The Balanced Lineup Theory

The Balanced Lineup Theory

You hear it all the time form your radio and TV broadcasters– you want to have a balanced lineup. But do you really? Or is this another one of those clunker phrases passed down from generations past, that conventional baseball wisdom that’s just flat wrong at its core?
Okay, so if you followed my series on the Homogeneous model, you know that we already have the expected values of runs for the perfectly balanced lineup. What about a ‘perfectly imbalanced’ lineup? On problems like this, I like starting at the extremes and working my way towards the middle and more normal considerations. Okay, so the easiest thing on this side is to have players who have OBPs of 1 or 0. With 8 guys who have an OBP of 1 (one guy who’s at 0), we cycle through the lineup 3 times every inning, and have 24 successes every inning and cycle through the lineup every inning as well. If all these guys walk, that means 21 runs. Seven guys with OBP of 1 and two with OBP 0 gets you a cycle over two innings – all the way through the order twice in the first inning, and only once in the second inning. We get a two cycle inning, with 21 successes per cycle, 10.5 per inning; all walks yields 15 runs a cycle, or 7.5 per inning. If we continue, we get the following chart:

# OBP 1 guys	Innings/Cycle	Successes/Cycle	Successes/inning	Runs/Cycle	Runs/Inning
8	1	24	24	21	21
7	2	21	10.5	15	7.5
6	1	6	6	3	3
5	4	15	3.75	6	1.5
4	5	12	2.4	3	0.6
3	2	3	1.5	0	0
2	7	6	.857	0	0
1	8	3	.375	0	0
0	3	0	0	0	0

And if we compare to the number of runs we score from walking in a totally homogeneous environment, we see this:

# OBP 1 guys	Equivalent OBP	R/Inn (Homogeneous)	R/Inn (Stacked)
8	.889	21.018	21
7	.778	7.624	7.5
6	.667	3.358	3
5	.556	1.469	1.5
4	.444	0.575	0.6
3	.333	0.179	0
2	.222	0.035	0
1	.111	0.002	0
0	0	0	0

And we can see that there are slight differences here. It’s slightly better to have a homogeneous environment than a stacked one when you’re at outrageously high run-scoring environments, and then it drops off so that stacked lineups do better somewhere between 5/9 and 6/9. And by the time you drop to only 3 successes, of course, the stacked lineup has no chance of getting enough walks strung along to score at all. Well, that has to do with only being able to walk– more on that later.Okay, that’s all fine, but that assumes an infinite number of innings. In reality of course, we don’t get that; we have 9 innings most often (you can do the same thing for 8 or 10 or 11, but I’m sticking with 9 for simplicity here). So what we have above tells us the effect of having your good hitters bunched together, one of the two positive effects of stacking your lineup. But the other effect, that the early part of the lineup has more chances to come up to bat than the later part, is getting masked right now. If we adjust for this, we get the following charts:

# OBP 1 guys	Successes	Successes/inning	Runs/Inning
8	216	24	21
7	98	10.88888888888	7.5
6	54	6	3
5	35	3.888888888888	1.5
4	24	2.666666666666	0.6
3	15	1.666666666666	0
2	8	.8888888888888	0
1	4	.4444444444444	0
0	0	0	0

# OBP 1 guys	Equivalent OBP	R/Inn (Homogeneous)	R/Inn (Stacked)	R/Inn (Stacked, Adj.)
8	.889	21.018	21	21
7	.778	7.624	7.5	7.778
6	.667	3.358	3	3
5	.556	1.469	1.5	1.556
4	.444	0.575	0.6	.667
3	.333	0.179	0	0
2	.222	0.035	0	0
1	.111	0.002	0	0
0	0	0	0	0

Clearly, we still have a long way to go before we get data that’s of much use. First of all, we have to overcome using only walks. That’s not too hard. We just need to come up with the distributions of successes for the final three successes in any given inning – since we have a stacked lineup, the last three guys in our stack. But ok, making specific calculations here is sort of pointless. Still, before we switch off this method, I think it’s somewhat instructive to look at for the opposite end of the spectrum from walks– every success is a home run. In this case, we get the following chart:

# OBP 1 guys	Equivalent OBP	R/Inn (Homogeneous)	R/Inn (Stacked)	R/Inn (Stacked, Adj.)
8	.889	24	24	24
7	.778	10.5	10.5	10.889
6	.667	6	6	6
5	.556	3.75	3.75	3.889
4	.444	2.4	2.4	2.667
3	.333	1.5	1.5	1.667
2	.222	.857	.857	.889
1	.111	.375	.375	.444
0	0	0	0	0

As we can see, the ONLY benefits of hitting someone up in the order when all you’re doing is hitting home runs come from those people coming up to bat more often. But this still doesn’t address the larger problem with this approach – it tells us very little when we have more realistic lineups, where every batter has an OBP between 0 and 1 rather than at the extreme.

Conclusions
It’s time for conclusions, and there aren’t many of them that are great, because it’s such a wacky, sideways (but, I think, fun) way of looking at things. But there’s some stuff we can gleam, and here they are:

• It makes pretty little difference where your OBP and SLG points are distributed, as long as they’re in the lineup somewhere
• There are two major reasons why stacking your lineup can be good – inter-batter synergy (i.e. you want your good hitters to have somebody to drive in), and earlier guys in the order come up more often than later guys
• In the extreme, all-power case, synergy is irrelevant; it’s most relevant when more of your offense comes from OBP
• You want your OBP to be spread out at least somewhat, because for it to produce a run at all, you need to string 3 or 4 successes together in a row

And the final point is this: If you hit a homer, then it doesn’t matter how the three guys who got on base before you in the inning got on, you score 4 runs. If the fourth guy hits a double or triple, it’s probably 3 runs regardless (occasionally two, if the trail runner is slow and was at first). So, if (and this is a big big if) you can pinpoint where an inning is starting, you want your first three guys (maybe only two if it’s a really bad offense, maybe four if they really get on base a ton, but realistically, with OBPs in the one-third range, three dudes) to just get on base whatever way possible, don’t care anything at all about how, and then starting with the next guy, a huge concentration of all the power in your lineup. Now, can you do that? Not nearly so much as you’d like. In reality you can’t split your points up to one guy who OBPs at .500 with all walks and another who clocks in at .150 but only mashes homers. Players are much more in the middle, and it tends to be that they do some of everything rather than being so specialized. Of course, if you have specialists, you can quite conceivably leverage them. I don’t know how much players can tailor their approach (my guess is not much while remaining roughly as efficient overall), but to the extent they can, this approach can be helpful, if a bit obvious.
As for the question of lineup construction, it’s probably better to have an unbalanced lineup than a balanced one, to the extent that you can get it. Once again, though, a fuller analysis will require a different method of looking at things. Watch for it here soon!

Edit: Can't get the charts to paste in correctly. Does anybody know a handy way of formatting things here? I'm writing these posts in a word document, and then the formatting is totally shot when I copy/paste it over - like paragraphs appear in random places, I can't get bulleting to work at all, and tables come out as a text dump. Any ideas on how to get around this?
Edit 2: On the site's suggestions, I switched to the 'new interface' which seems to work fine, at least for the tables and bulleting. We'll see about the other stuff when I do the next post, soon.