Sunday, July 27, 2014

Marginals V. Averages: The Value of Billy Beane

[In what follows, Let Billy Beane = BB.]

in "Billion-Dollar Billy Beane", Benjamin Morris @skepticalsports @FiveThirtyEight calculates that BB could have saved the Red Sox about $50.7 million per year, 2002-2013. Sifting through the article, and noting in particular that Boston won 56 more games than Oakland over that period (Morris says 50), the calculation in the article goes like this:

For its wins, Boston spent $1.714B
For its wins under BB, Oakland spent $736M
Morris' estimate of average league cost of 50 more games is $370M.

So, $1.714B - ($736M + $370M) = 1.714 - 1.106 = $608M

According to Morris's logic and calculations, BB could have produced the same winning result for at least $608M less than Boston actually spent, an average of $50.7M per season over the 12 seasons. The "at least" qualifier is mine based on Morris's claim that BB is much better than average.

On this, Morris argues that the $2.5 million offer Boston made to BB prior to the 2002 season was a huge mistake since Boston could easily have offered BB far more than that to get him to move to Boston (Morris focuses on $25M as an offer nobody could refuse) and not doing so cost Boston hundreds of millions of dollars.

It is tempting to go after what Morris did but that is already being done by others in his comment section. And it appears a jolly time is being had by all. I find that a massive waste of server space even at near zero cost, but the wasted time and energy is more disappointing.

Here's the deal: What Morris did is based on a theory of GM pay counter to the most productive explanation of how pay is determined for GMs. His estimates are simply measuring the wrong things because his idea of how GMs get paid is off base.

Basing pay on cost differences would put GM hiring in the same setting as bidding on construction projects. And while it's tempting to use the construction analogy of "building" a team, that analogy is just wrong for baseball GMs. Here's why.

The final product after construction is pretty much certain but the costs of meeting specifications are pretty much known to the construction company, not the demander. So bidding it out has a chance of eliciting the efficient, least cost production of the specification. [I know there is a whole literature on how to structure bids and construction oversight so they achieve this but that bidding is best is not contentious.] Morris is essentially trying to show that the owners in Boston took a higher bid over a lower bid.

But GM services are not construction services and there are very good reasons why GM services are not put out to bid. Baseball production is not so easily predictable nor is it so easy to figure out why the best efforts of all involved can fall short of a goal. This is one reason the compensation process in this case can involve a share of ownership. In addition, since they already have massive accumulated data, and a current provider, the owners may know a lot about the rest of the costs. So rather than bidding out the GM job, owners estimate the value they hope to obtain at their most profitable level of team quality and count on competition over GM talent to bubble up the candidates most likely to achieve that goal. But because of risk over the actual outcome, which may not be the GM's fault, salary offers are made rather than putting the job out to bid.

So, BB's pay is not based on cost saving, but on the usual labor economics idea of contribution to the value of output, This is the well known idea of marginal revenue product, or MRP for short. MRP is defined as the GM's added contribution to winning (marginal product, MP), multiplied by how much added revenue owners can make from that added contribution to winning (marginal revenue, MR). So MRP = MP x MR. A little notation for the case at hand.

MR-OAK = $ generated by one more win in Oakland.
MR-BOS = $ generated by one more win in Boston.
MP-BB = BB's contribution to wins when added to a roster of players.
MP-PAST = PAST Boston GM contribution to wins when added to a roster of players.

Crucial fact: All of the above depend on team quality in the different locations. The well known concept of diminishing returns would dictate that MP-BB in Boston would be lower than MP-BB in Oakland because team quality in Boston is higher (after all, Boston did win 56 more games than Oakland over Morris's comparison period). Note this does not preclude BB being worth more in Boston, as below.

In the hiring and payment decision for Boston, the question is whether BB's MRP in Boston is greater than the MRP of PAST managers, that is:

Big Question: Is MP-BB x MR-BOS > MP-PAST x MR-BOS?

The comparison does not simplify to MP-BB > MP-PAST. If that relationship were true, then MR-BOS under BB would be greater than MR-BOS under PAST GMs.

Now, if the answer to the big question is YES, then BB has a higher MRP in Boston than the MRP of PAST GMs (MP-BB in Oakland is data, but not the relevant comparison in Boston). If so, BB is worth more to Boston owners than PAST GMs were worth. So the analytical problem is forecasting BB's MRP in Boston when all that's known is MRP of PAST managers and BB's MRP in Oakland.

So here is what is likely. First, MR-BOS > MR-OAK, probably at any level of winning. Boston is just that much of a larger revenue market.

