December 23, 2014

Baseball Therapy

Do Stars and Scrubs Lineups Actually Work?

by Russell A. Carleton

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Is it better for a team to have a lineup with a couple of star hitters in it (and several not-so-good-ones), or to have nine guys who are all good-but-not-great? This is the classic balance vs. stars-and-scrubs debate. It’s a nice debate, but studying the answer has proved a bit of a challenge. We can study actual teams and see how balanced their rosters are then study their results. The problem there is that there aren’t many teams who have uniformly good players, but there have been a few who have uniformly mediocre ones. Teams that have a great diversity in their roster probably have a few good players. It’s a tough problem to get around by studying real life.

The idea behind a stars and scrubs lineup is that teams can do the obvious and bat the good players at the top of the lineup, thus giving the good hitters more chances to hit. But then, it also means that you have a few awful hitters at the bottom, likely bunched together. Surely, that’s going to take the wind out of a team’s sails? Three easy outs in a row equals the end of an inning and you only get nine of them.

The general consensus, to date, has been that a stars-and-scrubs approach gives a team a slight advantage. I decided to take a proper look.

Warning! Gory Mathematical Details Ahead!

Because there are so many confounding variables in studying actual teams, I decided to pull out the lineup simulator again. I’ve built a Monte Carlo Markov-style lineup simulator, which basically models baseball games the way that a dice-roll board game would. It’s not perfect, because there’s no room in there for pitchers altering their approach based on the fact that there are three easy marks up this inning and saving energy for the top of the lineup. But it will at least give us some idea whether there’s a structural advantage to the Stars and Scrubs approach.

To control for the problem of teams having varying levels of talent overall, I began with a team that was nine cloned versions of the average 2014 American League hitter. Last week, I ran 100,000 simulations and found that team scored 4.201 runs per game. Then, I took the leadoff spot and made the leadoff hitter 30 points worth of OBP better. I reduced his out-making event percentages (strikeouts and outs in play) proportionally to how often they happen. Strikeouts accounted for about 29 percent of out events, so I reduced the leadoff hitters strikeout rate by .009 (.29 * .030). I upped his walk, HBP, single, extra-base hit, and home run rates in a similar manner. I took the no. 9 hitter and reduced/increased his inputs by exactly the same amounts. In this way, we keep the overall level of talent on the team the same. If this lineup were required to have all nine hitters bat 1,000,000 times, we would expect the same numbers of all events for both lineups as a whole. However, they are not. Batters hit in a certain order and the ones at the top get more chances. We want to know the structural effect.

I pushed the envelope a bit more after that. I made the top two hitters really good (and the eight and nine hitters really bad, and the three through seven hitters all remain perfectly average). All lineups got 100,000 simulated games.

I wouldn’t go to the mat for the last decimal place on these, but the trend line is pretty clear. Making a team more unbalanced has a small upward effect on a team’s run scoring, ceteris paribus.

But Wait There’s More!
Now, this just looks at the effects of an unbalanced vs. a balanced lineup. It doesn’t consider defense. It doesn’t price in the fact that stars and scrubs teams, somewhat by definition, have a greater risk level associated with them. What if one of the stars gets hurt? It’s a bigger drop off from a star’s performance to a replacement level performance than from average to replacement level. Also, this ignores the question of cost-efficiency. A stars and scrubs lineup might be more productive in an absolute sense, but if it costs more to build, then the team will have less to spend on its pitching staff and might be worse off in the long run.

But for what it’s worth, that structural effect that the stars and scrubs lineup looks to take advantage of is worth roughly half to three-quarters of a win. Once again, not nil, but something that can probably be overwhelmed by simply making sure that you have better players on your roster. Once again, we find another strategic ploy that has a small effect size. The inputs into a lineup are much more important than the manner in which they are used. There’s little point in teams specifically trying to build a stars and scrubs lineup.

Now that we know this, there’s an interesting corollary. One of the big arcs in Sabermetric research was the idea that somehow, we might find an empirically optimal structure for a team’s roster. Or at least a series of recommendations that are better than the alternatives. Something beyond “Get good players.” Such a thing probably does exist in the sense that one strategy is bound to be better than the others, but in terms of ROI, it just isn’t that big a deal. Instead, we also know that players can show large shifts in their talent level, even over the course of a season. We also know that managers seem to be able to have an effect that is just as (or more powerful) just in terms of their ability to help players not get worn down by “the grind” over time. Instead of trying to figure out the optimal configuration of a roster, maybe it’s time to spend more time on how to get the most out of the players already on the roster. The question of whether stars and scrubs works should give way to how we can get Smith feeling (and hopefully hitting) like a star.

Russell A. Carleton is an author of Baseball Prospectus. Follow @pizzacutter4
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