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.


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When "Subsidies" Really Are Investments: Rutgers Athletic Department Unfairly Trashed

Carl Laemmle in his younger years.

[OK, so he is not really a monster.  But Carl Laemmle was the producer of all the original monster hits--Dracula, Frankenstein, The Mummy, and The Invisible Man.  Maybe somebody else would have anyway, but he did it.]

Just recently, the athletic department at Rutgers was trashed vigorously in the press for the largest per student subsidy of athletics of all FBS schools.  Berkowitz and Upton at USAToday.com, Adelson at ESPN.com, and Reed at Ralph Nader's League of Fans blog.  In 2010, Rutgers received $27 million from the university and student fees (42% of the department budget); $115 million in total since 2006.  I calculate that to be a growth rate of about 7.4%.  This put them at the top of some sort of ranking of university support and student fees in the FBS for 2010.

Sigh.

The USAToday article quotes Patrick Nowlan, executive director of the Rutgers teachers' union, "A student doesn't come to Rutgers to attend a football game.  They come here to get an education--and then maybe to attend a football game."

But (according to the same article) AD Tim Pernetti puts it this way, "With athletics being the big window into everything we do here at Rutgers, and being that we've been able to do it in a positive way, it is an investment in the branding and marketing of the entire place, not just the athletic department."

As with all things, the answer is surely in the middle.  Sports are neither a recess awarded to students chained to their desks all semester nor the end all and be all of branding the entire university.  But what does ring true is that university support of athletics is an investment with a return.

Interestingly, not a single article I could find put it in these terms:  "Investment in athletics at Rutgers grows 7.4% annually since 2006."  Instead, we get the following headlines.  From the USAToday pair, "Rutgers athletic department needs fees, funds to stay afloat"; from the ESPN writer, "Rutgers relies heavily on subsidies"; from the Nader blog, "Rutgers students forced to pay nearly $1,000 each to fund athletics."

This is the worst type of thoughtless shrieking and casts university support of athletics as a requirement to cover bad management at best and extortion from students at worst.  Nothing could be further from the truth.

Jason Winfree, my colleague here at Michigan, and I, in our upcoming Stanford University Press book, document the following from the work of many economists:

• University support of athletics is small relative to university revenues.
• There are returns to the university support of athletics.
• The returns are small in absolute terms.
• The rate of return on university support (as opposed to its absolute level) is quite sufficient.

For example, Rutgers' total university revenues for 2010 were in the neighborhood of $1.9 billion (Tuition and Fees, Grants and Contracts, Auxiliaries, State Appropriation, Federal Appropriation and Endowment Income).  So university support of athletics was in the area of 1.4% of Rutgers' revenues.  It doesn't take much return in terms of gains elsewhere across the university to make an acceptable return (student application quality, faculty quality, donations at large, appropriations from the legislature).

[By the way, academic support was $610 million, 32% of its total revenues, or 23.5 times larger than university support of athletics.  Moving the entire $26 million athletic support over to academics would represent a 4% increase.]

Do ADs ask university administrators for money?  Yes, at all but a very few universities.  Do university administrators have to give it to them?  No, and often they don't (during the recession, numerous ADs have had their support from their universities cut).  So why do administrators fund athletics?  Because the investment pays, just as it does for the English department or the Engineering School.  If ADs show increased value to the university, they get a larger allocation just as does any other department that can do the same.

By all means, there should always be an ongoing dialogue about the proper place of any activity at the university.  But a thoughtful and careful assessment would be wise rather than barely concealed self-interested ranting and raving by faculty and college sports haters.  For university administrators, athletic departments create value just as do the other departments on campus.  Investment is the better word than subsidy in this case.

Bet You Thought I Had Disappeared...

[My daughter's artwork this time, and appropriate for this post title.]

You may have noticed my absence for a while, or you may not have noticed. Not much of a blog if one doesn't blog, eh.

Explanation: Busy helping a pro golfer convince the IRS that he produces both appearance value and image value, and that the latter was larger. Also I'm teaching a new course for me, research methods of all things. But it has proven fun for me (hope so,for the students). And then there was no more time in the day.

But I'll be doing better from now on.

Note I've added my new colleague's blog to my list, Stef Szymanski's "Sporty Business."

Also, let me note that nearly nobody posts any comments, even though my "statistics" report shows you are lurking. Give it a try even though you have to identify yourself. I bet you will find it refreshing to be responsible for what you say.

Coming to a "Sports and Monsters" near you:

Did Manning really generate $233 million for the owner of the Colts?
The Mets, Sterling Equities, and the Madoff fallout.
Value of teams to communities.

And, as always, if you have a topic, hit the link!

THIS IS SO MISGUIDED I HAD TO POST RIGHT AWAY (SORRY NO MONSTER)

This so flies in the face of even Econ 101 that I had to post it right away.  Sorry no monster, I was in a hurry.

Sportsfans.org is a sports fan movement attempting to right many perceived wrongs.  But that should never get anybody off the hook for using really (really) bad logic that flies in the face of even the most basic economic concept.