Second, MP-BB in Boston will be less than in Oakland due to the aforementioned diminishing returns. Morris sweeps this under the rug in sticking to comparisons at averages when it is clear that the relevant comparison of BB's value is at the margin. Adding BB to the higher quality Boston roster (Boston did win 56 more games than Oakland since the 2002 offer) will win fewer additional games than adding him to the lower quality Oakland roster. Again, assuming this away undoes Morris, not the process that generated the $2.5M offer to BB, and not the business acumen of the owners in Boston.

Putting this the other way around, suppose that PAST Boston GMs were plying their trade in Oakland instead. Diminishing returns would also mean that MP-PAST would be higher in Oakland than in Boston because team quality is lower in Oakland! And Morris's same calculations would generate similar qualitative results for a consideration of moving PAST GMs to Boston (albeit quantitatively less if BB is the genius he appears to be). Now the Boston ownership could, under Morris's approach, offer PAST GMs an "insane amount" (Morris's words) and Morris would judge Boston owners harshly if they didn't.

So the actual analytical problem facing Boston owners, rather than the one Morris contrives for them, is what happens to MRP in Boston with BB at the helm, which reduces to estimating MP-BB in Boston, with a pretty good understanding of the subsequent impact on MR-BOS. Is MP-BB > MP-PAST (even though MP-BB is smaller in Boston than Oakland), and by how much, and what is the impact on MR-BOS? That difference is how much more they can offer BB over what they paid PAST GMs. According to Boston owners, that increment, plus what they were already paying PAST GMs, appears to have added up to $2.5M per year for 5 years, the 2002 offer made to BB to move to Boston. Looking at the margin, rather than averages, this offer is completely rational.

Two other factors come into play as well.

One is the difference in level of play required to get to the playoffs, AL East versus AL West. There's a reason Boston won 56 more games, 2002-2013. In all but one season (2008), the first-place winning percentage in the AL East was greater than or equal to its counterpart in the AL West. The second concerns the preferences of fans for winning. Fans in some higher income cities appear willing to pay more for wins produced by particular players (often called stars). This means that a player might be paid more than just their stats would suggest. Relative prices and attendance suggest this is true in Boston relative to Oakland.

Now, it is true that if MP-BB > MP-PAST by enough, then Boston might be able to maintain their wins, or even increase wins, by reducing team quality, that is, with a smaller payroll. But it will still be a consideration at the margin, not the average, that dictates such a possibility.

Thinking at the margin also allows some insights about BB's refusal of the offer. BB would need to consider:

Boston Offer + Boston Amenities versus Oakland Response Offer + Oakland Amenities

Now, maybe the Boston owners did try to low-ball BB. Or it could just have been that Boston owners made their best offer but the Oakland response/amenity comparison was the deciding factor. [The Oakland response included a 2.5% equity share, valued at $8M at the time, as this type of compensation can.] Let's not forget that BB also knows that MP-BB is smaller in Boston than Oakland! Staying in Oakland he will always be the wizard, that is, high MP-BB. And there are other great opportunities that go with that (Brad Pitt will never play me in a movie). But once in Boston, his impact on winning will be smaller even though it apparently was worth more. He won't appear quite the wizard, at the margin.

All of this considered, perhaps this is partly why BB looked at what he could do and chose to preserve his wizard reputation, and the leeway in Oakland to try more of the same. Well that and the $8M equity share in the A's.

None of the forgoing should be taken to detract from the fact that I admire the issue approached by Morris, namely, an assessment of GM prowess. But again this will always be an assessment of contributions at the margin relative to their resource base if nothing else. So rather than Morris's exercise of averages, past work on managerial efficiency in the sports economics literature (typically using stochastic frontiers or data envelopment techniques), applied to GMs, is a proven marginal approach.

I notice a tendency among some (not all) "sports analytics" practitioners to publicly criticize actual owner and GM decisions, rather than simply trying to understand those decisions. This often leads them to mistake the high variability of success across teams all as management prowess and ownership ineptness. People have offered these criticisms since Frazee sold Ruth to the Yankees and yet these same owners manage to hold on to their teams when there are plenty of wealthy competitors with which to contend.

Jason Winfree and I have a lot more to offer on this last point. Just go to 15 Sports Myths, click on the book, choose your favorite medium (print or electronic), and read Sports Myth 8: "Owners and GMs Are Inept."

No judgement on Billy Beane's impact in Boston, or the offer made to him in 2002, can be made by appeals to league averages or estimates of averages from regression analysis. Just estimate the margins! Economists studying sports have been empirically evaluating these margins for decades. Doing otherwise is like measuring liquid with a ruler and the results will miss the mark by a wide margin.

Posted using BlogPress on my iPad.

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