# Microeconomics And Offense (Part 1)

In Microeconomic theory, there are two factors in production: capital and labor. Labor is the manpower used to create output, and capital is the machinery and technology that makes that labor work more effectively.

At its core, there are two main factors in scoring runs: getting runners on base and knocking those runners in. By looking at these skills as capital and labor it reveals much about each team’s offense, and can give insight to where a team needs to invest.

True, there are other elements to a team’s offense that contribute to scoring runs, stealing bases for example, but there simply is no substitute for setting the table and knocking runners in. These two variables explain 94% of the variance between teams in runs per game in the majors last year.

In this two-variable system, maximizing output depends on finding the optimal mix of these two inputs, given a budget constraint. The key concept is that there are diminishing returns for both inputs, and therefore it is inefficient to continually spend on one or the other. For example, it would be inefficient to have one worker try to use a warehouse full of machines, and likewise it would be inefficient to have 50 workers waiting their turn to use the company’s one machine. The optimal allocation will be some combination of the two inputs.

What this all means for baseball offense is the theory that a team with good lineup balance will score more runs than a team full of leadoff-hitters or a team full of power hitters. A team looking to improve their offense will get more return for their dollar if they find the right type of player. Toronto, for example, will get more return from a top of the lineup table setter than they would out of another middle of the lineup slugger. Why? Because the Blue Jays led the league in clearing the bases last year, but the bases were just not occupied enough.

The blue lines in the above graph represent the league average. To no one’s surprise, Baltimore, Cleveland, Oakland, and Seattle lie in Quadrant II; below average in both categories. Seattle again shows us just how historically bad its offense was in 2010. The Mariners are not just far away from the other data points, they are on their own island.

Quadrant IV contains teams that were above average in both categories: Chicago, Tampa Bay, Texas, New York, Boston, and Minnesota. The Yankees led the league in runs per game by a quarter of a run, and that distance is shown quite nicely in the graph.

Quadrants I and III are where the interesting analysis lies. Kansas City and Detroit fall into Quadrant I, as they were above average in OBP, but below average in strand percentage. These teams were good at setting the table, but too often left runners on base. In the theory of capital and labor, these teams would get a good return on an investment in a run producer. True, the Tigers have Miguel Cabrera, but this graph shows that having Brennan Boesch and Carlos Guillen follow him in the lineup is holding Detroit back from reaching its offensive potential.

Quadrant III contains Los Angeles and Toronto. These teams were above average at clearing the bases, but below average at getting players on base. The Blue Jays are an interesting case. They show the potential to be the league’s top offense if they could more efficiently get on base. Toronto has a decent middle of the lineup with Jose Bautista, Aaron Hill, Vernon Wells, and Adam Lind, but they are handcuffed by the lack of a good leadoff hitter. Fred Lewis and DeWayne Wise simply did not get it done.

More thoughts on this concept next week and a look at the National League.

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Only intermediate micro has two inputs and attempts to make reference to everything in terms of capital and labor. Once you start talking about production functions at an advanced level, you assign shares to different types of capital.

There are very specific, arcane reasons why something like a Cobb-Douglas is used in economics. To put it simply, it’s so you can preserve certain things economists find important while making it mathematically tractable. Those things are unlikely to be the ones people care about in baseball.

What you’re saying seems to apply to 1960s-1970s macro more than modern micro. Those models did boil everything down to micro and macro. However, contrary to the point I think you’re trying to make here, the most prominent of these models, the Solow growth model, says what really matters for economic growth is the effectiveness of the use of capital and labor (generally thought to be “technology”), not the growth rate of labor and capital (power and OBP) themselves.

I was thinking the same thing. I’ve never seen a microeconomist use Y = K*L type equations, only macroeconomists.

Also, isn’t using OBP and strand rate to predict runs a bit like using ERA to predict runs against? The 96% correlation suggests this is near definitional.

A Cobb-Douglas production function, which is a generalized version of what you just wrote, is commonly used in micro.

Ironically, however, to solve such a maximization problem, an economist would take the natural log of the function. A Cobb-Douglas would often be Y=K^(alpah)*L^(1-alpha) where alpha is between zero and one. If you take the natural log, you get ln(Y) = (alpha)*ln(K) + (1-alpha)*ln(L).

When you look at it that way, all of this economics stuff simplifies to a kinda pretentious version of linear weights.

Footnote: the reason why taking the natural log is permissible is because what economists care about is just the point which is profit (or utility) maximizing, not necessarily the value of the profit, because logarithms are monotonic functions. After you figure out the optimal values of capital and labor, you can then reinsert them into the original equation and find out whatever else you care about.

Yeah, that is what used in intermediate micro classes. But I’ve never seen a microeconomist use it in anything but teaching intermediate microeconomics. I have seen tons of macroeconomists use it for their research.

“Yeah, that is what used in intermediate micro classes. But I’ve never seen a microeconomist use it in anything but teaching intermediate microeconomics. I have seen tons of macroeconomists use it for their research.”

Cobb-Douglas functions are used all the time in empirical micro papers, but in the log-linearized form that darsox64 mentioned.

I enjoyed the post, irrespective of the drill down. Solow Growth models are Macroeconomics, FYI.

duh.

“What you’re saying seems to apply to 1960s-1970s macro more than modern micro.”