One Star... and 24 Other Guys

That was the perception around the Texas Rangers from 2001-03, when Alex Rodriguez earned $66 million, hit 156 home runs, and led a team that compiled a record of 216-270, finished last in their division all three years, and never finished within 25 games of first place.

Baseball is a curious sport and the philosophies regarding team construction are numerous and incredibly diverse.  Some teams build their organization on a strong farm system and rarely, if ever, venture into the free agent market for a star player.  Others seem to frequently eschew that same farm system and attempt to purchase known commodities (or what they hope are known commodities) on the free agent market.  The most successful franchises, not surprisingly, combine the two; they combine a good farm system and high quality young players performing on below-market contracts with a handful of free agent veterans acquired to fulfill one need or another.

If there is a trend in Major League Baseball, it is that teams are flush with cash due to the skyrocketing revenues of the latter half of the Bud Selig era (he became the interim commissioner in 1993) and that they finally became sick and tired of watching their homegrown stars jump ship for sunnier financial climates.  Teams have been signing young players to lengthy, pricy contract extensions right and left over the past several years but each and every one of those contracts is likely less than those players would have fetched on the open market.

Think about it this way; a player has to sacrifice some value because they are still young and the market isn’t quite sure if they are going to be the same caliber of player over the longer term.  The team has to increase the value of the contract offer because they are attempting to increase their length of “control” over the player’s rights.  For star young players that might earn more than $10 million per season in salary arbitration before they hit the free agent market, this can be very costly.

Mike Trout is the perfect example of this practice.  He had just completed the most productive two year stretch for a player his age in baseball history and was widely considered the best player in the game.  If the Angels had allowed him to go to salary arbitration, a stepping stone before free agency, there is no telling how much he would have earned.  As ridiculous as it sounds, $25 million per season from arbitration would not have been outside the realm of possibility and if he kept performing, the cost of his services as a free agent would have been even higher.

Trout and the Angels agreed on a 6 year extension worth $144 million, buying out (I believe) three years of his potential free agency.  Trout gets paid and the Angels get his services at a discounted rate.  It should be noted, however, that due to the structure of the contract, his last three years will all be at a salary of $33.25 million.

GIANCARLO STANTON

All of this discussion brings us to the most recent small (ish) market team locking up a young superstar for years to come.  You may not think of Miami as a small market but when it comes to supporting a sports franchise (especially baseball) is most definitely is.

Stanton and the Marlins signed a contract guaranteeing the young slugger $325 million over the next 13 years.  Both the length of the contract and the total value are record-breakers.  It is possible that Stanton will opt out of the contract (as he is allowed to do) in order to attempt to secure another long term deal but I think this is somewhat unlikely.

This is what Stanton’s extension looks like graphically.  His salary will rise to $32 million from 2023-25 before tapering off slightly.  The important part is that it’s very backloaded and the opt out point in the contract is relatively early.  After the 2020 season, Stanton will be 30 and at that point, he will have 7 years and $208 million remaining (there is a team option for 2028 at $25 million or a $10 million buyout).  Even if Stanton does continue the pace he’s on, is he going to be worth that much as a 30 year old free agent?  I can’t quite wrap my mind around that but truthfully, anything is possible and it only takes one convincing agent and one stupid owner to have a contract like that come to fruition.

The question I’m going to attempt to answer statistically is was this a wise move on the part of the Marlins?  There are many reasons why it would be a good idea for them to offer this contract.  Stanton’s tape-measure home runs might help put fans in the seats, their willingness to open the pocketbook after a recent history of exactly the opposite might attract other free agents to south Florida, and most importantly, the Marlins’ local TV deal is about to expire.  They will get a far more lucrative deal if a cable company knows that Stanton will be in the fold for more than a decade.

However, does the move make baseball financial sense?  Despite the lack of a salary cap, I would argue that every team has a budget.  Some ownership groups are more willing to bend that budget than others but the budget still exists.  If one player is taking up a huge chunk of that figure, can a good baseball team be built around him?  That is what I will attempt to answer.

HAVES AND HAVE NOTS

Baseball already has extreme salary dichotomy.  While the league minimum is nothing to sneeze at (I believe it’s up to $400,000) by real world standards, it is just 1/83 of the highest single season salary ever paid to a player (Alex Rodriguez’s $33 million in 2010).  Stars stick around for a long period of time and make obscene amounts of money while just about everyone else is scrounging for whatever is left, often playing for something near the league minimum.

