THE BOOK--Playing The Percentages In Baseball

Jones on waivers?  Why wouldn’t anyone take him?  He’s due what, $3-4 million the rest of the year plus $13.5 million in ‘07? 

He’s 30 in 2007.  Alfonso Soriano will be 31, so will Carlos Lee.

Any GM thinking of signing either of those two who doesn’t claim Jones should be fired.

Well, he is 4 wins above replacement, which means 3.5 mil per marginal win next year, which is a little above average (average is now 2.5, I think).  And yes, many teams will overpay a lot more than that for worse players, like Soriano and Lee.

MGL, Is average no longer $2 mil per marginal win?  In other words, should it be stressed that we use $2.5?  Because this does make a difference when valuing a player.  If you use 2.5 as the baseline, he’ll be worth more obviosuly…

I do understand that finding each team’s marginal win worth is the BEST option (for the Yankees a win might be worth $7-8 mil), but we don’t have access to team financials.  Speaking of that the Yankees, taking on Abreu’s contract for one year, no matter how big it is, probably doesn’t really hurt them THAT much.

Trev: someone will claim him, and then the Braves will pull him back.  So, he ain’t going anywhere.

As for the Yanks/Abreu, don’t forget they get hit bigtime on being overlimit.  That Abreu contract is costing alot more than what they are paying him.

I think 2.5 is what the average team spends on FA marginal wins.  I have been convinced by people who do this kind of research and who know far more about economics than I that we have to assume that at the very least that allows teams to at least break even.  IOW, that the average increase in profit per marginal win is (around) equal to what teams spend per marginal win, again, on the average.

Of course, this is one of those instances that if you are a team making a decision, the league average means almost nothing.  The important variables in deciding how much to pay for a marginal win (how much to pay for a player) is what your team is expected to profit per marginal win, which could be anywhere from a few hundred thousand to 10 million or so, depending on who you are and where you are in the playoff hunt, and what your alternatives are.

The reason for the last variable (your alternatives) is the following:  The Yankees make so much money that they probably profit on almost any FA signing.  However, they often pay far more per marginal win than they could by signing other players or combination of players because they have traditionally been so bad at evaluating FA talent (at least Steinbrenner + Cashman have - I have heard that Cashman is actually pretty smart).

As far as picking up players at or after the deadline and assuming their contracts, it is a common misconception that it is no big deal to pick up, say, only a third of a player’s bloated contract.  Regardless of when you pick up a player, the same formula still applies.  How much in extra profit does a player provide your team (based on marginal win value, the “popularity factor”, and increased chances of making the playoffs) as compared to what you are paying him.  Of course there are other considerations, such as potential compensation picks if you pick up an impending FA and offer him arb at the end of the year, whatever that is worth (I don’t know).

We also cannot forget that you generally give up SOME prospects and/or other players when you pick up a good player mid-season via a trade.

I still use 2 mil per marginal win as a rough guide for whether a contract for a FA is a bargain or not.  If you pay 2 mil or less per win above replacement for a FA, you are generally getting a bargain and the player is generally underrated.  If you pay more than 3 mil, the player is generally overrated.  That does not mean that it is not worth it for your team ( to pick up a player for more than 3 mil per marginal win), although it does suggest that there might be some better alternatives (assuming you are a sabermetric team).  It also does not necessarily mean that your team should pick up a player for 2 or 1.5 mil per marginal win.  You might be a small market team that is not in the “sweet spot” for post-season chances, in which case, a marginal win may only be worth a few hundred thousand.

Of course, many, if not most, teams operate by giving the GM a certain budget and then letting him do whatever he wants with that money.  If I were an owner doing that, I would shoot myself, as it is a really stupid way to run a business.  Can you imagine any other business simply giving one of their managers a certain number of dollars and telling him to “do the best you can with the money?” Knowing that that manager is being pressured by fans and the media, and does not really give a hoot if the company makes money, only that he is perceived as doing a good job, which usually means winning as many games as possible (and making the post-season), regardless of how much money the company makes or loses?  What a pathetic way to run a business.

