Comparative Advantage: A Theory of Trade

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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46 Responses to “Comparative Advantage: A Theory of Trade”

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  1. John says:

    These seems a bit to oversimplified for me. Teams may have a slight comparative advantage in developing a certain type of player, but it is probably going to be insignificant considering that resources for “producing” players are mostly spread out throughout the league.

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    • Noah Isaacs says:

      It is overly simplistic (by design). Trade can become very complex very quickly. The example was merely to show that it can informative to think of trades through a certain vantage point. I plan on diving deeper into this idea later, and would be happy to hear ideas for further exploration.

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  2. bender says:

    The issue I see here is the one of “No Transaction Costs”, in that if a team has a clear surplus of one thing and a clear shortage of another, then when they attempt to trade odds are that they won’t “get their money’s worth” so to speak

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  3. Boomer says:

    Interesting stuff.

    You are using a Ricardian framework but might do better to try a Heckscher-Ohlin or Stolper-Samuelson model. The Ricardian model does not encompass “winners” and “losers” on either side; both nations benefit from trade unequivocally (but not equally), when in real life I think we can probably agree that sometimes teams do lose in trades, at least to the extent they weaken their player stock (i.e., labor) or their salary budget (i.e., capital).

    http://en.wikipedia.org/wiki/Heckscher%E2%80%93Ohlin_model

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    • Noah Isaacs says:

      I will definitely take a look at the other models. I am not an economist by trade, so these suggestions are really helpful. Thanks.

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      • Boomer says:

        BTW, taking this to the logical conclusion, you would expect to have poor teams producing lots of cheap middle-relievers and #5 starters (low capital-intensive) and rich teams producing power hitting corner infielders and ace SPs (high capital-intensive).

        The other thing to consider is that MLB has a dispensation to engage in a monopoly, so the lack of ability for others to enter into “production” of players and baseball capital could shift the dynamics away from a vanilla free trade model. That could lead you to adding some micro concepts to the overall macro model.

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      • Barkey Walker says:

        Boomer,

        First, MLB has no waiver. Look it up.

        Second, I don’t remember the Nats putting lots of capital into Strasburg.

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      • Fred says:

        The signing bonus is capital.

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      • Boomer says:

        Barkley, sorry if I don’t follow. What does waiving have to do with this topic?

        As Fed says, I was considering singing bonuses and development costs as capital expenses. Besides, this is a trade model, not a drafting model.

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  4. Frank says:

    So in other words, do as AA does. In his case, he stocks the farm with high-upside pitchers who are developed well by the organization, and uses them to trade for bats.

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  5. Tyranitar says:

    Ah basic microeconomic theory, this article really takes me back. I love the idea, what is the next step you are planning in your investigation?

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  6. Rob says:

    Really interesting article. While I completely buy in on the theory behind this, one important aspect that it ignores is the ability of certain organization to evalute hitters or pitchers more efficiently than others, instead of just developing them. You mention the Braves as one of the organzations that is good at developing pitchers. However, I’d argue that they are really very good at evaluating pitching talent, as evidenced by some of their recent trades to bring in quality pitching prospects (Jurrjens was practically stolen from Detriot for one-year of Edgar Renteria, while Arodys Vizcaino was acquired by trading the Yankees one-year of Javy Vazquez). So given that the Braves are great at evaluating pitchers, but not as good at evaluating hitters, I cannot figure out how they can leverage that through trade, since what they need (hitters) is the thing that they have a lower success rate at evaluating.

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    • Boomer says:

      In this model, since they have a comparative advantage in producing pitchers, they would trade pitchers for hitters at the MLB level and have an all-pitching farm system. Probably they could do a joint venture with a team that has a comparative advantage in producing hitters and thereby field an entire team that also maximizes each of their respective advantages.

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    • Noah Isaacs says:

      I was using development loosely. You are completely right. “Production” should be seen as the aggregate of development and evaluation. They go hand in hand.

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  7. Ryan says:

    I hope Frank Wren read this article.

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  8. JP says:

    This is interesting, but I have some issues/questions that would undermine the usefulness of this approach in analyzing trades, and in informing teams’ trade strategies.

    For one thing, even if a franchise’s farm system has a lot of success promoting big league pitchers or hitters, we could just be seeing the product of chance. This is especially so when we’re talking about something as volatile and unpredictable as the MLB draft. Are the Giants really “better” at “producing” pitchers, or have they just gotten lucky with pitchers in the draft (or unlucky with hitters)?

    Second, it is odd to talk about “creating” a pitcher or hitter. My sense is that over any stretch of time that would be relevant for draft/trade strategy purposes (several years) there is a fixed pool of talent. Teams cannot “create” more talent. They might be better or worse at fostering that talent, but there are real world limits on the extent to which a team can “produce” a big league pitcher or hitter. Probably no amount of coaching can fix a player without the latent ability.

