Of the many topics discussed in The Book is lineup optimization; essentially, the degree to which teams can extract extra runs throughout a season through better lineup construction.

The general consensus seems to be teams don’t do a great job at optimizing lineups. But the gains from proper optimization aren’t that great, anyway.

That being said, I was curious whether there’s evidence for league-wide changes in the ways players are deployed throughout lineups. Given the statistical research in the past few decades, is the league any more in line with setting lineups with the expressed idea of simply avoid outs?

Back in 2009, Sky Kalkman wrote a great piece at Beyond the Box Score about how teams should optimize their lineups based on The Book’s findings. Sky summed it up nicely at the end, with regard to on-base percentage (OBP):

Another way to look at things is to order the batting slots by the leveraged value of the out. In plain English (sort of), we want to know how costly making an out is by each lineup position, based on the base-out situations they most often find themselves in, and then weighted by how often each lineup spot comes to the plate. Here’s how the lineup spots rank in the importance of avoiding outs: #1, #4, #2, #5, #3, #6, #7, #8, #9

OBP isn’t the only way you organize your lineup — you need to take into account the ability to hit for extra-bases — but generally speaking, optimizing a team’s lineup is about which positions should be occupied by hitters with a the highest penchant for avoiding outs.

To depict this visually, I created a heat map of the optimized batting order Sky cited and then showed the actual rank of each batting order position aggregated by year. Darker green correlates with the highest rank; dark red correlates with the lowest rank:

In 1995, the OBP for the leadoff spot ranked third among all nine batting positions. Three-hole hitters earned the highest OBP, while two-hole hitters came in sixth.

The pattern that jumps out is how consistently managers placed their best one or two hitters — in terms of OBP — in the third spot in the order. Sky suggests that a team’s fifth-best OBP hitter should hit third, but in reality, this is never the case. League-wide, three hitters are overwhelmingly the highest OBP hitters. The three-spot has an average of 1.2, followed by clean-up hitters at 1.9, lead-off hitters at 3.5 and five-hole hitters at 3.9. The difference between what Sky suggest the OBP rank for three-hole hitters should be and what we actual observe by far the largest of any position (3.8). In reality, the biggest issues are found with the top three spots in the order, as the difference between the optimal rank and the average rank is below .5 in spots four through nine. This shouldn’t be surprising.

No. 4 hitters experienced a few odd years, specifically from 1990 to 1993. During that time, those hitters’ OBP rank varied between third and fourth. Outside that, though, they varied between first and second. Five-hole hitters jumped around quite a bit, despite the fact that their average rank was basically the same as Sky’s recommendation. That being said, No. 5 hitters’ OBP generally ranked third, fourth or fifth in every year except for 1998 and 2007 — when the position ranked sixth. Basically, the range of their variation was pretty narrow.

The biggest issues are in the top two spots. Leadoff hitters have never ranked above second in OBP and they only did that five times (the last was in 1993). There was a string of four years where leadoff hitters ranked second (from 1990 to 1993), which coincidentally, was the same four-year stretch in which the clean-up spot ranked outside the top two. Since 1993, the leadoff spot has put up an average rank of 3.7 in OBP — basically, the league is still significantly devaluing out avoidance at the top of the order.

The No. 2 spot has varied considerably from The Book and from Sky’s analysis. Theoretically, you want the two-hole to be the third best at avoiding outs. In practice, they’ve been about the fifth best and have varied between third and sixth since 1974. As with the leadoff spot, it seems to have only gotten worse. No. 2 hitters haven’t ranked better than fourth since 1992; the average rank is fifth. This includes being the sixth-best (or fourth-worst) spot in 2012’s batting orders when it came to avoiding outs.

At an aggregate level, the league hasn’t learned much. The best hitters at avoiding outs are primarily hitting third, while lesser on-base hitters occupy the first and second spots. If we looked at this by team, I’m sure we’d see greater variation. Perhaps some teams recognize the advantage (however slim) of placing greater value on out-avoidance at the top of the order? Still, the league-wide data make clear that those teams are in the minority.