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February 24, 2005

Crooked Numbers

More on the Lineup

by James Click

Last week's column about lineup order optimization generated a greater response than I anticipated, especially for one with such loose conclusions, so I'm going to dig a little deeper into the topic. So far, the only application of the lineup program has been checking various basic ideas--like sorting by descending or ascending AVG, OBP, and SLG and bunching of the better hitters--but there's a bit more that can be done before adding some more enhancements to the program to see if we can attempt to adjust for baserunning, steals, and platoons.

One of the more interesting questions left unanswered last week was just how important sorting by OBP or SLG is. By using two lineups for each metric--one in ascending order and one in descending order--it was clear that players with higher OBP and SLG should be near the top of the order. Sorting by absolutely the wrong way only changed the lineup output by 26 runs at the OBP mean and 13 at the SLG mean. Considering the sample size and the standard deviations, the results were close to statistically significant, but the confidence was not high. Thus, we could only loosely conclude that OBP is more important than SLG when determining a lineup order when all other factors are equal.

What was not addressed was the fact that teams often have to make the choice between the two. It's easy to choose to bat a player with a .260/.330/.500 line earlier than a player with a .260/.330/.400 line, but things become a little muddled with comparing something like .260/.310/.500 to .260/.360/.380.

To begin to take a look at that question, I put together a new team, but to keep things simple, this team only has three players. First up is Wily Mo Pena, the resident high-SLG, low-OBP sample point with a 2004 line of .259/.316/.527. Pena is the only player last year who slugged at least .500 with an OBP of lower than .320 in at least 300 PAs. Congratulations, Wily. Next is Luis Castillo, selected for his .291/.373/.348 performance last year. Castillo's OBP outpaced his SLG by one of the largest differences in the league, thus making him the perfect candidate for the high-OBP, low-SLG slot. Finally, we'll plug the last hole with Morgan Ensberg who comes in at an impressively league average .275/.330/.411. Though he is a little shy in the power department, Ensberg makes a nice "this porridge is just right" player between Pena and Castillo.

Each of these players was given three spots in the lineup and then all possible lineup combinations of these three players were run through the program (which runs each lineup through 1,000 seasons), giving us a sample size of well over a million seasons by the time things are all finished. The program outputs a minimum, mean, and maximum for each lineup. I also outputted the full results for the first 50 lineups to check standard deviations, all of which were between 39 and 41 runs. Of all the lineups, the highest mean runs scored was 834; the lowest mean was 816. Despite testing every possible combination with these three players, the range of means over the entire sample was 18 runs. There's just not that much difference.

Still, 18 extra runs can be hard to come by when shopping for players, so it's still worth looking into a little more deeply. For each player, I've averaged how many runs the team scored when they were in a given lineup spot. Here's what we've got: