With the winter meetings over and Opening Day months away, now is an interesting time to consider the economics of baseball.  Earlier this year, I developed a framework for estimating NBA team values for Mid Level Exceptional, which met with a positive reception.  With some tweaks, it can be adapted to MLB team valuation.

In my franchise valuation methodology, each team is priced based on a multiple of its revenue.  These multipliers reflect future earnings potential: the higher the multiple, the brighter the prospects for earnings growth.  This approach is common in finance; Aswath Damodaran, professor of finance at NYU Stern and author of Musings on Markets, used it to generate a back-of-the-envelope valuation for the recently sold Los Angeles Clippers.

Both Forbes and Bloomberg compute estimates of each MLB franchise’s value and annual revenue.  But I’m wary of their valuations.  Forbes consistently undershoots the sale price of NBA teams.  In January, Forbes pegged the Clippers’ value at $575 million; five months later, they sold for $2 billion. Prices for sports franchises have risen sharply over the past few years, as sports programming has become ever more valuable as live TV viewership dwindles.  The Forbes methodology hasn’t incorporated this shift in the value of broadcast rights, leading me to guess that its MLB valuations are also too low.  Bloomberg’s version reflects the same problem.  It values the average MLB team at 3.4 times revenue, not much higher than Forbes’ 2.9 times revenue.

In my version, I started with Bloomberg’s 2012 estimates of franchise revenue, which include revenue from teams’ stakes in regional sports networks and MLB Advanced Media.  (Forbes’ revenue figures are newer, but exclude these important revenue sources.)  To update the revenue numbers, I increased them by 20%, which is in keeping with MLB’s total revenue growth over the past two years.

Then, I created a range of revenue multipliers, which reflect the team’s market size (approximated by the size of the team’s MSA).  They are based on the multiples implied by recent MLB and NBA franchise sales.  In the model, big-market teams have higher multiples; I conclude that they generate disproportionate value from greater national media exposure, prestige, and ability to attract top free agents.  MLB’s lack of a salary cap makes the big-market advantage even more formidable than in the NBA.

I also chose multipliers that are slightly lower than the multipliers in my NBA team valuation model, since I perceive baseball to be a more mature industry than basketball (which means slower long-term revenue growth; this is analogous to Exxon trading at a lower P/E ratio than Facebook.)  Put the revenue and multipliers together, and the result is a range of estimated sale prices for each team.

Before jumping into the valuations, it’s worth explaining the shortcomings of the model.  The revenue multipliers are my best guesses, and I have no hard proof that they’re correct.  Using 2014 revenue data would be more accurate than assuming that individual teams’ revenue grew 20% since 2012, and multiple years of revenue data would be better than a one-year snapshot.  But to paraphrase Donald Rumsfeld, you go to war with the data you’ve got.  This is why I compute a range of likely values; unlike Forbes or Bloomberg, I don’t see the point of highlighting a single number of dubious accuracy.

With that said, here are the ranges of values for each MLB team.

A couple of findings that jump off the page:

• To no one’s surprise, the New York Yankees are the most valuable team in baseball, with an estimated price tag between $3.4 billion and $5.5 billion.  The Tampa Bay Rays are the least valuable team, with a value ranging between $630 million and $840 million.
• 21 teams have a median value of at least $1 billion; in my earlier research on NBA team valuation, only 11 teams out of 30 were valued as highly.
• The big brother/little brother dynamic of the New York and Chicago teams is reflected in their valuations.  The Yankees are worth more than twice as much as the Mets, and the Cubs are worth 40% more than the White Sox.
• The Boston Red Sox are the highest-valued team in a medium-sized market (with a median value of $2.4 billion), and the St. Louis Cardinals are the highest-valued team in a small market (with a median value of $1.1 billion).  This reflects their recent success on the field, as well as their fan base’s reach beyond their core MSAs.
• The Miami Marlins and Houston Astros appear overvalued in the model, since their recent poor performance and lack of popularity are only partially reflected in their revenue.  Their MSA’s sizes probably overestimate the size of their fan bases.  Furthermore, the model doesn’t reflect team-specific issues like fan disenchantment with a team’s owners (Marlins) or difficulty in making the team’s regional sports network widely available (Astros).

Next time an MLB franchise sells, we’ll have a clearer indication of how accurate this valuation method is.

