Predicting Major League Baseball Salary Growth

They tell you that baseball salaries are out of control. America’s crotchety old men tell you that it’s supposed to be a game for boys and they all nearly had heart attacks when they found out Robinson Cano was getting $240 million. America’s idealists ask why Cano deserves to be paid as much as 500 schoolteachers. So when I tell you that the deck is stacked against Cano in some way, I better have a pretty good argument.

Every team-centric baseball blog on the planet mentions how its team should be spending more money because of the well-known windfall of $25 million more per season from larger national television contracts. By my estimates, the average team payroll is up by only $7 million on average, about what you would expect in the absence of the large inflow of cash from the league.

Since just 2002, baseball player total salaries as a share of new revenue has declined from 56 percent to 40 percent. That’s right—even though the average payroll has gone up by 58 percent, revenue has gone up by 122 percent. (Revenues are from Maury Brown’s bizofbaseball.com website.  Salaries are from a mixture of bizofbaseball.com and Cot’s Contracts.)

So how do I connect these facts? How do I argue that Cano isn’t really getting his fair share? Simple—I just call upon Econ 101, and introduce the difference between total revenue and marginal revenue. Marginal revenue is the change in a team’s revenue due to the addition of a new player, and because so much revenue has come from national television contracts, local television contracts with only partial team ownership, or just MLB.tv, rather than straight-up ticket sales, marginal revenue growth just hasn’t kept pace with total revenue growth.

Let’s start by looking at the change in salaries and revenues since 1996, with their initial values both indexed to 100:

Although revenues  and salaries both seem to move in tandem until about 2002, revenues started growing much faster than salaries during the next few years and have continued growing faster than salaries since then.

This might be even clearer if we look at salaries as a share of total revenue during this period of time:

Most other major sports leagues have salaries close to half of league revenues, and baseball players were actually doing slightly better than until the last 10 years, when suddenly they started getting a smaller share. Although revenue has gone up so fast that even a smaller share of a rapidly growing pie has kept players happy, understanding why this has happened will be important if revenue growth falters or if the Major League Baseball Players Association (MLBPA) wises up to how much owners are earning nowadays.

Let’s start by ruling out the possibility that baseball has suddenly gotten more popular across the country. While it is not the most perfect metric, World Series ratings do not suggest that the nation has been overwhelmed by baseball fever:

With rapidly increasing numbers of competing options for television viewership, this has happened in many other sports too. Although that extra competition for entertainment dollars could be seen as a threat to baseball’s bottom line, revenue has increased in spite of this.

The reason is that there have been so many successful new ways to monetize baseball. With the growth in information technology and ability to stream games on MLB.tv or watch MLB’s Extra Innings package, teams have been able to get viewership from across the country in ways that were not possible before.

Furthermore, technology has allowed for competing television providers such as DirecTV and Verizon Fios, which have given bargaining power to local networks that broadcast the home nine’s games. While only one local cable provider may have had substantial bargaining power to hold down subscription rates, now satellite and Fios can compete for subscribers by paying hefty rates to the network that broadcasts local baseball games. That makes broadcasting the games more lucrative, and allows teams to charge higher fees to the networks that do so. According to Forbes, aggregate local television revenue increased from $328 million to $923 million from 2001 to 2011, a nearly threefold increase.

Teams have also gotten better at bringing in more revenue inside the ballpark.  Corporate suites at newer ballparks have  brought in even more revenue. However, this does not account for the revenue growth the way that television viewership has. According to bizofbaseball.com, total major league attendance in 2013 was about 74 million fans, which is actually slightly less than the 75 million who attended games in 2005 and just nine percent more than the total attendance of 68 million in 2002. According to Nate Silver, ticket prices averaged about $18 in 2002 and are now about $27.73.

Putting the growth in ticket prices and ticket sales together, I estimate that ticket revenue has grown by only about 68 percent, while league revenues collectively have grown 122 percent. Even though my estimates from various sources are far from perfect, they undeniably point to non-ticket revenues as the larger source of revenue growth. This matters for salary growth.

Now let’s talk about what a baseball team’s revenue sources are, and what drives the demand for baseball labor.

The primary sources of revenue for a major league team by far are ticket sales and local television revenue, but there are also several other factors. These include distributions of national television contract revenue from Major League Baseball, distributions from MLB derived from its other sources such as MLB Network and MLB.tv, and redistributive efforts by the league such as luxury taxes and revenue sharing. Let’s put these into a mathematical formula:

Team Revenue = Ticket Revenue + Local Television Contract Revenue + MLB distribution of funds + Adjustments due to Revenue Sharing + other small factors

In my first article in this series, I discussed the difference between teams that work on simple budgets and base spending decisions based on “affordability” and teams that base spending decisions on rational investment principles. The “affordability” approach does little to explain why the share of salary as a function of revenue has declined so much over the last decade, but the rational investment approach is illuminating.

According to this framework, when a team signs a free agent, it does so because it expects him to lead to more revenues down the line. How much he increases revenue is primarily about how many wins he adds. Sure, sales of jerseys and advertising opportunities matter a little, but they are far from the main source of revenue added.

Without doing any hefty calculus, let’s consider the derivative of revenue with respect to wins. The derivative is just the rate of change, so even without calculus you can think of the following formula as just being changes in each item.

d(Revenue)/d(Win) = d(Ticket Revenue)/d(Win) + d(Local TV Contract Revenue)/d(Win) + d(MLB funds)/d(Win) + d(Revenue Sharing)/d(Win)

Verbally, we are just breaking down the impact of a win into its dollar impact on each of these four general categories. The marginal revenue added per win added is the marginal revenue added from each of these sources.

