SABR-Toothed Triber: Logic on Batting Orders, Sizemore, Branyan & Brantley

Our last two posts focused on explaining some essential offensive and pitching statistics to help us evaluate the 2010 Indians.  Rather than introduce another stat this week, I thought we’d take a little break to discuss batting orders, their importance to a team’s ability to score runs, and how Manny Acta has begun to think about setting up a lineup for the 2010 season given the recent roster decisions.

There’s a lot of conventional wisdom about batting orders out there.  We’ve heard it all before.  Leadoff men should be speedsters.  Wait, no!  Leadoff men should get on base!  Batters in the #2 hole should be good at moving runners over, but shouldn’t worry too much about getting on base themselves.  Sluggers should always bat cleanup.  The best all-around offensive player on the team should bat the three spot.  Pitchers should bat last (in NL parks).  But why?  Can’t we explain any of these notions?  Are they correct, or just accepted because some guy who chews tocacco said so?

Let’s look at some numbers to try to find the answers.  (The subsequent charts are quoted from The Book, and have been compiled using actual game data.) 

The chart below presents how many times, on average, each spot in a batting order actually gets to bat in a game:

Order	PA/G	PA/Season
1	4.83	782
2	4.72	765
3	4.61	747
4	4.49	727
5	4.39	711
6	4.26	690
7	4.14	671
8	4.02	651
9	3.9	632

So if we’re concerned with getting our best hitter to bat as often as possible, we’d put him in the leadoff spot, and then fill each successive spot by the best remaining hitter, right?  This way, our best hitter would have 150 more PAs than our worst hitter over the course of a season.  Done!!

Not quite, of course.  We know that baseball games are more complex than this.  They require some planning toward “big innings”—chains of positive offensive events that lead to runs being scored.  These events happen more often in particular contexts, and those contexts cannot be ignored.  In addition to number of PAs, here are the two major contexts to consider, with accompanying charts: 

1. How many men will be on base when a spot comes to bat?

Order	PA Bases Empty	PA Men On	# of runners on
1	3.11	1.72	2.39
2	2.63	2.09	2.77
3	2.38	2.23	3.00
4	2.19	2.30	3.20
5	2.28	2.11	3.10
6	2.29	1.97	2.84
7	2.2	1.94	2.74
8	2.17	1.85	2.61
9	2.13	1.77	2.48

As the chart shows, the leadoff man will have more PAs with no runners on than any other spot in the lineup (because he’s the only one guaranteed to leadoff an inning in every game—the first), so his ability to do major damage will be limited.  He also bats with the fewest runners on base for an entire game.  And look at the cleanup spot: he bats with the most runners on base during a game.  Maybe we need to rethink our first theory about our best hitter leading off. 

2. How many outs will there likely be when a spot comes to bat?

Order	0 Outs	1 Out	2 Out
1	48%	26%	26%
2	33%	41%	26%
3	28%	35%	37%
4	34%	31%	35%
5	35%	33%	33%
6	33%	34%	33%
7	33%	33%	34%
8	34%	33%	33%
9	34%	33%	33%

You’ll notice that the 6-through-9 slots all bat pretty evenly across the various “out-states”: each about a third of the time (which makes sense).  But the 1-through-4 slots have more variation.  I’ll let you figure out why this is the case, but it should be pretty obvious.

Let’s jump forward.  I’ll spare you some of the ugly results of trying to combine these three charts, and skip right to the money shot.  What we want to know is how many runs, on average, are contributed by each spot in the batting order, by each event that can happen in an at bat.  This chart presents the run values (more on that in a second) for each spot in the batting order for the various outcomes: 

Order	1B	2B	3B	HR	NIBB	K	Out (non-K)
1	0.515	0.806	1.121	1.421	0.385	-0.329	-0.328
2	0.515	0.799	1.100	1.45	0.366	-0.322	-0.324
3	0.493	0.779	1.064	1.453	0.335	-0.317	-0.315
4	0.517	0.822	1.117	1.472	0.345	-0.332	-0.327
5	0.513	0.809	1.106	1.438	0.348	-0.324	-0.323
6	0.482	0.763	1.050	1.376	0.336	-0.306	-0.306
7	0.464	0.738	1.014	1.336	0.323	-0.296	-0.296
8	0.451	0.714	0.980	1.293	0.312	-0.287	-0.286
9	0.436	0.689	0.948	1.249	0.302	-0.278	-0.277

Again, this is a lot to digest, but let me take you through some of it.  That 0.515 run value under “1B” means that when a leadoff hitter gets a single, his team—ON AVERAGE—is going to score about a half a run (.515 runs) more that inning than they would have before he hit the single.  When the same batter strikes out (second to last column), he costs his team .329 runs compared to what they would have scored before the strikeout.  Since the average team scores a bit under 5 runs a game, when an inning starts, they’re expected to score .555 runs before the inning ends, so strikeouts lower that, while singles raise it.  This may be tough to wrap your head around at first, but this chart tells us everything we need to know about constructing batting orders.  (I was told there would be no math.)

Let’s start by asking some questions.  When is a HR worth the most?  Looks like the number 4 spot in the lineup (1.472 Run Value—higher than any other spot).  Conventional wisdom wins!  HR hitters should bat cleanup.  When is a walk worth the most?  The leadoff spot—by a lot!  Again, this corresponds well with our notions of high on-base percentage guys leading off.  The #6 through #9 slots appear to become less effective across all events as the batting order progresses, so we should probably just put the four worst hitters in descending order in those spots.  We’re doing great so far: all of this makes sense with what we already believe about batting orders.

