THE BOOK--Playing The Percentages In Baseball

So what’s the deal then?  Were our projections for the free agents way off?  Or was 4.5 mil wrong going in?

At $6.5 to $7.5m/win in a 930 WAR league, that would imply a total value for all players of $6,045m to $6,975m. Of course, that assumes teams will always make the rational economic choice (ie will replace a win as cheaply as possible, whether that be through free agency or player development).

I apologize for being stubborn and dragging in a discussion from another thread, but ... those numbers seem awfully high. Consider:

Total leaguewide revenue: $5,819m
Leaguewide operating income: $501m
Leaguewide operating expenses: $5,318m

(http://www.forbes.com/lists/2009/33/baseball-values-09_The-Business-Of-Baseball_Revenue.html)

Teasing out the player comp portion of those expenses is tricky, but there are a few sources kicking around. Player comp (salaries, deferred payments, bonuses, insurance, workers compensation and pensions) as a percentage of total operating expenses (player comp plus travel, marketing, administrative, media and venue expenses, but excluding non-cash charges, interest expenses and payroll taxes) in previous years was:

2001: 56.6%
1996: 60.3%
1995: 64.6%
1994: 57.0%
1993: 62.4%
1992: 61.1%

(2001 from http://www.usatoday.com/sports/baseball/stories/2001-12-05-focus-expenses.htm)

(1992-96 from: http://baseball1.com/bb-data/96-biz.html)

Using 60%, player comp in 2009 would be $3,191m ($3.4m/win). At a high 65%, comp would be $3,456m ($3.7/win).

Dollars per win of $4.5m would mean a total player value of $4,185m (79% of operating expenses). Or, it would mean non-player expenses of $1,133m ($5,318 less $4,185), or $38m per team per season to pay for travel, marketing, admin, hotels, stadium, media etc etc).

So, how much of the $/win for a free agent is the true cost of replacing a win, and how much is a premium resulting from bidding wars, or drumming up fan interest with a splashy free agent signing etc?

I have no doubt that a large portion of the free agent cost is the bidding war.  So, 3.5-4.0 would make more sense.  4.5 is bidding war.  And whatever Sky is showing is sampling issues or whatnot.

Also, if you’re a team turning to the free agent market, you’re more likely to have a hole to fill or be on the cusp of a playoff appearance, and therefore be perfectly willing to overpay for a win. If you have a job interview in 15 minutes, it makes good sense to pay $15 for a 10-minute cab ride instead of $2.75 for a 20-minute subway ride.

If you went 92-70 and finished three games out, and have a hole to fill at third base, then it would make rational economic sense to pay $6 or $7m/win for a 3 WAR free-agent third baseman.

So the free agent market would be a selective sample of teams willing to pay a bit more for a win to address specific circumstances.

Dackle: good point.  You are basically paying a premium, not only to meet an immediate need, but also because you have less uncertainty.  You know what you are getting if you put in 50MM$ in a player.  You have no idea what you are getting by putting 50MM$ in your player development system.  You might win the lottery on Evan Longoria, and you might not in most cases.

If Sky stops by, I wonder if he could just tell us the total 2009 WAR and total payroll for each of these 3 groups:  FAs, arbs, and pre-arbs.  I think it would help clarify why his FA valuation is so much higher than others.

This jumps out from Sky’s article:

To account for contracts potentially being backloaded or frontloaded, I used the average yearly salary over the life of the contract, rather than the actual salary given to the player in 2009.

If I’m reading that correctly, a one-year $20m contract is being treated the same as an 8-year $160m contract.  I know that Sky accounts for contract length later in the article, but I think a much better way to do this is to convert all long-term contracts to present value.

It would be interesting to see the $/win if Sky discounted all long-term contracts at 8%, 9%, 10%, 11%, 12% etc.

dackle: right, that’s what I do basically.

Dackle, I don’t think you can take the $7 million mark and say that it applies to the entire universe of players.  Only to free agents.  If everyone was a free agent, I think obviously that mark would go down.

Also, when I control for other factors such as length of contract, year of contract, etc, basically there is no change in the dollar valuation.  If anything, it makes the dollar value slightly higher. 

Those who are not inclined to believe a $7 million mark, can you point to other recent (2008 or 2009) research showing a lower figure (not being snarky, I’m actually asking)?  I don’t agree with Fangraphs methodology (dollars per projected WAR in the first year of the contract will be biased low) and Studes’ research is old and doesn’t use WAR.  I was willing to believe $6 million was an outlier a couple of weeks ago, but given that I found an even higher number this time, I don’t think it can be written off.

Dackle/7, You can’t just discount the price of the contract like that, otherwise you’re going to bias your estimate.  If you want to do something like that, you’d have to inflate the $ early in the contract and deflate the $ late in the contract, so that the total amount given is the same.  In any case, this is made unnecessary by the presence of the Year of Contract variable, which should account for this.

I don’t think the handling of multi-year contracts will make much difference.  Sky is saying that these 223 FAs produced only about 1 WAR each, at an average salary of $6-7M.  If the WAR numbers are right, then teams clearly paid a lot for that production.  I’m surprised the production is that low, and I assume that a lot of injured and poorly-performing pitchers is the main explanation.

This also means that teams got something like 27 wins from their arb and pre-arb players, on average, more than 3x the production they got from FAs.  Is that true?

Sky: I had posted the complete service time file for 2008 (and you can work backwards to 2007).  Why not use those, so that you can expand your sample?