I used to think that most owners were genuinely interested in making money first and foremost, but also wanted to win championships.  Recently I read (I forgot where) that most owners don’t really give a hoot about making money, and that they are rich, spoiled “kids” with gigantic egos.  I think it is somewhere in between, and that even the ones that are interested in making money first and foremost generally don’t have a clue how to do that (for baseball at least - I’m sure that many of them are successful in their other businesses).

From my own analysis, I believe teams are paying more than $4 million per marginal win on the free agent market (see the THT Annual).  I would think the $2.5 million is closer to the average per marginal win across all types of players.  I have a very hard time believing that could possibly apply to free agents only.

I use WSAB for my analysis.  If you use WARP, which pretty much equals total wins instead of marginal wins, you’ll get a lower figure.

What teams “should” pay for players is up to the team or individual, but I’m a big believer in markets.  If free agents get more than $4 million per marginal win, then that’s what they “should” get.

Studes is right. I’m in a rush right now, so I won’t go through the math, but I remember that when I re-did Nate Silver’s numbers in Baseball Between the Numbers using a “normal” replacement level, the VALUE of a marginal win jumped from what he reported (which I think was $1.5 million or $1.75 million) to $2.5 million. So that’s what a marginal win is worth. But teams are paying about $3.5 million per marginal win on the free agent market. What this means in practical terms, I’m not sure.

What teams “should” pay for players is up to the team or individual, but I’m a big believer in markets.  If free agents get more than $4 million per marginal win, then that’s what they “should” get.

I am a big believer in markets too, but in baseball free-agent auction, as in any auction, there exists a winner’s curse.  By definition this means that it is likely that free agents are overpaid.

Moreover, the baseball isn’t really a free-market, which means that some teams are able to pay more (or overpay depending on which way you look at it) for talent. The two NY clubs jump to mind.

Average payroll is now 90 million$.  Minimum payroll is about 10 million$.  So, that’s 80 million$ to play with for an average team.

Average wins is 81.  “Minimum” “true talent” wins for a team of “true” replacements is anywhere from 45 to 55 wins.  So, there’s 26 to 36 wins for a team with an average payroll to grab.

80/26 = 3.1
80/36 = 2.2

Could we have figured this out without “replacement” talk?  You betcha.

Average revenue is 150 million$.  Each win adds 2% to the revenue stream.  2% x 150 = 3.0 million$.  But, with all that revenue sharing, teams should have a new mindset.  They don’t get to keep all that 2%.  Probably more like 1%, or 1.5 million$ per win.

Any other way to look at this?  You bet again.

Average payroll is 90 million$, or 54MM$ for nonpitchers and 36MM$ for pitchers.  The average nonpitcher get 6MM$ per 162 GP.  Average nonpitcher is 1.8 to 2.5 wins above replacement.  6/1.8 = 3.3, 6/2.5 = 2.4

Average pitcher gets 4MM$ per 162 IP.  Average nonpitcher is 0.75 to 1.0 runs per 9IP above replacement.  Over 162 IP, that’s 13.5 to 18 runs, or 1.2 to 1.6 wins.  4/1.2 = 3.3, 4/1.6 = 2.5

So, any way you look at it, it’s around 3 million$ / marginal win, give or take.

Tango,

I assume that average payroll is calculated on a simple mean. This will be distorted, largely by the Yankees. Isn’t median payroll a better metric - which sits at $72m. Based on your first analysis this gives an answer somewhere between $1.7m and $2m ....

Sorry for the double post. I guess you could also argue that the teams at the bottom of the payroll range don’t compete for FA. Therefore perhaps a number of around $90m is fairer.

Anyway it is all rather moot—the answer stays in the same range.