    Also, even if fecundity of a franchise’s farm system is the result of skill and not luck, how do we know that it’s not skill in drafting talented players, as opposed molding raw material into big league-ready players? To the extent that is the case, then spending on “player development” might be a waste anyway. Maybe a front office should then draft more heavily based on it’s relative area of strength. But again, even here it’s not clear this would create any benefits. Perhaps a team brings up better pitchers because the team’s scouts are particularly good at assessing pitching talent. Again, talent is finite, and good scouts can’t “create” more good prospects.

    This is a nice exercise, but I’m not sold on any real world application without resolving these concerns first.

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    • Boomer says:

      You need to assume that any player drafted in a reasonable round (say first 20) has the raw talent to be a MLB players. That doesn’t seem like a massive reach, since there are players who become superstars even from very late rounds (Pujols, Piazza).

      You also need to believe that players are made, not born. There seems to be some pretty good evidence for that in looking at Dave Duncan and Dave Righetti’s work. If you have a farm system stock with Duncan clones, it seems possible to think that you can turn out MLB pitchers better than anyone else.

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      • JP says:

        I actually do think that it’s a reach to assume that any first or second round pick has the raw talent to be a successful big league player. There are TONS of 1st/2nd rounders who never have long careers in the majors, and I doubt that’s just for lack of quality coaching and development. Those guys probably just did not have the talent the scouts thought they did.

        I’m sure players are both made and born. There is clearly some mix of nature/nurture. However, to whatever extent players are made, a lot of that process probably happened before the prospects even enter the minor leagues. Think how many hours of practice and playing a 20 year old already has under his belt by the time he is drafted. Just as an example, with the Giants, it was Tim Lincecum’s dad who helped him develop that freakish delivery, not the Giant’s minor league coaches. They may have tweaked him here and there, but the vast majority of the “nurturing” it took to mold Lincecum into a nasty Cy Young winner was done before he was ever drafted.

        I think it’s likely that teams are not uniform in their ability to mold talent. However, I am more skeptical as to how disparate the ability really is. I’m also not sure how you can distinguish between good drafting (identifying latent talent) and development (molding that talent).

        To the extent that success at churning out big league pitchers or hitters is a result of good drafting, then trying to “create” more hitters or pitchers might be futile. Good scouting means spotting the best talent. Maybe the Giants scouts were good enough to recognize the talent of a Tim Lincecum, but they can’t create more Tim Lincecum’s to draft. Teams could probably tinker at the margins, say if they are undecided between a hitter and pitcher, perhaps they’ll err on the side of the pitcher if they’ve had success in the area.

        Also, how much do these minor league coaches get paid? If they’re really playing a large role in creating quality MLB level players, they are providing HUGE value to their franchises, by providing players at sub-market salaries. Maybe the minor league coaches deserve some raises?

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    • Noah Isaacs says:

      I edited Assumption 2) to “Some teams do in fact have a comparative advantage over other teams in “producing” (scouting and developing) hitters or pitchers.” I hope this makes more sense. This is in line with what I was trying to convey.

      As for your other point about randomness, The Giants’ success could purely be noise, but I think it is more likely that teams are not perfectly uniform in their scouting and developmental skills.

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    • ettin says:

      I think there is some randomness in how the pitchers/hitters develop but I do agree with Noah that some teams are better at developing pitchers and/or hitters than others, for example:

      San Francisco, Atlanta, Tampa Bay, and Oakland seem to consistently produce quality pitchers through their farm systems. To a lesser degree the Angels, Phillies, and Mariners also have a comparative advantage as well. On the other side you see teams like the Yankees, Marlins, Texas, etc… develop better hitters.

      Consistent scouting and picking help raise the level of quality prospects produced.

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    • Telo says:

      TLDR is appropriate for too many FG articles… but not this one!

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    • LTG says:

      There is always ESPN if you are looking for short, superficial analysis.

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      • Josh says:

        To be fair, this was just a joke. I’m Noah’s brother and have read every iteration of this article, going back a few weeks. So when I said tl;dr I was just continuing a pattern of belittling my little bro’s excellence that has gone on for decades.

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  9. Telo says:

    Here’s some spitballin, playing devil’s advocate. Really liked the piece, by the way.

    Assume an imperfect (read:realistic) but presiding entity that ranks all minor leaguers and prospects (aka BA) has ranked your pitching prospect as a B and another team’s hitting prospect as a B. On the surface a trade for these players appears equal (assume BA valued them equally). But in reality we should assume that you have better information of your own players than of other players around the league, and also better information of your own players than anyone else. Your biggest advantage in trading is the unique information you have of your own players.