Guy, yeah, about 3 times the value for non-free agents.  Also, the free agent eligible group excludes players who signed when they had <6 years of service, but are still playing under that contract when they have 6+ years of service.  That group includes, Pujols, Beckett, etc, about 30 players contributing value as well.

Sky, I agree with both of your points. I think $6.5m could very well be true—my criticism was more of the view that free agent $/win reflects the true cost of a win (salary + player dev) for all players.

Surprising that the year of contract variable doesn’t pick up on declining production. For example, a front office is evaluating an older player and projects the following WAR over the next three years based on an optimistic, fair or pessimistic scenario. The team is willing to pay $4/win this year and increase that figure 10% per year:

Scenario      Yr1   Yr2   Yr3
Optimistic   3.00  2.90  2.80
Fair         3.00  2.00  1.00
Pessimistic  2.50  0.00  0.00

Avg WAR      2.83  1.63  1.27

$/win        4.00  4.40  4.84
Value       11.32  7.17  6.15

So, if the player signs a one-year contract, it would be for $11.32m. He produces 2.83 WAR, and so $/win is $4.00. But, if he signs for three years, it would be for his total projected value of $24.64m (11.32+7.17+6.15). At an average value of $8.21m/year, it would appear that the team is paying $6.46m per win in year 3 (8.21/1.27), when really they’re paying $4m/year plus salary inflation.

If you combine this contract with other players, “year 3” might look expensive for this player, or it might look cheap for a player on an eight-year deal, and so the regression term would wash out.

Studes’ research is old and doesn’t use WAR

Old?  It was from three years ago! 

And he used WSAB which has a a very high correlation to WAR.  When you look at a huge group of players, there’s simply no way you’ll find much to any difference between WSAB and WAR.

Dackle, yeah, the year of contract variable is almost signficant, but not quite - with more data I’m sure it would pick up on it.

Tango, 2006 isn’t old in that the research is bad, but would you use 2006 values to estimate 2010 salaries?  Isn’t it plausible, in fact likely, that the $ per win is different now than it was back then?  People seem to have a very set opinion on $4.5M per WAR but I haven’t really seen a lot of hard evidence backing that up.

Sky: obviously the dollars per win change.  Before the economic downturn, I was proposing a 10% increase every year:
http://tangotiger.net/salary.html

That was based on salaries, revenues, and valuations of teams going up by 10% per year over the previous 15 years.

What you are suggesting however, is a skyrocket jump.  I don’t know what you think constitutes hard evidence that backs it up, but the Saber Rattling data is great evidence.

And the way dackle presents the presumptive evidence is also the starting point (that the cost per win is roughly 4MM$).

I’d also like to point back to your own evidence for each year of data shows a huge swing (4.8 to 6.1 or something).

No team is paying 7MM$ per win.  Look at Rally’s free agent tracker:
http://www.baseballprojection.com/2010/freeagent2010.htm

The range of implied $ per win in his chart is around 2.5 to 5.5, with a median around 3.5-4.0.

This is why people are so set at the 4-ishMM$ level.

Just discovered this discussion again now.  Once again, I liked Sky’s article but I don’t see why he switched to Fangraphs’ WAR when using Rally’s WAR showed a 0-intercept for 0-WAR in his regression last time.  It seems like Fangraphs’ WAR has too low of a replacement level.

Regardless, the discussion about “if everyone were a free agent” is useless.  If everyone were a free agent, it would be a different market entirely.  There would be totally different opportunity costs, totally different supply, totally different demand, totally different replacement level.

The problem with that is that you have increasing marginal revenue to a win as you go up from low win totals to borderline playoff win totals.  The end result is that the market would probably change drastically, and you would likely end up with situations where the same teams made the playoffs every year and everyone else only won a handful of games.  The fact that better teams don’t win much more often in the playoffs and the fact that getting to the playoffs provides a huge boost in revenue expectation as a result gives baseball a unique labor demand curve that would not be conducive to this kind of set-up.  It’s not entirely clear what would happen and I’m not sure the equilibrium is even unique, but you simply cannot say “what if everyone were a free agent?” It’s a useless question.

As to what teams pay on the margin in the current market structure, I think Sky has it right again.  And I think the problem is that looking at $/WAR for the first year of the contract or $/projected WAR is flat out wrong, ignoring that teams might have information other than what a projection system has and might pay more or less as a result.  Contract length is endogenous and everyone agrees that WAR generally declines as contracts go on.  I don’t understand why this is an acceptable way to compute things given the fact that we know later years of deals would clearly show higher $/WAR holding everything else constant.

"No team is paying 7MM$ per win.”

We can only use projections to answer this IF we know the projections equal actual performance in the aggregate.  But a lot of projections tell us what players will do if they are healthy enough to play, so actual performance is quite a bit less.  At least, that’s what Sky’s data is saying.  The discussion of how to handle multi-year contracts is largely beside the point.  The question is whether Sky’s total WAR and total payroll numbers are right.  If they are, then the $7M has to follow.

I’d like to know how many pitchers have negative WAR and the aggregate amount of negative WAR.  My guess is there is quite a bit.  And if so, that might suggest the replacement level for pitchers is being set too high.

"I’m surprised the production is that low, and I assume that a lot of injured and poorly-performing pitchers is the main explanation.”

That same thought occured to me—but I asked him in the comments of his latest article if he had split up pitchers and hitters, and he said he had checked that and it didn’t make any difference.

If I’m reading the threads here and at Baseball Analysts correctly, is this a difference of expected production and actual realized production after-the-fact? Are Major League teams expecting more production from their free agent signings that what they’re actually getting?