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Comparative Advantage: A Theory of Trade

Posted By Noah Isaacs On October 18, 2011 @ 2:40 pm In Daily Graphings,Giants,Mets | 46 Comments

With the season nearing its end (and my team out of the playoffs), I believe it is time to start thinking about the offseason, and more specifically; trades. Trading is something that has been deeply studied in economics and international finance and it may be informative to employ economic theory to baseball. The law of comparative advantage is one such theory, and I am going to try and apply it to baseball in away I haven’t yet seen.

 Assumptions:

1) Teams try to maximize both the number of pitchers and hitters that they develop over a given time period.

2) Some teams do in fact have a comparative advantage over other teams in “producing” (scouting and developing) hitters or pitchers.

3) For simplicity, in the example all pitchers are of equal value and all hitters are of equal value.

4) There are no transaction costs

Example:

Lets focus on trade between two teams. One team, lets call them the Giants, are very good at developing pitchers, while another team, lets call them the Dodgers, are fairly mediocre at developing both pitchers and hitters. For every million dollars spent, the Giants can produce 7 Pitchers or 3 Hitters (over a five year period) and the Dodgers can produce 3 Pitchers or 2 Hitters (over a five year period).

Productivity (over 5 years) Giants Dodgers
Pitchers 7 3
Hitters 3 2

Both Teams have decided to invest $10 million in player development. The Giants, hoping to have some balance in their production invest $7 million in Hitters and the remaining $3 million in Pitchers. The Dodgers apply a similar approach, and invest $4 million in Pitchers and $6 million in Hitters.

Productivity (over 5 years) Giants Dodgers Total
Pitchers 21 12 33
Hitters 21 12 33

Here we can see that the Giants have an absolute advantage over the Dodgers, meaning that they are more efficient in producing both hitters and pitchers. At a glance it may appear that the Giants are therefore best off not trading and solely relying on their superior player development, but this is not the case. Specialization and trade will always* improve the outcomes for both teams when compared to not trading at all.

When it comes to trading, absolute advantage is meaningless. Relative or comparable advantage is what counts, and we can measure relative advantage by looking at the opportunity costs associated with producing Pitchers and Hitters for each team. Below is the same table as the first, but this time I have included the opportunity cost of producing one unit of either Pitchers or Hitters in parentheses.

Productivity (over 5 years) Giants Dodgers
Pitchers 7       (3/7 = .43) 3       (2/3 = .67)
Hitters 3       (7/3 = 2.33) 2        (3/2 = 1.5)

Here we see that the opportunity cost for creating a pitcher is .43 hitters for the Giants and .67 hitters for the Dodgers. Similarly, the opportunity cost for creating Hitters is 2.33 pitchers for the Giants and 1.5 pitchers for the Dodgers. The lower the respective opportunity costs, the greater the relative advantage for each team. We can then deduce from the table that the Giants have a relative edge producing Pitchers (.43<.67) and the Dodgers have a relative edge producing Hitters (1.5<2.33).

Using this information, we can now determine the optimal trade strategy. The Giants should focus more on pitching than they did in the past, and the Dodgers should focus entirely on hitting. Then, they should trade and reap the benefits. Here is how it looks; The Giants spend $5 million hitters and $5 million on pitchers and the Dodgers spend their whole $10 million on hitters.

Productivity Giants Dodgers
Pitchers 35 0
Hitters 15 20

Then, the trade would be as follows:

Productivity Giants Dodgers Total
Pitchers 35 (Trade away 13) 0 35
Hitters 15 20 (Trade away 7) 35

The Giants would happily trade away 13 Pitchers for 7 Hitters, and the Dodgers would gladly accept such a deal, as they both benefit from such a trade. In parentheses are the results before specialization and trade

After Trade Giants Dodgers Total
Pitchers 22         (21) 13         (12) 35         (33)
Hitters 22         (21) 13         (12) 35         (33)

It is important to note that this is an extreme case, and that often times a trading partner will not have an absolute advantage. In cases where there is no absolute advantage, specialization and trade become far more profitable.

This is all very interesting (to me), but the real question is what are the implications. What can we glean from the rule of comparative advantage? For one, I think that GMs should focus more time, money and energy on what they excel at and trade for the positions that they struggle to develop. This is not to say that they should give up on a position, but merely shift their focus.

More importantly, I think that this example should at some level change the way we view trades. In July, the real San Francisco Giants traded away a young stud prospect pitcher by the name of Zachary Wheeler to the New York Mets for Carlos Beltran. At the time of the trade I was very upset (as a Giants fan), thinking that two months of Beltran would not be worth giving up the tremendous potential of Wheeler. After reviewing this trade through a comparative advantage lens, I feel much better about the trade (though still not happy). It is far easier/cheaper for the Giants to replace a Wheeler, than it would be to produce a bat of Beltran’s level (even if it was only for two months). The Giants and all other teams with a comparative advantage in developing pitchers (Braves and friends), should focus on developing pitchers and trading their prospects for hitters. The advantages of specialization and trade are real.

 

 

*When there exists a comparative advantage

Note: The production numbers are arbitrary and are solely for the use of the example


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