THE BOOK--Playing The Percentages In Baseball

>“Teams are given a budget and will spend to that budget.”

Ah, but you’re begging the question.  Why were they “given” *that* particular budget amount?

To figure that out, how much their budget should be, teams need to project revenues at every level of spending.  The model *they* use is the one we’re looking for.

I agree with Phil.  The budgets are “fake”.  They can be pushed beyond.  Few teams publish their budget, and most teams, if not all, will go beyond that budget if they are in contention in late July.

They are given that budget historically.  “We gave you 70MM$ last year?  We won 75?  We’ll give you another 10MM$… do the best you can with that.”

“We gave you 110MM$ last year, and we won 75?  Listen, that’s above the MLB average for payroll, and obviously below average for wins.  Our profit level was down this year, in the red.  We’re slashing 15MM$ from the budget.  Do the best you can.”

I believe this is how sports teams operate.

But for the free agent market, not everyone was in play for Dunn or Werth (overpaying notwithstanding), even if those guys would produce dollars to the same level for most teams.

The Royals are not in the Dunn play precisely because they are told that they can’t spend that much money, even if they would get an ROI on Dunn.  They were in play for Gil Meche a few years ago exactly because they were given the money to do so.

This is no different than corporate america.  I had to put in a request for a 50$ software that had to go through four (FOUR!) levels of authorization before it being approved, even though the ROI on the software was virtually instantaneous.  That’s because everyone is on a budget, and what we think of investments is better characterized by the uppity-ups as expenses.

The determination of the budget is just a matter of different individuals performing different tasks.  The owners’ selection of a budget is based on what they perceive the GM will create with that budget (how many wins).  Using the intermediate stage of internal discussions as a model is going to miss most of what is going on.  All you will be modeling is that GMs will try to do the most wins/$, and different ones have different skills and luck.  To determine willingness to pay, you need to figure out what the profit function of the business looks like.

The owners’ selection of a budget is based on what they perceive the GM will create with that budget (how many wins).

Well, that’s our point of disagreement.  This may be what happens in a normal american company, but I would not treat that as an economic principle that would apply to a sports league, or other enterprises that has “Picasso” value.

One derivative of winning is… winning.  An owner may in fact earn a 20MM$ personal satisfation dividend for winning the World Series.  That is, if you asked an owner: spend 20MM$ too much, and I’ll guarantee the World Series: he may very well do it.  That’s his Picasso.

"One derivative of winning is… winning.  An owner may in fact earn a 20MM$ personal satisfation dividend for winning the World Series.  That is, if you asked an owner: spend 20MM$ too much, and I’ll guarantee the World Series: he may very well do it.  That’s his Picasso.”

Yes, of course.  Which is why someone, I forgot who, a long time ago, developed the idea that utility and not money is the currency that drives behavior in economics.

In prof. baseball (all sports teams actually), what screws things up is that different owners have different utilities.

Right, I had tried to say: use utility instead of profit. But that doesn’t screw anything up; teams have different revenue functions and different utility functions. You just adjust the profit function to add in utilities. Same argument holds: budgets are just an intermediate step, and holding them fixed eliminates most of what is useful about modeling players salaries.

Tango/4: The reason not everyone is in play for the top free agents is that not everyone needs that big a bucket of wins right now.  If a team is at 86 wins, and wants to be at 88, a 5-win player is going to be more than what’s profitable for it.

However, if that team lost a couple of free agents and is now sitting at 79, they need those 5 wins and more, so they’ll make a play for that player.

>“I had to put in a request for a 50$ software that had to go through four (FOUR!) levels of authorization before it being approved, even though the ROI on the software was virtually instantaneous.”

That’s not inconsistent with profit maximization.  Maybe the four levels of authorization were to confirm that the ROI was indeed instantaneous, and they stupidly didn’t make an exception for $50 software as opposed to $500,000 software.

>“One derivative of winning is… winning.  An owner may in fact earn a 20MM$ personal satisfation dividend for winning the World Series.”

If you price a World Series at $20MM, that means an extra 10% chance at a WS is worth $2MM.  There’s no way to buy a 10% additional chance for $2 million, and so it won’t happen.

If you want to raise the satisfaction bonus to $200MM, then we’ll talk.  But there’s no way it’s that high.

If I recall correctly, my original Picasso theory (well, I used Van Gogh, but who’s counting?) had the value of owning a team at about $8 MM a year.  My view is that owning and winning isn’t worth that much more than owning.  Suppose winning is worth just as much as owning.  That’s only $8MM for a World Series, not enough to make much difference.

There’s a natural experiment currently running: George Steinbrenner is dead.  If he had a personal Picasso value that was higher than anyone else’s, we should see new ownership reduce payroll and make more profit.  Let’s wait and see how much that happens.  I predict: not that much.

Send questions to JC:

http://freakonomics.blogs.nytimes.com/2010/12/06/bring-your-questions-for-the-baseball-economist/

However, if that team lost a couple of free agents and is now sitting at 79, they need those 5 wins and more, so they’ll make a play for that player.

