Monday, October 05, 2009

Stacey Brook on salary caps and competitive balance

You'd think that when a sport introduces a salary cap, it would lead to greater competitive balance in the league. That would make sense; with a cap, you won't have teams like the Yankees, who spend two-and-a-half times as much on players as the average team, and about five times as much as the Marlins. If you forced the Yankees to spend only the league average, they would have to get rid of many of their expensive star players, and they'd win fewer games.

In theory, if every team had to spend the same amount, they'd all start the year with equal expectations. I say "in theory" because, in practice, different teams would have different philosophies, some of which might work better than others. Certain teams might spend more on scouting, wind up drafting better, and win more games with the same payroll (at least until the draftees reach free agency). But, generally, you'd expect more balance among teams.

It seems that Stacey Brook, co-author of "The Wages of Wins," doesn't think that's true. He thinks that the salary cap (and floor) the NHL instituted in 2005 has had no effect on competitive balance.

Here are Brook's "Noll-Scully" measures of competitive balance for the last few years of the NHL (lower numbers = more balance):

2000-01 1.858
2001-02 1.581
2002-03 1.592
2003-04 1.633
salary cap begins

2005-06 1.637
2006-07 1.600
2007-08 1.037
2008-09 1.369

It does seem, Brook acknowledges, that competitive balance has improved the last couple of years. But, he says, that's part of a trend that's been going on for a long time. For one thing, there was virtually no change in the Noll-Scully the first two years after the cap. For another, balance has been improving since at least the 1970s:

1970s 2.557
1980s 1.969
1990s 1.796
2000s 1.538

Since competitive balance has been increasing even through most of hockey history that had no salary cap, he argues, it's just a continuation of the trend, and the salary cap doesn't have anything to do with the recent decline. He writes,

"As we argue in The Wages of Wins, and detail in our paper - The Short Supply of Tall People - competitive balance is declining not because of changes in league institutional rules - such as payroll caps - but rather due to the increasing pool of talent to play sports, such as hockey."

But that doesn't make logical sense. Sure, there's already a decreasing trend, for whatever reason, but that doesn't mean a change to the rules can't contribute to the trend. Does having the ability to send text messages lead to people using their phone more? Of course it does! But if you apply the same argument, you get something like, "well, cell phones were becoming more and more popular even before text messaging, so text messaging can't have anything to do with it." That's not right.

And, indeed, it contradicts their own findings in "The Wages of Wins" itself. The authors found that there was an r-squared of .16 between salary and performance in MLB. Which means that if you were to flatten out salaries, so that each team paid an equal amount, it would reduce the variance of wins by 16%. So, absent any compensating factors, "The Wages of Wins" is argues a salary cap MUST reduce the Noll-Scully measure!


By the way, take a look at the value of 1.037 for 2007-08. That's really, really low; the lowest you can expect Noll-Scully to be is 1.000, and that's when every team is of exactly equal talent. A value so close to 1 suggests a combination of (a) the league being really balanced that year, and (b) teams, by luck, playing closer to .500 than their talent suggested.

If you look at the standings, you see the usual suspects at the top of the conferences, so it doesn't really seem like all the teams were equal that year. Could it be that Brook used a formula for Noll-Scully that didn't consider the extra point for an overtime loss?


But what about Brook's (and Berri's) argument that balance has increased because players' skills are becoming more equal? Well, sure, that's been part of it, no question. But effects often have more than one cause. You may be earning more money because you're working overtime, but that doesn't mean winning the office hockey pool will *also* make you richer. Whatever was causing the levelling of team talent before might still be there ... but, now, there's an additional effect, the salary cap effect.

Now, maybe I'm not interpreting Brook's argument correctly. Maybe he's thinking that the salary cap does contribute to balance, but so much less than the other effect (players getting more equally talented) that it's not worth considering. But I think it's the other way around. With a salary cap, it doesn't matter much how the players' talent is distributed.

Suppose players vary a lot in talent, 100 players equally spaced from 0 to 100, with an average of 50. A team that has lots of money might buy players with an average of 70, and a team owned by Harold Ballard might buy players with an average of 30. Big difference.

