Controlling Baseball Salaries

As you may have noticed, I’m not putting a lot on this site. I have to be inspired to figure something out, or be inspired to write at a time that I actually have time.

That being said, Jason Stark at ESPN wrote an interesting article the other week.  In his Rumblings and Grumblings column, Jason talked about Pushing for a minimum payroll threshold. In it, he discussed how teams get a LOT of money from the luxury tax on salaries.  He then suggested that their should be a penalty for teams that don’t spend a lot of money.

I had thought a lot about that previously and had come up with a system.  Essentially, I think that both the luxury tax, and the related reduction of that cap for “cheap” teams, should be based upon a more statistical measurement rather than some arbitrarily set maximum and minimum. By basing it on the number of standard deviations from the average (mean) salary, the amount would be market based.  This would make the levels change based upon the current spending levels.

The upshot is that if a team maintained a constant payroll, and the average increased, then they would pay less tax, or collect more tax.

Playing with Numbers

Using the numbers in Jason’s article, I determined that the average salary in 2009 was $95.8 million.  The standard deviation was $37.2 million.  So if you were between $58.6 and $133.0 million in salary, you were within one standard deviation.

That was broad, so I played with the numbers and came up with some rules:

  • The bottom 15 spending teams could not be taxed.
  • The top 15 spending teams were not eligible to receive funds.
  • The tax starts at an eighth of a standard deviation above the mean ($100.4 mil) and increases at every additional eighth.
  • The tax begins at 5% of total salary and grows by 2% plus an exponential component at every level.
  • The tax payback starts at half a standard deviation below the mean ($77.2 mil) and increases at every additional fifth.
  • The tax payback begins at 5% and grows by 5% until the first standard deviation and then increases by 10% from there. (5, 10, 15, 25, 35, 45…..)
  • Rather than getting fancy, the money returned from teams spending too little are redistributed to all 30 teams evenly.  This only amounts to less than $2 million per team using my current calculations.

To help you get the idea, here are the two tax tables, skipping several rows for the tax levels so you can see the Yankee tax level. Notice that you can get to the point were you are paying more in taxes than you pay in salary if you go too high.

Maximum Minimum
Salary Pct. Salary Pct.
$95,783,476 0% $77,198,912 5%
$100,429,617 5% $69,765,086 10%
$105,075,758 8% $62,331,261 15%
$114,368,040 11% $54,897,435 25%
$123,660,322 14% $47,463,609 35%
$132,952,604 18% $40,029,784 45%
$142,244,886 23% $32,595,958 55%
$25,162,133 65%
$207,290,860 78% $17,728,307 75%
$216,583,142 89% $10,294,481 85%
$225,875,424 101% $2,860,656 95%

I was looking at a following article, and a reader had suggested that a winning team shouldn’t have to give back any of the received tax money.  That sounded very sensible.  Jason also mentioned not penalizing a team for the first drop, but I disagree.  It becomes complicated and if you don’t remove that exception, then only teams that are really doing it will try.

From those, I came up with some more rules:

  • Teams with a .500 winning percentage or higher can keep all payments.
  • Teams with a .450 winning percentage or lower have to give back the fully calculated enough.
  • Teams between .450 and .500 are on a sliding scale, reducing the amount returned by 2% for every .001 winning percentage points above .450.

It is simpler than it sounds, especially ones you plug the formulas into a spreadsheet.

The Results

Well, here are the results.  The tax collected totals $348.7 million.  That is less than the $400 million Jason reports as collected. Here are the teams, salary, and taxes collected.

Team Payroll Tax
Yankees $215,080,715 $166,835,116
Mets $141,302,331 $25,995,093
Cubs $141,007,248 $25,940,808
Tigers $138,477,723 $25,475,456
Red Sox $137,199,512 $25,240,306
Phillies $136,107,962 $25,039,496
Dodgers $127,592,034 $18,096,075
Angels $120,423,691 $12,722,065
Astros $106,424,382 $7,995,356
White Sox $104,751,673 $5,237,584
Mariners $101,182,454 $5,059,123
Cardinals $100,892,097 $5,044,605

As you can see, the Yankees would pay a hefty chunk.  They are paying around $150 million now, and I tried not to increase their chunk too much.  I do believe that an exponential growth is required though.  That means that the 2nd $50 million over the average costs more than the 1st.  It should get more and more painful to increase payroll.

Now for the return.  I don’t have the formula that determines how the money is distributed, but here is the analysis of the teams that if they did receive funds, would have to return it.  The “Raw” values comes directly from the table above.

Team Salary Win Pct. Raw Win Adj. Net
Rangers $76,524,452 0.537 10% 0% 0%
Indians $75,512,530 0.401 10% 100% 10%
Diamondbacks $73,495,966 0.432 10% 100% 10%
Reds $72,146,812 0.481 10% 38% 4%
Twins $71,903,577 0.534 10% 0% 0%
Rays $70,682,817 0.519 10% 0% 0%
Nationals $68,430,665 0.364 15% 100% 15%
A’s $60,954,872 0.463 25% 74% 19%
Pirates $47,482,564 0.385 35% 100% 35%
Padres $41,306,652 0.463 45% 74% 33%
Marlins $36,803,494 0.537 55% 0% 0%

As you can see, the Marlins who would have had to give back 55% of what they collect can keep it all because they won 87 games.  The Pirates weren’t as successful and have to give back the 35% that they are docked.  The Padres were going to have to return 45%, but they managed a enough wins to reduce that by 26% and only have to return 33% of what they collected.

My Spreadsheet

I uploaded my spreadsheet to Google Docs, but it didn’t like all of my formulas.  It is there, but it isn’t as dynamic as it should be.  You can view it there and see all of the numbers and download it for your tinkering pleasure.  Change the payrolls of some of the teams and see how it impacts everyone’s totals.

If you want the raw Spreadsheet, I’ve uploaded it as a ZIP file, and renamed it with a .PDF so WordPress would be happy.

Let me know what you think.


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