No, there’s no reason to do that.  The total payroll is 2.7 billion$.  This would be true, regardless of the Yankees hogging-effect.  ARod was signed by the Rangers.  Abreu by the Phillies.  Bernie could have been by the Redsox.  Giambi could have been signed by many teams.  Same with Sheffield.  Matsui, too, etc.  Randy was signed by the DBacks.  If you think the Yanks paid a premium, because of Steinbrenner, then remove the premium amount.  Say, he overpaid, purposely, by 20 million$.  So, instead of a league payroll of 2.7 billion, it’s 2.68.

Even if you insist that you are right, then remove the Yanks altogether.  2.5 billion divided by 29 is 86 million$.  Assuming the Yanks are a 100-win team, then the average number of wins per non-Yank team is 80.3.

Use these figures, in my framework, and come up with sans-Yanks numbers.

Moreover, the baseball isn’t really a free-market, which means that some teams are able to pay more (or overpay depending on which way you look at it) for talent. The two NY clubs jump to mind.

I certainly agree that the free agent market isn’t a perfect market and there are huge inequities between teams.

But there are few perfect markets, and that doesn’t change the basic idea.  There may be a “winner’s curse,” but salaries have risen at a steady pace (10%) except for the collusion years and a stall a couple of years ago.  Which means there are always owners willing to risk the winners curse.

I haven’t thought it all the way through, but I’ve begun to think there is a better way to talk about minimum salary levels.  There are many star players who make less than $400K because they have less than 3 years major league service.

Isn’t it a useful thought exercise to ask, if Team A only spends the minimum salary per year (and has an average farm system), how many games might it win?

The Marlins are one example, but they reaped a lot of value from older players they traded away at the end of last year.  The Kansas City Royals are at the other extreme.

In my data, I have 524 players making the minimum (many have only had a cup of coffee this year).  They have 1,327 “expected” Win Shares and 1,190 actual Win Shares.  If I did my math right, that’s a .450 winning percentage, or 72 wins a year.

Obviously, this doesn’t mean a lot, because most teams are cherry picking their best young players.  But here are the teams that have pushed the envelope the most with minimum-salary players:

FLA: 104 Exp WS, 97 WS, .466 WP
COL: 74, 65, .440
PIT: 74, 61, .412
TB: 66, 45, .341
KC: 57, 35, .307

It’s interesting that for the first five teams, the WP goes down, the opposite of what I would have guessed.

Anyway, KC’s is the fourth worst.  Some of the best teams in this have obviously been selective with some fine young talent: Boston is first at .627 then MIN at .625.

Anyway, does this spark an interest from anybody?

We can’t do a free market analysis in baseball because, as I said, there are owners who are not out to make any money necessarily, whether they know it or not.  Baseball players are a combination of commodities and collectibles.

We can’t do a free market analysis in baseball because, as I said, there are owners who are not out to make any money necessarily, whether they know it or not.

I’m not sure how you’re distinguishing a “free market,” in this case, but the market is what it is, and it’s been sustainable at these rates for many years.  Baseball owners know that they almost certainly won’t go out of business; they have an incredible support system in the community and in Bud.  They spend like it.

Plus, when you factor in long-term revenue contracts (such as broadcast rights) and franchise resale valuations, I believe most of these owners will make good money on their investments.

As one example, the minority owners in the Red Sox made $12.5M for each share sold to John Henry in 2002.  They bought the shares for $500K in the late 1970’s.  If I did my math right, that’s a 14% compound annual rate of return.  The S&P 500 returned about 8.5% during the same time period.

So, the question is, would the Sox have sold for as much money if they hadn’t bought top players many of those years?  My hypothesis is no, marquee players keep franchise value high, and I think most baseball owners have that dynamic in mind when bidding for free agents.

Seems to me that focusing on the short-term bottom line may be missing the bigger financial point.  I come down to two points: salaries have maintained a 10% inflation rate for many, many years, and many (most?) owners are making good money on their investments.

Payroll, revenue streams, and enterprise value have all risen at around 10% a year.  I’m not sure what we’re supposed to read from that.