Last month, Dave Cameron published a brilliant yet simple free-agent pricing model.  Using only projected 2014 WAR (ZiPS and Steamer projections are averaged) and the assumption that one incremental win is worth $5 million, it accurately projects the contract length and cost of last offseason’s free agents.  Cameron also made some minor tweaks to his model to project 2015 free agent contracts.  Both articles are absolutely worth checking out in full.

It’d be fun and easy to extend Cameron’s model to predict what David Price (2016), Chris Davis (2016), and Giancarlo Stanton (2017) would make on the free agent market.  (If you’re curious, Price would get 6/$136, Crush would get 6/$112, and Stanton would get 9/$260, assuming that the value of an incremental win increases annually by $500,000.)

But the recent slate of massive contract extensions illustrates the folly of this exercise.  Savvy front offices lock up top talent before it hits free agency, usually at a discount relative to the free agent market.  Young players often prefer an immediate certain payday rather than rolling the dice in free agency, when their future value will be far more unpredictable.  A model that predicts the value of contract extensions would thus be a useful counterpart to the free agent pricing model.  You’re in luck, because I just built one.

I kept the basic contours of Cameron’s model in place; as before, the only inputs are projected 2014 WAR and an estimated value of an incremental win.  This gives us the contract length (projected 2014 WAR times a multiplier that scales up depending on the WAR projection) and average annual value (projected 2014 WAR times $5 million).

To test the accuracy of this approach, I compared the extension model’s output to 32 contract extensions that have been signed since July 1, 2013.  I excluded players projected to produce less than 1 WAR this season.  I estimated the value of an incremental win produced by a closer as $10 million, which lines up with what closers earned in free agency last offseason.  If a player’s extension kicks in after the 2014 season, I counted the remainder of his current contract as part of the extension.

Free Agent Model vs. Actual Contracts

The initial results are mixed.  The model comes very close to the actual average extension contract length (prediction of 5.1 years vs. actual of 4.8 years), but badly overshoots the actual AAV.  Again, this is because GMs pay more for a win on the free agent market than for a win produced by a player already on their roster.  To account for this, I set the value of an incremental win at $3.7 million, the average WAR / $ of the 30 non-closers’ contract extensions.  (For closers, I used $7.4 million.)

Extension Model vs. Actual Contracts

With the adjustment to $/WAR, the results look much better.  The predicted average AAV ($11.3 million) is now only 6% higher than the actual average ($10.6 million.)  For the 31 players on the list (excluding Mike Trout, an outlier if there ever was one), the model projects a total of 147 years and $1.87 billion in contracts; the actual sums are 146 years and $1.67 billion.  Not perfect, but decent.

The model misses very badly for unusual situations.  Jason Heyward and Ian Desmond are projected as 8/$121 and 6/$70 respectively, but they both signed 2 year contracts worth less than $20 million last offseason.  Both players were unable to come to terms with their teams on longer deals.  This is probably because they are the odd men out on teams that have either just made it rain on prodigious young talent (Kimbrel, Freeman, Simmons) or will do so in the near future (Strasburg, Harper).  Instead, Heyward and Desmond opted for shorter contracts in order to avoid arbitration and set themselves up for 2016 free agency.

Mike Trout is a unique case.  The fishy outfielder signed a 7 year, $146 million extension last month, which looks like a massive underpay compared to the 17 years, $541 million (!!!) the model says he is worth.  Don’t get me wrong: for the Angels, the Trout signing is still the best deal since the Louisiana Purchase.  But it’s unrealistic to conclude that the Angels saved $395 million, since nobody would wait until Chelsea Clinton’s second term to test free agency, least of all someone who is currently breaking baseball.

Despite these shortcomings, the model can still evaluate the wisdom of recent extensions.  Plotting the 32 players on a 2×2 matrix (the x-axis is the difference between actual and projected AAV, and the y-axis is the difference between actual and projected contract length) shows which front offices overpaid and which got steals.

Scatterplot of Contract Extensions

The extensions fall into four groups: locked-in bargains, short-term bargains, “win now” splurges, and albatrosses.

