ago.

So, I'm always reminded of that every time someone posts about a simulator they wrote.  People seem to forget at times that we don't set out to prove something.  We're simply interested in the question, and we just build the application to answer those questions, and we report on our findings.  That's all we really do.  If you don't like the answer, then build your own method of figuring the answer.

***

Anyway, the reason that batting orders have such little impact is that the lineup turns over: everyone hits!  If you swap your #2 hitter for your #6 hitter, you are swapping 0.444 PA per game (1/9th of  PA difference per lineup slot, times 4 lineup slots), or 72 plate appearances per season.  This is what you are really doing, just taking 72 PA from one guy, and giving it to the other guy.  (There are synergies also, with the guys coming up after, but there's also synergies with guys batting before you too.  Those count, and if you want to know more, it's in The Book.)

Then, we know that a really good hitter generates about 35% more runs than an average hitter.  So, if an average hitter generates 0.12 runs per PA, the really good hitter will generate 0.16 runs per PA.

This is what all the argument is about!  Transferring 0.04 runs per PA and 72 PA from one guy to the other.  And 72 x .04 = 3.  Three runs!  Over 162 games.

It's why we have such a hard time finding it.  Not to mention that if a guy's ego is placated by having him bat at some supoptimal spot, then let him stay there!  It doesn't make sense to increase your chance of scoring by 3 runs over 162 games, if the player will then become a worse hitter and cost your team 10 or 15 runs.  Hence, batting order construction is more art than science.

***

So, all you guys learning programming: keep on writing those baseball simulators.  But do so purely for the satisfaction of writing the simulator, and playing with it.

Tuesday, March 05, 2013

Optimal Batting Order Paper

This was from Sloan last year (pdf).  I don't remember reading it or commenting on it.  It covers several topics, a few of which I either don't understand at all, or I don't understand how relevant it could be for optimizing batting order.  The one part I agree with is this conclusion:

basic question - what is the expected run production prior to optimization compared with the actual runs produced in the game? On average, the actual mean score was 4.54 while the simulated score before optimizing the batting order was 4.44.

0.1 runs per game, or 16 runs per season, is pretty much inline with expectation.  I would have expected a range of 5-15 runs per season.  The other stuff presented would seem to include a better job of picking the right players, which I agree with.  More than setting the order correctly is picking the correct players.

?