Enough with the conventional wisdom; it’s time to blow your mind a bit.  Compare the 2^nd hole in the lineup to the 3^rd spot.  Which one has a higher value to its team?  Where should we put the better hitter to maximize run scoring?  That’s right.  The second spot in the lineup can contribute more runs with the same hitter than the third spot can.  So you should put a better hitter second in the lineup rather than third.  Why would this be?  Well, believe it or not, the extra plate appearances over the course of a season for the #2 hitter end up adding more value than the fact that more people are on base when the #3 hitter bats.

I’ll let you look over the chart for yourself to verify, but I think we’re ready to make a fairly unconventional conclusion: the most valuable spots in the lineup are the first, second, and fourth spots, followed by the three and five spots.  Take a look.  Seriously weird stuff.

So how does all this affect the Indians in 2010, and Manny Acta’s insistence that he’d like to have a consistent lineup everyday—especially with the recent news that Grady is scheduled to bat second this season?  Rather than accepting my logic above, let’s run some simulations.

Last week, Scott sent me a link that attempts to optimize batting orders.  Try it out for yourself, but basically, you enter nine players’ OBPs and slugging percentages, and it calculates the best and worst lineups by runs scored. 

Here are the ten guys I believe will be vying for spots in an everyday lineup.  I’ve used CHONE’s projections for their OBP and slugging, but feel free to adjust these according to your own projections.  Either way, I don’t think the table below is unrealistic: 

	OBP	SLG
Sizemore	0.370	0.484
Cabrera	0.365	0.432
Choo	0.372	0.460
Hafner	0.351	0.446
Branyan	0.329	0.473
Peralta	0.328	0.408
LaPorta	0.337	0.457
Marson	0.344	0.352
Valbuena	0.328	0.400
Brantley	0.349	0.363

Notice that CHONE projects Choo and Sizemore to be the two best players on the team (no surprise there), with Branyan, Hafner, and Cabrera the next three in some order.

Ready to be surprised?  Let’s leave Brantley out for the first simulation, since all signs point to Branyan effectively taking his spot in the everyday lineup.  Here are the best and worst batting orders determined by run production:

Spot	Best		Worst
1	Choo		LaPorta
2	Sizemore		Valbuena
3	Cabrera		Hafner
4	Branyan		Marson
5	Hafner		Peralta
6	LaPorta		Cabrera
7	Peralta		Choo
8	Valbuena		Sizemore
9	Marson		Branyan
RPG	5.257		4.96

Quick.  Who are our three best hitters?  I bet you’d say Choo (highest OBP), Sizemore (high OPB, higher slugging), and Branyan (he slugs close to .500, remember).  Look at where those three fall in the most effective lineup!  First, second, and fourth!  Exactly what we’d expect from the work we did above!  And we fill out the top five with Hafner and Cabrera.  Since Hafner has more pop than Cabrera, he should bat fifth, which leaves third for Cabrera!  Math works!

Now look at the worst lineup.  What I find most interesting is that even with the worst possible lineup, we’re only costing ourselves, 0.31 runs per game over the best possible lineup.  Yes, that’s a cost of 50 runs over the course of season, or about 5 wins, but we’re talking about THE WORST LINEUP against the BEST.  No manager would bat Sizemore eighth and Marson fourth, but even if you did, you’re talking about fractions of a run per game!  This is why a lot of the talk over Wedge’s batting orders was misplaced: it wasn’t that he was putting guys in the wrong order so much as he was putting the wrong guys in the lineup (I’m looking at you David Dellucci).

Now let’s look at the lineup with Brantley in there rather than Branyan, just to check if we really should be starting the Love Muscle over the Rookie.  According to CHONE’s projections, Brantley gets the nod in OBP by .020, but he gives up .110 in slugging.  I find this fairly believable.  Here are the best and worst lineups with Brantley:

Spot	Best		Worst
1	Cabrera		Peralta
2	Sizemore		Marson
3	Brantley		Hafner
4	Hafner		Brantley
5	Choo		Valbuena
6	LaPorta		Cabrera
7	Peralta		Choo
8	Valbuena		Sizemore
9	Marson		LaPorta
RPG	5.171		4.89

Best case scenario with Brantley in the game?  5.171 runs per game.  Best with Branyan? 5.257 runs per game.  That’s comes out to 14 more runs over the course of a season with Branyan over Brantley—or an extra win or two over the course of a season.  An added bonus?  Playing Branyan for a year keeps Brantley’s arbitration clock from ticking!  This way, we get an extra year of club-control for Brantley, while only paying Branyan $2 million. 

Now, if I were the GM, would I have signed Branyan?  Probably not.  After all, what’s an extra win or two worth on a team that is expected to finish below .500?  Furthermore, I’m all for young players getting opportunities.  But it’s not my $2 million, and for the Indians, an extra year of cheap Brantley in 2016 (due to a delayed arbitration clock) might be worth a $2 million dollar investment in Branyan in 2010.  So while I know it wasn’t a popular move to effectively send Brantley back down for more seasoning, once the team signed Branyan, there was no reason to let Brantley start the season with the big league club.

As always, feel free to ask questions, and I’ll do my best to point you toward an answer. 

Next week we’ll be talking defense.  See you then!

-Jon

Thanks to the guys at WFNY for picking me up as an occasional contributor.  Much of the research in this series is built on ideas from The Book: Playing the Percentages in Baseball, the ongoing work at FanGraphs, StatCorner, The Hardball Times, and Tom Tango’s blog, and the countless other blogs and books that refuse to stop thinking and arguing about baseball.

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(Original Photo by Ronald Martinez/Getty Images – Branyan’d by WFNY)