*This is Part 3 in a series on Microeconomics and Offense. Part 1 can be found here and Part 2 can be found here.*

The next step in using microeconomic theory for baseball offense is to draw isoquants. These reveal a lot of characteristics of the dataset, and they are just plain neat to see on a graph.

An isoquant is a line that represents the various combinations of inputs that can be used to produce a given level of output. In this analysis, the two inputs are the abilities to put runners on base and drive runs in, and the output is runs per game.

Before the isoquants can be built, some variable manipulation needs to be done. On-base percentage is a great statistic to use in this analysis. It measures a definite skill, it is clearly important to scoring runs and is not very susceptible to luck. However, strand rate is not an ideal variable to use going forward.

Strand rate was used up until this point because it describes exactly what needed to be measured: the ability to score the runners that are put on base. However, for further analysis strand rate is not a great statistic to use. First, it is highly collinear to OBP, which will muddy up any regressions that use both stats. Second, some baseball researchers have claimed it is a luck statistic. This analysis is not aimed at proving nor refuting this claim, but will attempt to err on the side of caution. For these reasons, isolated power will be used to measure a team’s efficiency in driving runs in. ISO is a clearly defined variable, it is less collinear to OBP, and it adequately measures the skill of driving in runs.

In order to build the isoquants, the two variables of interest, OBP and ISO, were entered into a Cobb-Douglas production function, which measures the elasticity of each variable as it relates to runs per game.

It is important to note that it is not necessary to build separate models for the two leagues. There is no question that National League teams, on average, score less runs than American League teams. However, the reason for that difference is included in the model. In other words, the lower OBPs and ISOs in the NL are the reason why runs per game are lower.

Team data from the 2009 season was also included for added sample size. All variables in the estimated Cobb-Douglas function were significant at the 99 percent level, and the model overall had a R-squared of .90.

Based on the results of the model, isoquants can be built and graphed. Then, overlaying the data points of the 30 teams produces the following graph:

The blue lines are the isoquants. Each point on a line represents the combination of OBP and ISO which would produce that level of offensive output. For example, every point along the four runs per game line is a combination of the two independent variables that would produce about four runs per game.

These isoquants reveal that OBP has a much higher elasticity to runs than ISO. This is seen by the way the curves are slanted more horizontally than vertically. A team looking to increase runs per game could get to the next highest isoquant quicker going due East than due North.

The fact that these lines are curved at all shows that these two offensive inputs are compliments to each other. Moving Northeast on the graph would get a team to the next isoquant quicker than moving solely North or East.

Diminishing returns is also represented on this graph. The isoquant lines are closer to each other near the origin, and gradually get farther away from each other. For example, the 4.5 run per game line is closer to the 4.0 line than the 5.0 line.

The Blue Jays 2010 offense continues to facinate. They are clearly different than the pack of teams in the middle of the graph. In fact, they are farther away from the pack than the offensive powers Boston and New York. However, Toronto has a poor combination of OBP and ISO, and therefore they lie just ahead of the 4.5 runs per game line. It is easier said than done, but the Blue Jays have more to gain by moving East on this graph than any other team in baseball.

This graph is useful for diagnosing offenses like Toronto’s, but it can also be simply used as a predictor of offense. By simply plotting a team’s predicted OBP and ISO, it reveals an accurate prediction of a team’s offensive output.