A few quick notes… For this project, I’ve obtained volumes of data from baseball-reference.com, including as much salary information as I could find.  It’s not perfect, but it will be good enough for what I’m looking at.  I’ve arbitrarily decided to go back ten years (2005-14) and perhaps in the future, I’ll expand that and go back further.  One class of players was excluded from this analysis; players that played for more than one team in a season.  I felt that it was a small enough group that it wouldn’t throw off the numbers too much and for the most part, the players that were traded were making smaller amounts of money.  This does eliminate Adrian Gonzalez in the year he was traded from the Red Sox to the Dodgers while earning $21 million, but he is an extreme outlier.  I eliminated them because I wanted to examine the salary structures of different teams.  This task would become infinitely harder if I tried to break down how much of his salary was paid by the Red Sox and how much by the Dodgers.  Instead, I simply got rid of them and hoped for the best.

Over the past ten years, $23.7 billion has been paid out to the 2,112 players (over 7,344 individual player seasons).  That works out to an average of $11.24 million per player but the median is only $2.25 million which highlights some potential problems with this analysis; every team has fairly extreme pay dichotomy from the top to the bottom of the roster.  In fact, over the past ten years, 28 players have earned over $100 million each, accounting for 15.5% of the total payroll by themselves.  Despite the sense of foreboding in the back of my mind, we press onwards…

MEASURING INCOME INEQUALITY

This is one of the more important aspects of this entire project; measuring the inequality so I can attempt to correlate that with the number of games a team wins.  Thankfully, there already exists such a metric in economics; the Gini Coefficient.

The Gini Coefficient is found by finding the area A in the graph above and dividing it into the total area under the perfect distribution curve. 

Gini = A / (A+B)

Now the graph above is not some random income distribution to illustrate a point, this is the income distribution in Major League Baseball using individual player seasons (in other words, Alex Rodriguez’s $33 million salaries in 2009 and 2010 are considered different data points.  This calculates out to a Gini Coefficient of 0.6269.  For comparison, the Gini Coefficient of the United States was 0.48 in 2014.  According to this metric, Major League Baseball would be one of the countries with the least income equality in the world (according to the World Bank).

What would happen if we look at players’ total incomes over the sample instead of player seasons?  The disparity grows even greater and the Gini Coefficient goes up to 0.738.

I then took this same process and applied it to each of the 300 teams in my data set (10 seasons and 30 teams per season) and obtained a Gini figure for each team.

By now you’re all saying, ok, we get it, move on… well fine then.

The following were the variables used in my fixed effects model:

- The number of All-Stars on a given team

- The number of players on a team that had ever been an All-Star (perhaps an overpaid veteran)

- Estimated payroll

- Gini Index

- Highest, 2^nd highest, and 3^rd highest individual salaries

- Total of the top three salaries

- The number of players in the following salary ranges:

o   Under $5 million

o   $5-10 million

o   $10-15 million

o   $15-20 million

o   Over $20 million

As a dependent variable, I ran the model twice and used wins and Pythagorean wins.  In you aren’t familiar with it, Pythagorean wins is a metric developed by Bill James to attempt to better explain the quality of a team based on the number of runs scored and runs allowed.  Historically, this has proven to be a better predictor of future results than a team’s winning percentage.

RESULTS

Uh-oh, this isn’t exactly what I was hoping for.  In fact, this scatter plot seems to imply to me that the Gini Coefficient has little bearing on the success of a team given that there doesn’t seem to be any sort of pattern.  Nevertheless, we’ll push on and let our model shed more light on the subject.

OUTPUT STATISTICS, N=300, DEPENDENT VARIABLE = WINS,                      ADJ R^2 = 0.455
	COEFFICIENT	STD. ERROR	T-RATIO	P-VALUE
Const	38.22	6.73	5.68	0.0000
No_A_S	2.60	0.30	8.56	0.0000
No_a_tA_S	0.75	0.22	3.41	0.0008
Est__Payroll	0.04	0.06	0.63	0.5317
Gini_Index	-5.55	13.14	-0.42	0.6733
Highest	-0.37	0.24	-1.52	0.1297
Second_Highest	0.23	0.31	0.74	0.4620
Third_Highest	-0.16	0.29	-0.54	0.5913
Total	23.94	13.73	1.74	0.0825
Players_under_5	0.81	0.20	4.05	0.0001
Players_5_10_m	1.39	0.43	3.22	0.0015
Players_10_15_m	0.78	0.56	1.40	0.1620
Players_15_20_m	1.74	0.83	2.09	0.0373
Players_20__m	0.58	1.52	0.39	0.7018

As I suspected from looking at the scatter plot, the p-value of the Gini Index variable is 0.6733 meaning that it is not statistically significant.  The variables that are significant are the number of All-Stars, the number of players that have ever been an All-Star, the total salary of the top three players on the roster, and the number of players with salaries under $5 million, between $5 million and $10 million, and between $15 million and $20 million.