Headline Dec. 6, 2011:  "High Costs of Sports on TV Always Passed on to YOU"

Grab Line on the webpage:  "Think your cable/satellite bill is high now?  Wait till the costs of the latest NFL TV rights deal are passed on to you."

Weak Thinking:  NFL charges cable/satellite providers whatever it wants for rights fees.  The media providers then pass it along, with markup, to poor slack-jawed NFL fans.  Which they pay because, well, that's just how badly they need their sports fix (I guess; this part is never really covered by anybody who adopts this view).  The cruel, insensitive, and eminently greedy NFL laughs all the way to the bank.

Econ 101:  Both the NFL and media providers are constrained in what they can charge by the willingness of NFL fans to pay for games, given the other options that fans consider to be substitutes.  It is the job of both the NFL and cable/satellite providers to estimate this willingness to pay.  They set their agreement on the basis of those estimates.  If the NFL and media providers are correct, fans pay as estimated and they make profits.  If they are wrong, they sell less than they had hoped, because they charged too much, and they make less than they planned.  This is true whether the NFL has market power or not.

Possible Motive for Publishing Such Weak Thinking:  Sportsfans.org is trying to build membership and interest in their cause.  They say inflammatory things to fuel that interest.

************

Now, perhaps pushing this kind of misinformation serves the needs of sports fans.org, but that can only be in the short run.  In the long run, what will sports fans.org do when it cannot come through on this issue--as long as fans are willing to pay more, the NFL and media providers will gladly charge them for it.  If this is stymied, politically somehow, we are in a regime of price controls that we know will simply reduce the availability of what buyers want most.  Fans will get lower cable/satellite bills because they get less sports programming than they are willing to pay for.

Garbage in, garbage out.

A HARD RAIN'S A-GONNA FALL

Click for IMDB Including Trailer

The discussion is already occurring:  "What to do at Penn State?"  I have my opinions as well.

But this blog is a place for sports economics rather than opinion.   It isn't the economist's job to take sides as an economist.  We reserve that to our non-professional side where we are free to have our opinions like everybody else.  The economic contribution I think of goes like this.

The athletic department is part of an organizational hierarchy at the university at large.  As such, there are levels upon levels of principal-agent oversight going on.  For university oversight, at large (we'll get to the athletic department shortly), there is an immense of amount of slack in this oversight.  This produces quite a bit of independent action by all units at the university with the reckoning coming at budgeting time.

By and large, while not without failures here and there, the monitoring works pretty well across campus.  It has its greatest chance for catastrophic failure as follows.  With lots of slack, an ideologically homogeneous unit with strong external clientele will obtain more freedom than other units.  The chance that this type of unit will do something counter to the welfare of the institution, at large, goes up.

And this special set of circumstances describes the oversight relationship between university administrators and the athletic department to a tee.   [This has been known for years by economists, but has been ably presented by Prof. Clotfelter in his current book Big-Time Sports in American Universities.]

Now, as long as this independence is constrained to just hiring multi-million dollar coaches, or putting up multi-million dollar scoreboards when other academic units struggle, no real harm is done.  That money comes from athletic boosters (by donation or paid attendance, etc.) explicitly for an athletic purpose and never would go to academics in the first place.

But this independence (especially the homogeneous ideology part) has a chance to produce unit cover ups of rule breaking and even criminal behavior.

Unfortunately at PSU, university administrators allegedly committed acts of complicity instead of taking decisive, public, counter-action.

The lesson from economics is that the oversight process is flawed.  Indeed, that the probability of a PSU-type episode was non-zero is clearly predicted.  But hindsight is 20/20 and the question now concerns future action.

On the one hand, just don't play the game at all.  This was the choice early on at The University of Chicago when then President Hutchins abolished big-time football after the 1939 season.  If the costs are so high for university administrations, they can follow suit.

Football fans will scream, but the impact will be small.  Most university administrations spend very little on athletics (trivial percentages of their operating budgets), some none at all.  And the returns to the university end up to be quite small as well (again, as a percent of operations).  The primary hit would be on student leisure choice.  Any number of high-quality institutions simply do not have big-time football.

On the other hand, administrators can recognize the holes in the monitoring process and fix them.  This does not drive the chance of a PSU-like occurrence to zero (nothing can).  But it will reduce them, probably dramatically.  This will undoubtedly result in curtailing the independence of athletic directors, with accompanying pain.  But all administrations face this same possible negative outcome and they have collective decision bodies to do the job across all of college football.

Pulling a third hand out of my hat, it could be that the monitoring process is as efficient as it can get.  This makes for the dismal (science) prediction that, on rare occasion, as in the rest of society, bad things will happen in college sports.  What to do about it now becomes a society-wide issue and beyond the college sports arena.  If the small probability of a truly bad outcome is onerous enough, politically, then Congress can act.

As Bob Dylan put it:

And it's a hard, it's a hard, it's a hard, and it's a hard
It's a hard rain's a-gonna fall.

