Microeconomics and Offense (Part 3)
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.
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“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.”
Of course, by changing the scale, you could change this appearance. Is there an obvious way to normalize ISO and OBP as some function of “labor” and “capital” availability/cost?
“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.”
This is a neat and, in my mind, unintuitive observation. I would think the effects of sequencing would create an amplifying effect, particularly with OBP. For example, a team that has 10 men on base in a game is more expected to score more than double the number of runs of a team with 5 MOB. I’m surprised this isn’t observed in wins vs obp.
If the scale were more square, i.e. each dash were equidistant and represent a change of .01 OBP and .01 ISO, then it would actually be more obvious that the curves are slanted more horizontally than vertically.
But it doesn’t matter whether the dashes are equidistant–what matters is the “real” x-y relationship. Moving one point in OBP is not necessarily equally as substantial as moving one point in ISO, and I would almost guarantee you that it’s definitely not.
Erik’s right: to draw a conclusion about elasticity based on the curves you need _both_ proportional perspective _and_ a standardized version of both variables.
Yeah the scaling is a problem, but evenly correctly shown, it would still be that OBP is more “elastic” as the term is used here. This is known intuitively by users of this site who know that OPS undervalues OBP, which is why we use wOBA.
What would be more interesting is to show elasticity as a function of how much the skill costs on the open market. So for example say that upgrading your team OBP by costs you x dollars for every point, while ISO costs x per point. Then you can see who assembled offenses more efficiently.
For example, perhaps Toronto realized that the cheapest way to score runs was assembling a team with tons of HR hitters rather than patient types. With dollar values we could how much ISO it would cost them to move up in OBP, and if it was a worthwhile tradeoff. I smell Microeconomics of baseball Part 4!
I would love to read the next article if it can give a proportional graph of ISO to OBP and push it even further while incorporating real dollar costs.
At worst you’ve given me something to think about Uday
+1
Fascinating series.
Good job! Apply the production function concepts to baseball are something I have thought about in the past, but never taken the time and effort to work through.
Two great stats that were both brought into use by Branch Rickey, excellent approach.
Dangerous to draw conclusions on elasticity without normalizing the axis by marginal cost to move in each direction. An interesting proxy might be scaling teach axis to have the same standard deviation.
I think you mean to say that because the isoquants are closer to each other near the origin we have decreasing returns to scale. The curvature of the lines does reveal that there are diminishing marginal rates of technical substitution.
What were your OBP and ISO elasticities? Their sum must be less than one.
Neat.
Now I think you should use salary data to estimate the cost of OBP and ISO. Simply do something like estimate Salary = a + b1*OBP + b2*ISO + other stuff. Do another regression that includes an interaction term OBP*ISO, which I’d guess is statistically significant and, unfortunately, complicates the analogy to a firm choosing separable inputs. You’d get iso-price curves (budget constraints) shaped similarly to your isoquants. Who knows, maybe Toronto happens to be exploiting such a market feature. They did have almost identical 2010 payroll as the Washington, Cleveland, Florida, and Royals!
This is much better than the previous ones. One thing: you need to worry more about outliers (SEA, NYY, TOR). the Jays are probably a very influential point. I’d run the regression without them. I’d also try removing SEA and NYY to see if the results are the same. Also, when projecting the Jays value, the model is probably least appropriate. After looking at this, and given the impressive R-squared, I think I could say with good confidence what a change in runs would be for adding this or that player to a team. However, I don’t see that for the Blue Jays. There, I’d say they are so far from the rest that the results can not be predicted.
Quick question regarding this:
“A team looking to increase runs per game could get to the next highest isoquant quicker going due East than due North.”
If we’re assuming that you can increase in both categories linearly, wouldn’t it be easier to increase your ISO to get to the next level? For example, let’s say my OBP was .295 and my ISO was 0.07 (the bottom left). If I increase my ISO to about 0.08, I can get into the 3 run/game range, whereas I’d have to increase my OBP more than 10 points.
No, you’d only be increasing your OBP by 0.010 points.
The statement that you would improve “quicker going due East than due North” is counter-intuitive on this graph, as the graph it is skewed in a way that seems to show the opposite is true.
Thats because the graph’s x axis (horizontal) spans 0.060 points, while the y axis (vertical) spans 0.140 points.
To exacerbate that issue… distance between points is greater on the x axis than the y axis.
So, the statement is accurate, but the graph seems to show the opposite.
Love to see a part four that includes the monetary value to increase .001 OBP vs. .001 ISO based on the current market and how a team would best find value in this manner (ie if OBP cost $3 Million to increase .005, and ISO $3 Million to increase .004, where is the best deal?)
How would this look if plotted to represent team defences?
The trade-off is the interesting thing. Because guys who can put up a .300 OBP and hit 30 HRs are relatively cheap (see Toronto) and guys who can put up a .370 OBP and a .040 ISO are also really cheap (see Oakland), but guys who can do both are exponentially more expensive.
I definitely think the Jays are exploiting the market. I’m just not sure if it was on purpose.
It seems like the next step would be to plot the Engel Curve.