Interestingly, the coefficients on all of these variables are positive, meaning that if you were to add one more unit to any of those categories, the number of games a team is expected to win goes up.  Having a current All-Star is worth 2.6 more wins than not having one.  The 2008 Cubs, 2010 and 2011 Yankees, and 2012 Rangers would expect to win 18.2 more games, all else being equal, due to the fact that they had 8 All-Stars each.  Note that 18.2 wins is 2.6 per All-Star multiplied by 7 All-Stars since every team has at least one.  Therefore, the teams mentioned above had 7 more All-Stars than the minimum.  It shouldn’t be surprising then that those four teams won an average of 95.5 games.

When you switch dependent variables, the results are quite similar:

OUTPUT STATISTICS, N=300, DEPENDENT VARIABLE = PYTHAGOREAN WINS,                    ADJ R^2 = 0.4
	COEFFICIENT	STD. ERROR	T-RATIO	P-VALUE
Const	46.66	5.27	8.86	0.0000
No_A_S	2.49	0.29	8.67	0.0000
No_a_tA_S	0.75	0.21	3.53	0.0005
Est__Payroll	0.01	0.07	0.14	0.8916
Gini_Index	3.22	11.82	0.27	0.7859
Highest	-0.38	0.26	-1.42	0.1562
Second_Highest	0.40	0.29	1.36	0.1763
Third_Highest	-0.21	0.30	-0.70	0.4853
Total	10.23	14.16	0.72	0.4703
Players_under_5	0.57	0.19	3.05	0.0026
Players_5_10_m	0.99	0.38	2.59	0.0102
Players_10_15_m	0.79	0.53	1.49	0.1365
Players_15_20_m	1.08	0.91	1.18	0.2392
Players_20__m	0.73	1.55	0.47	0.6400

This time, the variables that are significant are the number of All-Stars, the number of players that have ever been an All-Star, and the number of players with salaries under $5 million, between $5 million and $10 million.

CONLUSIONS

What does all of this mean for an MLB general manager and the Miami Marlins in particular?  Not all that much.  While there is a slight correlation between the payroll of a team and the number of games they win, how a team distributes that money throughout their roster doesn’t appear to matter all that much.

For instance, in 2014 the Seattle Mariners paid their top three players $24 million, $22.86, and then $7 million for a Gini Index of 0.6759, the 5^th highest in the sample.

Meanwhile, the 2010 Boston Red Sox had players earning $18.7 million, $14 million, and $13 million with a Gini Index of 0.4394, the 9^th lowest in the sample.

The 2014 Mariners won 87 games and the 2010 Red Sox won 89.

The narrative that I threw out there at the opening where a team would struggle with a locker room of one star and twenty-four other guys doesn’t seem to hold water when it comes to payrolls or on-field performances.  Where it can come into play is locker room dynamics which can occasionally affect on-field performance but not in any sort of quantifiable way.  Happy players play better and if there is a huge divide between the superstar and everyone else, that can make people unhappy, leading to inferior play.

That brings me to the central conclusion of this entire exercise; salary should not be mistaken for value.  For the lion’s share of his 10 year, $252 million deal (of which he opted out of the last three years) Alex Rodriguez was worth every penny and in fact quite a bit more.  Despite the fact that he was making ludicrous amounts of money, by any statistical measure, he was earning it.  Meanwhile, there are a litany of long term contracts that a player signed and then apparently forgot how to hit or pitch.

You can have a team with a very high Gini Index that gets enormous value from younger players who aren’t making all that much money, leading to higher win totals.  Albert Pujols and Mike Trout both produced three MVP quality seasons while making less than $1 million per season.

You can also have a team with a lower Gini Index that is lower because the payroll is so high.  The World Series winning 2013 Red Sox had a very low Gini Index of 0.4672 despite seven individual salaries in excess of $10 million.  However, when the overall payroll is $177.9 million, none of those contracts take up all that large of a chunk by themselves.

MIAMI MARLINS GOING FORWARD

In my mind, the Marlins have two main options for the foreseeable future (in other words, the next six years before Stanton can opt out of this contract); they can attempt to pinch pennies and extract maximum value out of younger players or they can delve into the free agent market more to search for those elusive wins.  Either route involves risk and can be potentially very costly; missed draft picks and prospects can cost a franchise time while free agent blunders can cost huge amounts of money.

Either route, the most important aspect is a commitment to build a winning team.  Over the past ten years, the Yankees and Cardinals rank first and third, respectively, in regular season wins (with 934 and 889) despite very divergent management philosophies.  What they have in common is ownership and management groups that want to win.  It’s no coincidence that the Dodgers are 2^nd, the Red Sox are 4^th, the Phillies 5^th, and the Tigers 6^th on that list.  They all want to win, regardless of how they acquire the talent to do so.  Likewise, it’s no accident that the Marlins have won only 763 games, 23^rd most in the league.  Over the past decade, they too have been consistent.  They have drafted and developed good players, and then shipped them out of town before they got too expensive.

For Stanton’s sake, I hope this signals a drastic shift in their organizational mentality.  If they don’t, I hope he doesn’t opt out and forces the Marlins to pay every penny of that $325 million.