That’s fascinating.  I didn’t know that.  To me, that means that it’s a good business (10% increase in valuation is a pretty steady business), and the player “market” is pretty darn rational on a macro basis.

10% is probably proper for this kind of business.  It’s not overly risky like those that grow at 20%, or safe, like those that grow at 5-7%.

Don’t quote me on the 10% exactly.  It’s pretty much close to that.  10% growth means doubling every 7 years.  So, a team worth 400 million today is worth 200 million in 1999, 100 million in 1992, 50 million in 1985.

According to Forbes data, since 1990 average revenue growth has been 7.4% CAGR (this is on a per club basis so ignores expansion), average valuation growth has also been 7.4% CAGR and average operating income has fallen 14% CAGR.

This is interesting, not least because value should be driven by profitability and growth prospects. That operating income (EBIT) has fallen and value gone up is a bit strange. This would only happen if investors perceived huge growth which would lead to bigger future profits (and hence more cash in their pockets).

However, my view is that one has to take the EBIT numbers with a bucket of salt. Owners do all they can to ofuscate their finances, so they can play the poor man act to win stadium concessions and have a strong CBA negotiating position. So, I think for the sake of argument it is very likely that this number has increased too. The most profitable team in 2004 according to Forbes? Yup, the D-Rays! Bucket of salt, as I said.

Based on this 10% sounds a little high, 7.5% is probably about right, which isn’t too bad a return. If you include retained profit it is probably a touch higher—I’d certainly expect it to be ahead of the S&P500 for two reasons 1) emotion drives valuations, and 2) baseball is a monopoly with arcane competitive rules that in all other businesses would be deemed illegal.

Good nums, John.  I looked it up, and the average salary has grown 9.9% CAGR during the same period, which explains the declining margin, of course.  I’m suspicious of the EBIT numbers too.

Looking at the data, three of the five teams with negative bottom lines are the three most valuable franchises (Yankees, Red Sox, Mets).  The only exceptions are the Marlins and Angels.

The Angels have experienced a very large increase in their valuation the past couple of years—26% since Arte Moreno bought the team—even though their salaries have risen from $62M to over $100M in the same time.

IOW, there appears to be a negative correlation between profitability and valuation, driven by the unique situations of the major market franchises.

I certainly agree with your assessment of the competitive situation in baseball.  But I still believe the baseball player “market” is rational on a macro basis given the way the business works (I’m not sure how you and MGL are defining a “free” market) and that a valuation of $2.5M to $3M for a marginal win and over $4M for a free agent marginal win are valid benchmarks.

I am by no means an economics expert, and I have no idea what the definition of a “free market” is.  It seems that under a liberal definition, and perhaps one that Studes prefers, almost anything constitutes a free market.

What I simply mean when I say that baseball is not a free market, and I am probably using the wrong terminology, is that while teams appear to appreciate, that it is not necessarily driven by team profit (it could be the same type of appreciation you see in collectibles, which is driven solely by supply and demand) and there is no guarantee that the average baseball team must make a profit (say at least 5% per annum) in the long run, as you would expect from every business (or else they would not be in business).

IOW, in every business, if the cost of doing business is X, you can assume that if you are in that business and you pay X, you will make money.  The cost of doing business in baseball is essentially player salaries.  In baseball, however, you CANNOT assume that the average payroll gurantees a profit (on the average), because I believe that there are many owners who consciously or subconsciosuly do not care if they make any money.

One of the problems with my theory is one, even if teams are partially or even predominantly like collectible items, they may make money in resale (and therefore appreciate) even if they don’t make money in operating revenue. In that case, even though it may seem like owners overpay for players (based on revenue versus cost), they may have to pay that much for players in order to achieve the appreciation that comes from teams being collectible items.  In other words, if you want your team to appreciate, you need to eventually put out a winning product, even if that means you are in the red, operating income-wise.