• Locked-in bargains are the best kind of extension: these contracts are cheap and relatively long.  Yan Gomes is a good example; the model thinks he’s worth $11 million a year for 4 years, but the Indians locked him down for $4 million a year for 6 years.  Initially, I felt bad that Yan missed out on an extra $20 million, but then I remembered that he’s a millionaire in his mid-20s who probably sleeps well at night, whereas I am a non-millionaire in his mid-20s who does not play a sport for a living.
• Short-term bargains are contracts that are cheap but shorter than projected.  According to the model, Andrelton Simmons is worth $13 million a year for 9 years; the Braves signed him for $16 million a year for 7 years.  So the Braves paid a below-market AAV for Simmons, but deprived themselves of controlling him for two more years (at least in theory).  One caveat here: as explained earlier, Heyward and Desmond fit into this quadrant because their teams were unwilling to pay out for longer contracts, and Trout is simply a freak show.
• Win now splurges are contracts that are expensive but relatively short.  Clayton Kershaw fits here because he makes $14 million more per year than the model thinks he deserves, but has a 7 year contract rather than the 8 years the model would give him.  One could argue that Kershaw is a potential albatross, but if he leads the Dodgers to a World Series this year, their fans, like the Honey Badger, won’t care.
• Albatrosses are exactly what they sound like: excessively long, pricey contracts that make fan bases cry.  Hunter Pence and Homer Bailey are the biggest albatrosses on the list; they were paid an extra $42 million (Pence) and $67 million (Bailey) than the model says they’re worth.  Miguel Cabrera really belongs in this quadrant as well.  The model considers Miggy a win now splurge, but only because it thinks he deserves 12 years rather than 10.  No, Tigers fans, Mike Ilitch did not help me build this model.

Finally, the model can estimate how much your team should pay to extend your favorite young star.

Extension Model for 2015-18 FAs under 30 with WAR > 2

To return to our earlier examples, Chris Davis would get 7 years and $89 million, David Price would get 7 years and $109 million, and Giancarlo Stanton would get 9 years and $148 million if they signed extensions this season.  Of course, it’s tough to predict who will sign an extension and who will try their luck in free agency.  Build me a model that can do that, and I’ll eat my Mets hat.

While watching the playoffs last October, I realized that I had never seen rookies play such a prominent role in the postseason before.  Pitchers like Michael Wacha, Gerrit Cole, Hyun-Jin Ryu, and Sonny Gray propelled their teams into contention during the regular season, and took the hill in multiple elimination games.  The inimitable Yasiel Puig had a similar impact on the Dodgers’ fortunes in 2013.

This observation led me to investigate rookie performance during the 2013 regular season.  Were rookies contributing to the success of their teams more so than in the past?  Were rookie pitchers outperforming rookie hitters?  How about rookies on playoff teams versus non-playoff teams?

Using WAR data from Baseball Reference (sorry, guys) I measured rookies’ contribution to overall team success in 2000-2013, defined as rookie WAR divided by their team’s WAR.  A few definitions before jumping in to the findings:

• Rookies are players who have accumulated less than 130 AB (or 50 IP) and less than 45 days on an active roster prior to their rookie season
• For consistency across time, teams that won the second wild-card slot in 2012 and 2013 are not considered playoff teams (u mad, Reds and Indians fans?)
• Rookie pitcher WAR = amount of WAR created by a team’s rookie pitchers
• Rookie pitcher share of WAR = % of a team’s WAR created by rookie pitchers
• Rookie batter WAR = amount of WAR created by a team’s rookie batters
• Rookie batter share of WAR = % of a team’s WAR created by rookie batters
• Rookie total WAR = Rookie batter WAR + Rookie pitcher WAR
• Rookie share of total WAR = Rookie pitcher share of WAR + Rookie batter share of WAR

In chart 1, rookie share of total WAR for the average team in 2013 (11.3%) is above the long-run average of 8%, and was only exceeded in 2006 (12.7%).  But there was no discernible difference in rookie share of total WAR between the average playoff team (10.9%) and non-playoff team (11.4%) last season.  So far, it would appear as though I need to adjust my TV.

The data becomes more interesting when the average team’s rookie share of total WAR is decomposed into pitcher and batters’ contributions (chart 2).  There is a rapid rise in rookie pitcher share of WAR between 2010 and 2013, peaking last season at 6.7% of the average team’s WAR.  This increase was so strong, it more than made up for a decrease in rookie batter share of WAR during the same timeframe, from 6.5% in 2010 to 4.6% last season.