Now, suppose the talent pool gets bigger, and competition gets tougher, and now the players are all spaced between 40 and 60. Now, no matter how much you want to spend, you can't get above 60. And no matter how cheap you are, you can't get below 40. But the league average is still 50.

So, yes, Brook is correct, a narrower range of talent leads to more competitive balance.

But, now, suppose that every team has a salary cap and a floor: they all have to spend exactly the same amount of money. Now, it doesn't matter how the talent is distributed: assuming every team is equally good at evaluating players, they'll all sign a team with an average of 50. Even if the distribution of talent is like it was in the 1970s, with lots of spread, it doesn't matter -- because even if there are lots of players in the 90s and 100s, no team can afford to sign more than one or two. The more talented the player, the more likely a team who signs him will have to sign *less* talented players to stay within the cap.

Even if you have the Babe Ruth of hockey, a player who's (say) a 500 when the other players top out at 100, it won't matter, because the teams will bid up the price of his services until they pay him what he's worth. The team who gets him will have less money to spend on other players, and it all evens out in the end.

What's happening is this: in the past decades, competitive balance decreased steadily for many reasons, including the increase of the talent pool that Brook cites. But, now, with a salary cap and floor, most of that stuff doesn't matter much any more!

It matters a bit, because not everyone is a free agent. The distribution of talent does matter for draft choices, because the top draft choice doesn't cost that much more than the others (but can be a whole lot better, as in Sidney Crosby).


Of course, NHL hockey teams are more than collections of free agents priced at market value, so we shouldn't expect competitive balance to be perfectly level. There are some factors that might cause the Noll-Scully to actually rise a bit from the theoretical bottom created by the salary cap.

For instance: the first draft choice goes to a team near the bottom of the standings. Back in the days of less competitive balance, that went to a team that was probably legitimately awful. Now, with teams closer in talent, it could go to a team that was just unlucky. If the team that gets the next Sidney Crosby is an average team, rather than a bad team, that won't reduce competitive balance the way it used to.

Also, scouting: an investment in scouting now pays off more than it used to. Before, if you were a low-spending team, maybe a better draft choice might move you from .400 to .450. Now, if all teams are medium-spending, maybe it'll move you from .500 to .550, and give you a legitimate shot at the Stanley Cup. So more teams should be willing to spend the money to improve their drafting. And so, the rich teams could "buy" better players, not by spending to pay them, but by spending to identify them better.

And there are probably other ways to get around the cap: didn't companies introduce employee health plans to get around wage controls in World War II? If a superstar free agent has knee problems, and I wanted to sign that player, I'd offer to hire the best knee doctor in the business and keep him on staff. Whatever he costs, it's not going to count against my cap. That may not actually be practical, but I'm sure rich teams will figure out ways to buy better teams, one way or another.

My point is not to say that these factors will push inequality back to where it was when teams could sign all the free agents they were willing to pay for, just that there may be other theoretical reasons that Noll-Scully may bounce back up a little bit. I think all those factors will be minor, and as long as the salary cap and floor stay within roughly the same range of each other, we'll continue to see a balanced league, regardless of how the talent pool changes.

Hat tip: The Wages of Wins

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At Monday, October 05, 2009 10:48:00 PM, Blogger doc said...

I think you're missing what we economists think is one of the primary mechanisms by which the Noll-Scully effect works. And that's on the value of players (with different skill levels) to different teams.

Back in the 1950s (in the not-to-be-regretted-passing-of) reserve clause days, Simon Rottenberg argued that, regardless of the rules governing player compensation or movement of player talent, we would expect talent to flow to the employer who values it most highly. And, he argued, this did not mean that the richest teams would acquire all the best talent. After all, what's the *additional* value of (say) Prince Fielder (or even Albert Pujols) to the Yankees? Not all that much.

So, he argued, even with the reserve clause (and by extension with salary caps), player talent would move toward its highest vauled use.

In terms of competitive balance, then, the argument is that, at the margin, talent will move regardless of the mechanisms that determine salary. In Marxist terms, those mechanisms are simply a redundant superstructure which hides the real forces that operate out of sight.