Good thoughts, MGL.  To me, the definition of a free market is one in which goods and services (i.e. players) can be sold, bought or transferred without undue regulation or other types of interference.  Certainly, I don’t think the market for all ballplayers is “free,” but I do think the market for free agents is a relatively free one.  In fact, given the extent of publically held information, I think it’s a lot “freer” than other markets I’ve personally been in.

I don’t think that’s a particularly liberal interpretation of a free market.  There are lots and lots of markets that aren’t free markets.  Most health care markets aren’t free (due to the nature of health insurance), nor are any markets in which government purchases services (due to governments being governments).  In those markets, I don’t believe that you can properly say that the price for goods equals their value.  However, in a free market, price will closely approximate actual value.

That’s why the distinction is important to me.  Some folks will say that free agent salaries don’t reflect actual value, but it’s hard to justify that point of view if a the market is free.  I think the free agent market qualifies.

Of course, you can say that the owners are acting irrationally, and I wouldn’t doubt it in some (maybe many) cases.  I also believe, as John says, that MLB is a government-sanctioned monopoly.

But baseball teams mostly stay in business.  In fact, their valuations keep rising at a healthy rate.  And salaries keep rising.  To me, this feels like a business in equilibrium.  Most owners are probably acting in a relatively rational manner, given their skewed business realitites.

One other thing: a good cash flow analysis will usually include the eventual resale value of the business in situations like this.  It wouldn’t surprise me if MLB owners pay more attention to Forbes’s valuation metrics than their own bottom line.

OK. We are starting to get into interesting territory here. MGL—in principle I agree with your view. But just a few comments.

You draw a good analogy between baseball and collectables. Supply and demand are the root of free markets, actually the market for everything is driven supply and demand. The interaction of supply and demand sets the price / quantity equation. Since, in your example of collectables, the supply is fixed the change in demand drives price.

The same is true for any business. Take, I don’t know, ipods. If the price goes down more people will buy them. However, a floor has been set on the minimum price: Cost. The same is actually true of the collectable market. There is a cost there, however, depending on what the collector paid for it the cost may be way below the market price so you don’t notice it so much.

So what does this mean for baseball? Well, the number of ball clubs is fixed. Therefore if more people want to own ball clubs then the price (read valuation) will increase.

If you believe that owners have to overpay for players to achieve capital appreciation what you are effectively saying is that you are moving the price (read valuation) floor (by incurring additional cost). However, you are making an assumption that payroll drives valuation. While it may do to an extent it is likely a second order effect. That is why the Expos went for $400m. They didn’t have a big payroll. As we all know it was due to the potential of the market—nothing to do with winning. If Nationals do nothing on the field will their value appreciate less than other clubs. Probably not by that much. The DC market will always give any owner the “option” of having a bigger payroll (as the market can support it). That is why the highest payroll clubs are generally in the biggest markets. The market supports the payroll. The market supports the valuation. The market determines the returns (capital or operational) that are possible from any club.

I guess what I am saying is that in a market with fixed supply even the worse clubs will appreciate. Afterall you can always fix things (or move), and that in itself has an option value that is worth a considerable amount.

______

Studes, you raise an interesting point about the Forbes’ valuation. I have no idea how they do the valuation but I imagine it is comp based rather than using a DCF approach. Whether the owners’ pay attention to it I have no idea. Without knowing the methodology (which based on my very limited research in the value of the Braves (sample size 1) is suspect) I would only be paying a cursory glance.

Studes - I also agree with you about the free agent market. It is probably the most free market that exists in baseball.

Oh and to qualify my earlier post early on I sort of imply that all markets are governed by supply and demand. This obviously always isn’t the case. This doesn’t happen in heavily regulated businesses (as studes correctly points out).

Great post, John.  I have nothing to add, but I was being a bit flip when I referred to the Forbes valuation.  What I’m trying to say is that franchise valuation will be more important than the annual bottom line for almost all owners.  And I think you can make a convincing case that winning boosts franchise value, even if a team finishes in the red. 

That’s just a generalization, of course.  But I think it helps explain the phenomenon of ever-increasing player salaries.