These trends become starker when the analysis is limited to playoff teams (chart 3).  On the average playoff team in 2013, rookies provided 10.9% of WAR, a step down from the high reached in 2012.  But there is still a huge rise in rookie pitcher share of WAR between 2010 and 2013, to 8.7% last season, and a concurrent decrease in rookie batter share of WAR, to 2.2%.  In other words, 80% of the average 2013 playoff team’s rookie total WAR was generated by pitchers.  If not for a certain Cuban-American hero with a penchant for bat-flipping, that share would have been even higher.

But some evidence, as well as anecdotal observation, suggests that pitchers in general have become more dominant over the past few seasons.  Is this trend, observed so far among rookies, true of all pitchers?  Over the past fourteen seasons, the average team has generated between 36-44% of WAR from pitchers (chart 4).  This share has been consistent over time, and has edged up only slightly during the past few seasons.  This suggests that rookie pitchers, especially those on playoff teams, really did excel in 2013.

Now, let’s look at just how good the rookie pitchers on playoff teams were last season (chart 5).  Together, the 54 rookie pitchers on 2013 playoff teams generated 29.6 WAR, which is slightly higher than last year’s total (29.1 WAR) and much higher than the long-run average (16.0 WAR).  What’s even more impressive is that last season, 57% of all 30 teams’ rookie pitcher WAR was generated by the rookie pitchers on playoff teams, a higher share than in any other season since 2000.  Cumulatively, 54 rookie pitchers on 8 teams outperformed 151 rookies on 22 teams.  Not bad.

But wait…there’s more.  By focusing on the best rookies on playoff teams (arbitrarily defined here as those who generated 1+ WAR), we see that there were 20 such players last season (chart 6).  Of that number, 16 were pitchers, like Shelby Miller, Hyun-Jin Ryu, and Julio Teheran.  Five of those pitchers were on the Cardinals (Miller, Siegrist, Wacha, Rosenthal, and Maness.)  The concentration of top rookie pitchers on playoff teams last year is the highest in at least fourteen seasons.

My initial observation, “Wow, there are lots of rookie pitchers killing it in the 2013 playoffs!” looks to be borne out in the data.  This raises two other interesting questions:

1.  For any of last year’s playoff teams, did rookie pitchers provide enough value to get their team into the playoffs?

2.  Is the rookie pitcher observation a one-time anomaly, or indicative of a larger trend?

The first question is relatively easy to answer.  We can compare each playoff team’s rookie pitcher WAR (essentially, how many more games the team won because of rookie pitchers) to the number of additional games each playoff team could have lost and still made the playoffs without tying a second-place team (let’s call this the buffer). 

For four out of eight playoff teams (again, I exclude the second wild-cards), rookie pitcher WAR is higher than the buffer (chart 7).  But since Detroit and Tampa made the playoffs by one game, and since Pittsburgh’s rookie pitcher WAR is less than one game higher than the buffer, it’s hard to argue that rookie pitchers definitively moved the needle for them. Andy Dirks or Yunel Escobar could have just as easily gotten their teams over the hump, since they also created more than 1 WAR.

The Cardinals are the one team whose rookie pitchers probably got them into the playoffs.  They got 9.7 extra wins from their rookie pitchers (almost 23% of the entire team’s WAR), and made the playoffs by 6 games.

The second question is harder to answer, since the 2014 season hasn’t started yet.  There’s no clear reason why rookie pitchers on playoff teams would suddenly start playing extremely well, especially since it doesn’t look like they’re causing their teams to make the playoffs.  The likeliest explanation is that the top teams in the league happened to have outstanding rookie pitchers last year.  Sometimes, “stuff” happens.

But if you want to prove me wrong, and show that last year’s playoff teams have developed great farm systems capable of producing more top rookie pitchers, pay close attention to what Jameson Taillon (Pirates), Carlos Martinez (Cardinals), Jake Odorizzi (Rays), and Allen Webster (Red Sox) bring to the table in 2014.  All four pitchers are on Baseball America’s list of top 100 prospects, are on last year’s playoff teams, and are projected to crack the majors this season.  If they get off to a hot start, and if they help their teams return to the playoffs, I might have to revisit my conclusion next winter.