Right now, it's falling on Penn State.  If the same homogeneous ideology of football exists at other places (an empirical question that will be simply stated as true without any investigation, I suspect), the forecast is cloudy with a chance of rain.

Transcontinental College Football--A New Subdivision in the Making?

Click for IMDB Including Trailer

WOW!

That's all I can say.  If the Big East successfully woos Boise State, it will be the first transcontinental football conference.  If it had wooed Utah instead, it would be reminiscent of driving the transcontinental railroad "golden spike"; Promontory Summit is about 90 miles from SLC.  On the other hand, Boise is a good 250 miles farther west than SLC!

Whether Boise State accepts or not depends on their expectation of improved chances regarding the BCS National Championship.  This is truly a great case of decision making at the margin for BSU since it isn't clear they can do any better in the Big East than they've done in the Mountain West.

But to me the more interesting response is by The Mountain West Conference and C-USA... their own transcontinental response if you will.  They have a new college football "association" on the drawing board.  Details are completely sketchy at this point but just the two of them span a vast part of the U.S.  It also is important to note that the two stress that this is a football only "association".

An "association" of 22 FBS football programs, none of which really has any hope of making a BCS game, smacks to me of the creation of a new college football subdivision.  The two tout right now that they have terrific TV appeal to go with geographic match ups.  All they need now is the MAC and Sun Belt to buy into it.  Programs in this larger version of the "association" play in 25%-30% of the non-BCS bowl games and could easily create their own version of the BCS.

Which brings us back to BSU.  It's perhaps a little more likely that Boise State's decision at the margin will lead them to refuse the Big East.  Then what?  The Big East could easily leave the BCS (or be forced out by the rules that specify BCS conference size) and join with these other conferences in their "association".

The rise of rival associations is naturally to be expected in the current conference shake out.  After all, it is the FBS that is the novelty, D-IA used to mean that ANY team could contend but FBS means a team can only contend from a BCS game.

So, what do you all think?  What will BSU do?  And what of the Big East?  Informed economic perspectives welcome (as opposed to arguments based on past allegiance and "money crazy" athletic directors).

The University of Texas and the SEC

Click for IMDB including Trailer

So Texas A&M is bound for the SEC.  Two questions arise.

One.  Why does the SEC want A&M?  Two.  Why is (what's left of) the Big 12 just sitting there?

One answer seems to work for both questions.

The University of Texas is moving to the SEC.

["Aha!  Watson, the game is afoot."  Basil Rathbone was the most famous Holmes, but the picture and link here remind us of an earlier monster movie role.]

Logic.  None of the so-called "equity conferences" needs to add anybody unless they bring enough revenue potential with them to raise the conference average (this could happen by increasing conference membership to 12 so there can be a Conference Championship).  A&M alone does not do this for the SEC, but A&M and Texas fits the bill.  And the strategy is enviable--first make sure that A&M wants to go so there is no interference from the Texas legislature.  Not only was there no interference, but the board of regents (all appointed by the governor) has already given its blessing.  For those doubters--who raises the average for the SEC besides Texas?  Somebody from the ACC?  Miami is now a leper and that leaves FSU or Clemson.  Nope.

Logic.  What's left of the Big 12 sits there because there really are only two teams that fit the "raise the average" requirement, BYU and Notre Dame (let's not even get started on the likes of Boise State or Houston, economically weak sisters).  Even if BYU would come (they could have just said so when they went independent, but they didn't), ND has made it clear by passing on the Big Ten that they prefer independence.  So what's left of the Big 12 may not even be able to get back to 10 teams, let alone the 12 that it takes for a believable Conference Championship.  And Texas knows this.  If they stay, it's the annual Texas-Oklahoma game and that's it.  Since the Longhorn Network is only of value to people in the state of Texas, it is completely portable and no threat to the SEC Network.

Prediction Consistent with the Logic.  Oklahoma and ND join the Big Ten (or Oklahoma and Mizzou, if ND stays indie).  That makes two conferences of 14.  The Pac 12 is right behind with BYU and somebody to go to 14 (the Pac has always been the weaker of the Big 4 and will have to settle for "somebody" to round out 14; I think Oklahoma State, but maybe this is Boise State's big chance).

Logic.  This allows the BCS to squeeze more schools out of the "equity conference" distinction.  The BCS would benefit from dumping the Big East and, if both of the premier Texas schools move to the SEC, and Oklahoma moves to the Big Ten, the BCS can dump the remaining Big Rest as well.  That makes 4 equity conferences rather than 6; the money gets preserved for fewer teams.

Slowly but surely, the Big 12 is working its way backward through history.  Originally, the Big 12 was the Big 6 and then the Big 8.  It never would have made it past 8 if it weren't for the wandering Texans-- Texas, Texas A&M, Baylor, and Texas Tech left the SWC to join the Big 8 in 1994.  That move was the final nail in the coffin of the SWC.  The move of A&M to the SEC, soon to be followed by Texas, and ultimately Oklahoma, signals the end of the Big 12 as well.