America's Favorite Pastime: Doing Math


The 2013 baseball season is barely a month old, and there is already an abundance of analysis by sports media outlets and fans alike about how teams are performing. These analyses range from simple couch mathematicians looking at wins and losses to heavy tomes of statistical measures that would fit perfectly in any Stanford research paper.  

Statisticians have always delighted in analyzing baseball – some would say, analyzing it to death. More than any other sport, baseball is filled with statistics and arcane-sounding metrics that leave the average person cotton-mouthed and dull-eyed. So-called "sabermetricians" (followers of the Society of American Baseball Research, or SABR) pore over fascinating stats like "batting average on balls in play" (a measure of how many balls in play against a pitcher go for hits, excluding home runs, used to spot fluky seasons) or "value over replacement player" (a measure of how much a player contributes to their team in comparison to a fictitious replacement player who is an average fielder at his position but below-average hitter).  

Now there's a whole new category of relevant statistics for front offices and fans alike to sink their teeth into. The Journal of Sports Management has just accepted a paper from Fordham University business professor Stanley Veliotis, titled “Salary Equalization for Baseball Free Agents Confronting Different State Tax Regimes.” If the title doesn’t perk you right up, maybe the abstract will:    

"This paper derives equivalent gross salary for Major League Baseball free agents weighing offers from teams based in states with different income tax rates. After discussing tax law applicable to professional sports teams’ players, including 'jock taxes' and the interrelationship of state and federal taxes, this paper builds several models to determine equivalent salary. A base-case derivation, oversimplified by ignoring non-salary income and Medicare tax, demonstrates that salary adjustment from a more tax expensive state’s team requires solely a state (but not federal) tax gross-up. Subsequent derivations, introducing non-salary income and Medicare tax, demonstrate full Medicare but small federal tax gross-ups are also required. This paper applies the model to equalize salary offers from two teams in different states in a highly stylized example approximating the 2010 free agency of pitcher Cliff Lee. Aspects of the models may also be used to inform other sports’ players of their after-tax income if salary caps limit the ability to receive adequately grossed-up salaries."  

Whew. Isn’t baseball fun? In layman’s terms, Veliotis’ new statistical measure can help a free agent decide between different teams based on how much taxes he would owe in each state.

Just imagine the debates this paper will inspire! How will interleague play affect equivalent gross salaries for NL East teams playing even more games in tax-heavy New York? Does A-Rod really come out ahead by sticking with the Yankees? Will fists fly when Canadians realize none of this has any meaning for the Toronto Blue Jays?  

Taxes have always played a role in professional sports. Lebron James of course chose the Miami Heat because he felt that would give him the best chance to win a championship, but really, Florida's sunny tax-free climate had to have been noticed, right? And who can blame golfer Phil Mickelson for threatening to abandon California to escape a 63% tax rate? But only baseball would apply a statistical framework to the idea of players paying taxes!  

If anything could give the tax code a run for its money as the most complicated collection of numbers and rules in America, it would be baseball’s sabermetrics. Joining forces, they are now a super code of mathematical calculations! Now not only can stats geeks use measures like the "player empirical comparison and test algorithm" to guess how players might perform for the rest of the season, they can also use ‘salary equalization for free agents confronting different state tax regimes” to analyze a free agent’s every move. Huzzah!