    Put another way, if I gave you a list of prospects that looked like this:

    Player A: Projected as a 4th starter, 4.00 career FIP, 90% confidence
    Player B: Projected as a 4th starter, 4.00 career FIP, 60% confidence
    Player C: Projected as a 4th starter, 4.00 career FIP, 30% confidence

    You would take Player A all day (don’t assume less confidence in the 4th starter projection means a possibly higher ceiling).

    My point is, more trading dilutes the information you have of your own assets. And in the game of developing prospects, information (traditional and saber) and confidence levels of your projections is everything.

    Just a thought. Also have some more thoughts will post in a few.

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  10. Matt says:

    Very interesting. I enjoy seeing economics being used in non-typical situations (That’s what drove me to study it in college). That being said, I’m not sure that international trade models are the best comparison. It doesn’t take into consideration the ultimate goal of the parties involved. In the end, they are competitors. Because of this, it may be more beneficial to use a model for an oligopoly, like the Cournout Model.

    On a little side note about your model, with the current example you have, you must take into consideration the comparative value between a pitcher and a hitter.

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    • Boomer says:

      I think it’s a hybrid, because most MLB teams don’t compete in the economic field. Unless you have two team in the same market space, each team has a distinct fan base and revenue sources. TV and 2-team cities complicate things, but there is enough of a macro flavor that I think starting there is interesting. Even 2-team cities are in different leagues and don’t compete on the field that often.

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  11. Scott Myers says:

    Great article, well thought out.

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  12. In a sense there are very real transactions costs though, so I sort of take exception to the #4. While there is no cost imposed by MLB, there are very real and very different costs associated with players and the terms and length of their contracts.

    Taking the commonly mentioned Vernon Wells trade, if all things were equal salary/contract wise – at the time of the trade (hindsight makes this one look even worse) one could argue that the trade was not so one-sided. It is the addition of the salary/contracts that made the deal so laughable. That the Angels were accruing so much cost, while giving up a high level of talent as well.

    To me the contracts and their ramifications make a lot of difference. In your example, while Wheeler is comparatively not such a loss to the pitching rich, and pitcher-development enabled Giants, compared to their anemic offense and presumed inability to develop hitters, one has to say that Wheeler isn’t a “random pitcher” and that much of his appeal to the Mets is his lengthy years of control at a very diminished cost.

    In fact many baseball trades are made in some ways more due to contract and salary issues than as related to talent levels, so I think there are very real and tangible transaction costs, even if they don’t fit the traditional economic model of transaction costs being the R/D, the act of going to get a product, etc. Whereas in economic theory if you bought a car in Texas because it was cheaper, the transaction cost would be the cost of needing to go to Texas versus your local dealer, in baseball transactions its an after the fact cost of retaining the “purchased” or “bartered” product.

    Great article though and I think it touches upon an often overlooked part of trades which is that some people are more valuable to one team than another due to what they have in their organization.

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  13. Joe says:

    You can apply this philosophy to your own life; there’s actually a lot more focus on leveraging strengths and ignoring weaknesses, rather than seeing your least favorite subjects as “opportunities”.

    Essentially, you’re going to figure out what you like and what you’re best at before long, and there probably won’t be very strong returns from spending resources (money, time, effort, stress, etc.) on other things. The post on the Braves’ ability to find pitching exemplified this to me – why should they change their strategy? It’s kept them competitive for two decades.

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    • Boomer says:

      I agree with your point to some extent, but be careful to distinguish absolute advantage from comparative advantage. This sounds like absolute advantage, which is not what drives the Ricardian model.

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  14. Jason says:

    As someone who applies these types of theories in a business context, I think your idea is spot on. Does it make sense that teams could become expert in developing one type of product — e.g., pitchers? Absolutely! Be it through scouting, development, minor league ballparks, etc., it stands to reason that a team could focus its resources on one area, and that doing so might yield a competitive advantage in that area. And as you point out, the availability of trading partners makes this approach feasible.

    Seems like Strategy 101. Of course, as a Mets fan, I’m more familiar with strategery, so you probably can’t take my word for it…

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  15. Blue says:

    Nice article. The problem that I have with it is that baseball is zero sum game–the number of wins in a season is finite and defined. It may be more important to prevent wins on another team than to gain marginal wins on one’s own team, particularly for divisional rivals like the Giants and Dodgers.

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    • Noah Isaacs says:

      True, it is a zero sum game, but it is also easy to see that both teams could invest less, save money, and still produce the same number of pitchers and hitters as they did with no trade.

      Also, I am not suggesting that the Giants and the Dodgers should be trade partners, I (as a Giants fan) just wanted to point out the mediocrity of the Dodgers.

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