So it's possible to observe two things happening simultaneously--increasing competitive balance (as teams become better at evaluating talent, as the number of talented players increases, and so on) and decreasing total payroll differentials between teams (because of salary caps). But the fact that the two things are happening simultaneously does not mean that salary caps cause competitive balance (doesn't mean salary caps are irrelevant, either).

But the salary cap-leads-to-competitive-balance story doesn't do a very good job of explaining increasing competitive balance in the absence of salary constraints. And the alternative story--that talent flows to where it's most highly valued (which, in the presence of salary caps *does not mean* to whichever team is willing to pay the most)--does work even in the absence of restraints on salaries.

(Note also that salary caps and compression of salaries are not the same thing. It's equally possible to have a small number of very highly paid players on the one hand and a large number of players making something near the minimum allowable player salary on the other.)

(Note also that causation may run from performance success at the team level to higher salaries rather than from higher salaries to performance success. As far as I know, no one has done a good job of testing that hypothesis, but it would explain the more-or-less random shedding of talent that goes on by successful teams in the the NFL.)

I would agree that it is possible that salary caps have an effect on competitive balance. But I'm not persuaded that the effect is large--or even real.

At Tuesday, October 06, 2009 12:46:00 AM, Blogger Phil Birnbaum said...

Hi, Doc,

I agree with what you say about Rottenberg (I guess it's normally referenced as the Coase theorem when not applied to sports?). But I think that doesn't apply when you have a salary cap.

The idea, as I understand it, is that if a season of Derek Jeter is worth $20 million to the Yankees but only $10 million to the Royals (because of how much revenue he will generate), he will wind up with the Yankees one way or another. The Royals will trade him, or sell him, or let him go as a free agent.

But, with a salary cap, how does that happen? You could have the situation where the Yankees desperately want a free agent who costs $10 million but will generate $15 million ... but they're not allowed to sign him! So they're stuck. The Coase Theorem has certain assumptions about a (mostly) free market, does it not? And a salary cap doesn't satisfy those assumptions.

Let me put it to you this way: let's suppose that you and I have a two-person rotisserie auction. We each have $260 to spend. We *have* to spend it all.

However, you're the Yankees and I'm the Royals. If you win, you win $500. If I win, I only win $300.

Still, doesn't the salary cap/floor mean that we will bid roughly the same for all the players, and your chance of winning is exactly the same as mine?

At Tuesday, October 06, 2009 2:43:00 AM, Blogger doc said...

Part 1 of this rant.

I think you miss one of the salient points. The salary cap--if it's effective--will drive down the salaries of the best players, and thus will drive down the cost to any team of employing them.

Then, to employ a player to whom I cannot pay as high a salary as I want, all I have to do is acquire that player from a team that can sign him, to a lower salary than I am able to pay him. So, if Derek Jeter is worth $20 million to the Yankees, but is signed to a $10 million salary by the Royals, then all that's required is for the Yankees to transfer $10 million worth of something (minor league players, cash, whatever) to the Royals and take on the $10 million salary.

It's not what I pay directly to the player that matters, it's what I pay to acquire the player's whomever I pay it. Just as the Red Sox made a huge side payment to the Japanese team which held the contratual rights to Dice-K. And that's something that would become, in one way or another, even more common.

The result is to transfer wealth from teams for whom talent is worth more to teams for whom talent is worth less (rather than transferring it to the players). It just doesn't show up as a salary expense.


Part 2

I should have noted (and will take the opportunity to do so here) that the assumption that absolute competitive balance (perhaps define as an equal probability over time of each team's winning championships) may not be an ideal outcome from the point of view of the league.

If we treat the league as a cartel seeking to maximize its joint profits (and then figuring out how to redistribute them), it may be more profitable if teams in some markets (e.g., New York, LA, etc.--population and media centers) win more than "their share" of championships. And so a degree of competitive imbalance is then desireable. In fact, I think there is at least some research (unfortunately, I'm not at my office right now) suggesting that this is true.