We know that ticket revenue increases with wins, not just in the present season but also from playoff ticket sales and ticket sales in subsequent seasons. This effect is substantial and is by far the largest share of the revenue value of a win.

Local television revenue is often shared between the network and the team, but the team receives a smaller share of local television revenue than it does of ticket revenue, so the impact on viewership is not as important as the impact on ticket sales.

MLB funds are distributed equally regardless of whether a team won 100 games or 50. This is why the estimated $25 million outlay distributed to each team this offseason did not translate into higher salaries. It is a lump sum transfer. To make teams spend more on salaries, they need to have a higher marginal revenue product per win. This has not changed one cent by any cartoon-sized check the league distributed to its member teams.

Revenue sharing actually has a negative effect on the price of a win, since teams that win more and make more revenue have to share it. So clearly that is not a big part of the growth in the price of a win, since it actually may have gotten more teeth in recent years. However, it could be a small part of why salary growth has trailed revenue growth.

The relative importance of ticket revenue compared to other sources of revenue cannot be understated. Above, I estimated ticket revenue is about 68 percent higher than it was in 2002 and my estimate of the change in the dollar per WAR since then is about 72 percent higher. These numbers are obviously very similar, and the reason is that ticket revenue changes are what drive changes in player salaries more than local television contracts and especially more than national television contracts.

This has implications for the analysis below, but it also has a very interesting application for revenue sharing. One of the obvious consequences of revenue sharing is to reduce the incentive to build a winner,  because teams keep a small share of the revenue generated from doing so. Disagreements between players and owners over revenue sharing generally relate to player concerns about the implication for player salaries. The obvious inference that the MLBPA should draw from the above analysis is that it should push for revenue sharing to occur by distributing more television revenue to smaller market teams, rather than having ticket revenue be shared. Of course, this might mean that larger market teams would have more incentive to spend (without a tax on winning) so it may exacerbate competitive imbalance—the owners would presumably fight this for both that reason and the fact that they don’t actually want to fertilize the ground for higher salaries.

Baseball revenues tend to track the size of the United States economy fairly well, but baseball revenue has  recently grown much faster. Indexing nominal Gross Domestic Product and baseball revenue to 100 in 1996, here is a graph of their growth over time:

However, the United States economy has not evolved uniformly over time. Two things have happened that are significant. One is that we have gotten richer, and the other is that income has been distributed less evenly. Getting richer lets people spend a larger share of their incomes on leisure goods, like enjoying a baseball game at home or at the park, so baseball revenue would grow faster than GDP on its own. But especially since national income has grown unequally, the gains in income have gone disproportionately to the rich, who spend a larger share of their income on leisure already. Combining these two factors, we see why baseball revenue was bound to grow as a share of the economy.

That does not mean that predicting baseball revenue using national income data is useless, especially because the Bureau of Economic Analysis data breaks down nominal spending by industry. The smallest industry subgroup that matches baseball is “Performing Arts, Spectator Sports, and Museums,” which you can see in the graph below. Notice that with the exception of some unsmooth changes in baseball revenue data, they tend to move even more in tandem than baseball revenue and nominal GDP do.

As I mentioned above, ticket revenue is only a share of total baseball revenue, but it tracks salaries much better than total baseball revenue. This is why the PA-SS-M (Performing Arts, Spectator Sports, and Museums) share of nominal GDP is so important to predicting baseball salary growth. In fact, from 2002-11 (the most recently available year of data for this subgroup of national spending), PA-SS-M grew by 67 percent. How much did my estimates of the cost per WAR grow during that time period? By 65 percent, a rounding error away.

So to predict baseball salary growth, we need to see what to expect from this sub-industry. The Federal Reserve projects real Gross Domestic Product to have some “catch-up growth” of about 2.05 percent, and by adding its real GDP projections to the Federal Reserve inflation projections to get nominal Gross Domestic Product projections, we get 4.50 percent, 4.95 percent, 4.70 percent in the next three years, and 4.30 percent thereafter.

The next step is figuring out how much more quickly Performing Arts, Spectator Sports, and Museums should grow relative to nominal GDP. Consider the following graph of three-year average changes in spending of these two categories over the last 25 years:

Up until a little before the recession, PA-SS-M consistently tracked about 2.1 percent higher than nominal GDP (annual average from 1996 to 2007), but this slowed down during the recession. During the slowdown in spending and income, they grew at roughly the same pace. Since the Federal Reserve projects a catch-up period (as do pretty much all models), the growth in PA-SS-M, and hence ticket revenues—and hence cost per WAR—should grow more quickly than just 2.1 percent faster than nominal GDP. I suspect that it will grow about 0.5 percent faster than that to roughly make up for lost ground, so it should exceed nominal GDP grow by about 2.6 percent over the next three years and average about 7.3 percent for 2015-17. Thereafter, I expect it to stabilize at about 2.1 percent faster than nominal GDP, which means 6.4 percent.

Using this data, I project the following changes in the cost per WAR from my $7.6 million estimate of 2014:

Projected Cost per WAR, 2015-2020
Year	$ / fWAR	Inflation Rate
2014	7.6	—
2015	8.2	7.3%
2016	8.8	7.3%
2017	9.4	7.3%
2018	10.0	6.4%
2019	10.6	6.4%
2020	11.3	6.4%

Of course, television revenue will grow at a substantially quicker pace, so while schoolteachers might lament earning 0.2 percent of what Robinson Cano earns, Cano and his fellow ballplayers will know they are still getting a smaller piece of the ever-growing baseball pie.