While I accept the “playoff sweetspot theory” (I think I may have been one of the first ones to even bring it up at the old Baseball Boards I think… maybe, I don’t know), the problem is: we don’t know who is a true talent 79 win team.  Furthermore, we don’t know who will actually be observed to be at 86-90 wins by the end of the season.

The question to ask is this: given that you have a true talent team with 79 wins, where your uncertainty of that estimate is one SD = 3 wins, and that this team will be observed to play for 162 games, what is the chance that it will perform in the sweet spot of wins?

I would bet that if you work it out, it would really reduce the “premium” for sweet spot money substantially.  Basically, in practical application, the sweet spot effect is somewhat muted.

Tango/12:

The probability is probably low for a 79-win team.  But it’s definitely higher for a 88-win team.  That’s why the 9 wins from 79 (perceived talent) to 88 are worth more than the 9 wins from 70 to 79.

It doesn’t matter that there’s randomness involved—teams are playing the probabilities.

What I mean is if the win from 87 to 88 wins is worth 6MM$ and the win from 77 to 78 wins is worth 3MM$, that doesn’t mean the 77 win team is going to spend half as much than the 87 win team on that next win.

If you apply the probabilities, it might come out to 4MM$ and 5MM$, respectively.

I think it’s all about the same value in the low-80s to mid-90s range.  Here’s how I discovered this.  I called a 90-win team as having a 55.6% chance of winning each game, and then got a density function representing the probability of each of the possible actual win totals from 0 to 162 that team could have.  Then I did the same thing for a 91-win team (91/162 chance of winning each game, found density).  Then I took the difference at various win levels.  Suppose that it takes 90 wins to make the playoffs-- how much more likely is the 91-win-talent team than the 90-win-talent team to win 90 actual games.  The answer is always right around 5% increase in hitting a given playoff-bubble win total per win for most teams in the low 80s to mid 90s range, more or less.

The issue for teams not near the playoff bubble...let’s say the Nationals signing Jayson Werth...it’s really about the splash effect.  It happens enough that I’m guessing it does affect their books when they do something like that, and it might do more to draw Nats’ fans to get a big name player than signing Werth would do to attract Red Sox fans, who already trust the organization.  It’s not a good baseball contract, but it might very well be a net positive transaction.  But the reason this is important is that the Nationals still had to outbid the Red Sox and other teams willing to pay about $5MM/win.  They will only bid if they also happen to be willing to pay $5MM/win, which on occassion, you will get a splash effect that makes that worthwhile.  Hence, the observed fact that all teams pay about the same per win.

I would like to sponsor Matt to be one of the representatives for sabermetrics among baseball economists.

What did Matt do wrong to deserve that assignment?

Tango/14: Yes, agreed 100%.  In my April post, I took Nate’s curve and spread it out for exactly that reason.

When I say “buy the 86th win”, I mean “buy the 86th win of talent”.  The reason the 86th win of *talent* is more valuable than the 81st is because of the higher probability of making the post-season, even though 86 wins of *performance* is very unlikely to be enough.

Matt/15: How big do you think the “splash effect” actually is?  Just an intuitive guess is good, if that’s all you’ve got.

Matt/15:

Your calculation sounds very useful.

Where does the increase start taking off, and where does it top out?  The post-season probability curve might be good start for drawing the marginal revenue curve.  I had to just guess.

Phil/19:

I would guess it’s a distribution.  I think on the extremes, it’s something like what we observed for the Nationals here, but for most teams, the splash effect is nowhere near as large as the playoff bubble effect. 

It’s kind of the perfect storm for a splash effect in Washington though.  You have a city of mostly bad sports teams where a good team can stand out (and lately a bunch of Americans caring about hockey as the Caps have been good), a relatively big market, another baseball team with similar middling results an hour away to which a lot of the potential fanbase is still following more, and a nice little example of the value of an individual player fresh in owner’s minds (strasburg games’ attendance was absolutely insane comparatively.  It’s also an expansion team to the fans-- they don’t have the benefit of local dads taking sons to the game and telling them about how the home nine fared twenty years ago.  This is a brand new team without a history. 

Trying to put a dollar figure on it...well, I can only throw numbers out there, but I’ll try.  They spent $126MM on Werth over 7 years, where you have that even if the Werth was only willing to sign a seven-year deal, the next competitor was going to spend about $110MM.  The difference between maybe the Red Sox and Nats values on Werth due to the Nats not being on the playoff bubble is maybe on the order of $15MM less revenue from Werth in 2011 & 2012 combined.  And I figure 2013-2017 is probably similar playoff bubble effect given the uncertainty of projecting that far in the future.  So I guess we’re looking at like a $30MM splash effect based on that.  That’s probably the biggest splash effect you could possible get.

Interesting that you think the Nats paid $16MM more than the next highest bidder would have.  Not that I know any better, I’m just surprised the gap is that high.

So $15MM a year for two years.  That’s a lot ... over 3 wins a year.  But maybe for a team as low in the standings as the Nats, 3 wins are worth a lot less than a splash, so that’s the best way they can get a bang for their buck.

Phil/20:

About 84-94 wins I guess was the sweet spot.  Using 90 wins as the baseline, the value of the 90th win is 6.3%, the value of 85th and 95th win are both around 4.6%.

Thanks.  I think that’s roughly compatible with what I guessed ...