Finally, the notion that the current arrangement benefits "big market" teams is somewhat ill-defined. Which teams are big market? New York, to be sure, but the Yankees do have to share the sports market there with the Mets, and, at least for parts of the year, with the Jets and the Giants and the Knicks and the Nets and the Rangers and the Islanders. And the entertainment market with even more. Boston? LA may be a better example because of the absence of an NFL team and the presence of only one NHL team. But, then, there are a lot of other summertime entertainment activities in LA.

Part of the problem is that we tend to identify "large market" with teams that have large payrolls (Yankees, Mets, Dodgers, Angels, Red Sox). What we need is an independent definition of "large market." Which I could develop, but, again, other people have already done it (and, again, I'm at home). But Houston and Dallas would count, as would Chicago. And Philadelphia. Probably Atlanta. But probably not St. Louis. Probably not Minneapolis. Probably Miami, for that matter. Maybe Seattle. Maybe San Diego.

Without doing a lot of work, here are the places I would identify as likely small market (at least in MLB, which is the sport I know best):

Milwaukee (9th in MLB in 2009)
Detroit (not based on population, but on disposable income)(12th)
Tampa (24th)
Kansas City (25th)
Cleveland (26th)
Cincinnati (27th)
Pittsburgh (28th)

Florida, which I think is in a large market ranks 29th, and Oakland, which shares a large, and fast-growing market, ranks 30th. Toronto, another large market, is 23rd.

So, of course, market size matters and there are revenue streams not tied to attendance. But I would argue that we regard Boston as a large market team because the management has developed large revenue streams. And Philadelphia, which a decade ago was generally one of the places referred to as a small market--3rd in attendance this year.

Why do the Cubs rank 6th in attendance and the White Sox 16th? Mostly, I would argue, because of differences in the management of the teams (and secondarily in the less-desireable location of the Sox), not because one is in a large market and the other in a small market.

I suppose ultimately I'm troubled by salary caps and other salary limiting devices for a moral, not an economic reason. Ultimately, what salary restrictions do is transfer wealth from the players--who produce that wealth--to team owners. And I'm not sure why I want the Steribrenners (and the other partners in the Yankees' ownership) of the Ricketts' (now that they apparently have the Cubs) or the Morenos of the Hicks to have more of that wealth. (Or Jerry Jones, in the NFL.)

What I am sure of is that salary restrictions will not lead to lower ticket (or concessions or souvenir) prices, or to teams/leagues accepting lower media payments. Why should they?

At Tuesday, October 06, 2009 8:34:00 AM, Anonymous Guy said...

Doc: Are NHL teams allowed to sell players? I doubt that is the case. And if not, then it's hard to see how the transfers take place. (There aren't enough minor league players with certain value to provide enough "currency.")

Also, I'm not sure how it helps the Yankees to spend $20M for Jeter in your example. Assuming a free market for salaries, Jeter's salary reflects his talent relative to other players. The Royals would gladly take the Yankees' $10M, then go out and buy a comparable player (or 2 $5M players) -- KC has the same talent, but it's free! Why isn't that a great deal for the Royals?

I think rich teams can only game the salary cap if there is some kind of system of exploitation of young players, like MLB's salary limits for younger players. Then there is excess value relative to salary, and poor teams would sell/trad those players to rich teams.


I would also note that the impact of the NHL cap was phased in over a few years, as the minimum payroll was raised relative to the top, narrowing the spread of payrolls. So the very high levels of competitive balance the past two seasons (assuming Brooks' calculations are right), which represent a much faster change than prior years, certainly looks like evidence that the cap is working. It's a small sample, and maybe the trend will reverse, but it's positively bizarre to look at that data and conclude the cap is likely not working.

At Tuesday, October 06, 2009 8:43:00 AM, Blogger Phil Birnbaum said...


Sure. But then the Yankees' payroll goes up by $10 million, which puts them over the cap!

If the Yankees have (say) a $100 million cap, they've already signed 10 Jeters to fill the cap. As much as they'd like to have the 11th, which looks like a bargain, the rules prohibit it, even if the 11th is worth more to them than to the Royals!

Am I missing the point? Suppose the Yankees are already at their cap limit. The Royals have a $10 million Jeter that they Yankees value at $30 million. It would be in both parties' interest for that player to be sold to the Yankees for $20 million.

How do the Yankees make this transaction work and still remain within the cap?

At Tuesday, October 06, 2009 8:44:00 AM, Blogger Phil Birnbaum said...


Ah! Thanks, Guy, that explains why there was no apparent effect the first two seasons. I was wondering.

Do you know where we can find the details of the "phase-in"?

At Tuesday, October 06, 2009 9:46:00 AM, Anonymous Guy said...

Wikipedia has an entry on NHL salary cap here: Assuming the info is accurate, the ratio of minimum:maximum payroll was 55% in year one, but is now 72%. So the allowed range is tightening. I don't know the exact pace of tightening over the 4 seasons, nor whether any other transition steps were taken (e.g. grandfathering of certain contracts) that might explain less balance the first two years. I suppose one could look at SD of payrolls, relative to the mean, to see if payrolls in fact became more uniform the last 2 seasons.

At Tuesday, October 06, 2009 1:21:00 PM, Blogger doc said...

"How do the Yankees make this transaction work and still remain within the cap?"

That's easy. They give up a player worth $10 million (to them) obtan a player worth $20 million (to them), to whom they only have to pay $10 million...

At Tuesday, October 06, 2009 2:07:00 PM, Anonymous Guy said...

In your scenario, every player is more valuable to the Yankees, because each win is more valuable to them. So they will make a big profit on all players. But they won't get better players than any other team that can also afford a payroll equal to the cap. They will make more money than other teams, but not win any more games.

Tell us the rest of your story. The Yankees have just paid $20 for Jeter. The Royals use the Yankees' $10 M to buy an equally talented player. But, you may say, that other $10M is worth more to the Yankees, so they will again pay the Royals for his rights. BUT, the Yankees still have to come in under the payroll cap (let's say $100M). They can only have $100M worth of salary on the books, same as everyone else. They have no advantage on the field.

Again, that changes if you have non-free-agent players, whose salary is less than their real value. Those players are extremely valuable, allowing a team to beat the cap, and rich teams would pay for those players if the rules allowed that.

At Tuesday, October 06, 2009 2:41:00 PM, Blogger doc said...

Guy, I don't think I ever said that every player is more valuable to the Yankees. In fact, I explicitly said that (sor example) Prince Fielder and Albert Pujols would add very little additional value to the Yankees.

To an economist, the issue is the player's *marginal* productivity--by how much does the player improve the team? If we take the Yankees' talent level to be a "true" 100-win team (I don't, actually, but that's irrelevant), then the issues are (a) by how much will Player A increase the Yankees' wins and (b) for a 100-win team, how much is an *additional* win worth? Remember that in making the calculation in (a), we're interested in what the player adds, we have to account for who gets replaced.

To answer (a), we have to know the productivity of the player that Player A will replace. Suppose we replace Teixeira with Pujols. According to Baseball Prospectus, Pujols in 2009 has a VORP of 98, while Tex is 50. That translates into about 5 wins (if I recall the translation correctly) for an *average* team, which I actually don't buy as a correct measure of the difference for these two players. Replacing Tex with Pujols on a team that is already a 100-win team is likely to be worth maye 2 wins.

Then, what are those two additional wins worth to the Yankees? Well, probably less than they're worth to a 90 or 92 or 94 win team; they're unlikely to make the difference between the Yankees making and not making the playoffs for example. I'm vaguely recalling that at the level of a 100-win team the marginal (dollar) value of a win (help me out here, Phil) is something around $1 mmillion. So the marginal value of Pujols compared with Tex is around $2 million--you'd be willing to pay $2 million more for Pujols than for Tex.

But a 90-win team might be willing to pay $4 or $5 million more.

The *marginal* value of a player *falls* as the *team* in question is better--he adds less to the performance and to the revenue of a better team.

There's evidence dating back more than 20 years that the marginal value of a "star" player is higher to a mid-level team, for whom that player might come closer to pushing them over the boundary and into the playoffs than to a really good (or a really bad) team.

So the issue is not the average value of a player's performance, it's the marginal value of that performance. And if you already have a star player at a position, then adding a bigger star won't add all that much.

Of course, this assumes what economists call optimizing behavior on the part of management, which we (i.e., economists) think is an OK assumption even in professional sports, but which you don't have to agree with,

At Tuesday, October 06, 2009 2:45:00 PM, Blogger doc said...

Guy, another thing. Your argument assumes that the overall level of salaries remains unchanged. With salary restrictions (the form of the restrictions isn't particularly relevant), I think we have to assume that the average player salary will fall.

And you're right about non-free agent (and non-salary-eligible) players. And to prevent movement of those players to their highest-valued employers--which is what we're talking about, after all--we need an additional set of rules governing player movements.

That's worked out well in the NBA.

At Tuesday, October 06, 2009 2:51:00 PM, Anonymous Guy said...

The most important difference between teams is their market, not their strength. Wins are worth more to the Yankees because they generate more revenue for them. That's what I meant by the statement. That's true at 81 wins, or 90 wins, or even (I'd guess) 100 wins.

I agree there is a sweet spot for wins, btwn say 85 and 95 wins, and after that the value declines a bit. But I doubt the falloff is anywhere near as sharp as you speculate. Even after 95 wins, a stronger team has advantages: winning homefield advantage in the playoffs, and maximizing your chance of reaching/winning the WS. Not to mention the huge uncertainty each team faces in terms of injuries, underperformance, etc. Even a true-talent 95 win team would fail to reach the postseason some years. In the end, I don't think you would be far off if you just said every extra win above 85 had the same value for any given franchise.

Finally, I don't see how this addresses the issue you raised. With a salary cap, Tex and Jeter and Pujols and everyone else will still be paid according to their win value -- the only difference is that the $/win could be lower (assuming cap is set at lower % of revenues than current payroll). The fact that the Yankees receive more revenue per win doesn't allow them to get any better or different players than anyone else.

At Tuesday, October 06, 2009 3:02:00 PM, Blogger doc said...

Guy, I continue to think you're conflating the average value of a win to the Yankees with the marginal value of a win. I tried to indicate that my conclusions are based on actual research on the marginal value of wins--and, yes, if I recall the research correctly, the marginal value of wins does fall off quite rapidly above about 95. Yes, the Yankees take in more revenue that anyone else, so Revenue divided by Wins is larger for them. But *if I remember the research correctly*, Marginal Revenue divided by Marginal Wins isn't all that different for them.

At Tuesday, October 06, 2009 4:21:00 PM, Anonymous Guy said...

Doc: the marginal value of wins after 95 is a trivial issue -- very few teams have >95 wins of true talent (even the Yankees).

Anyway, I don't see what this has to do with the salary cap issue. Can you respond to the points that Phil and I have raised? I still don't see what the Yankees gain by paying $20M for a player they can get for $10M.

At Tuesday, October 06, 2009 8:08:00 PM, Blogger JavaGeek said...

A few comments about the NHL in particular:
1. Very difficult to get rid of "salary cap".
- buyout: you're stuck with 66%
- trades: you've have to find a partner. Who wants lots of CAP, generally charges high premium (lots of draft picks...)

2. Loopholes
- Retirement contracts (contracts signed passed expected retirement - if player retires contract retires w/ him)
- IR room (this makes long NHL contract like a free medical insurance policy - continues to pay when injured, but doesn't affect cap).

3. Some other issues
- Non-market benefits (players will choose to sign in the market they prefer, rather than their best $ offer). Edmonton vs. Anaheim.
- Bad teams have a harder time improving b/c no one wants to sign there.

In regards to cap "shouldn't affect comp balance". Just look what has happened to Colorado, there's a team that is willing to spend about $20-30M more on salary to get 5 or so more wins/year, but cannot. Marginally speaking spending $30M would make the team more money (let's say spending $1 would give them $1.1), but they simply cannot make the choices that would make their team more profitable b/c the cap wont let them.

At Tuesday, March 08, 2011 10:10:00 AM, Blogger Deron R. Pope said...

Competitive balance has more to do with the draft, and the ability of a team to resign its own players. Check out these short studies.


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