# Non Linear Luxury Tax

Discussion in 'Fugu's Business of Hockey Forum' started by Orange, Dec 11, 2004.

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1. ### OrangeRegistered User

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Talent doesn't follow a linear fonction, neither do salaries. I don't see why a luxury tax system should. Maybe it would be simpler for fans to understand, but I don't see think it helps the league that much. Here's my plan for a luxury tax :

Definitions :

SM : Salary Mass. A single team's total salary paid out during the year.
LT : Luxury Tax. Amount paid over a certain excess.
USM : Updated Salary Mass. A team's salary with luxury tax included. USM = SM + LT
AS : Average Salary. Average player salary for the season.
BM : Base Mass. Average base salary mass. BM = AS * 22 (for a 22 men roster).

So here goes : USM = SM*1.01^([SM-BM]/AS)

This formula is based on compound interest calculations and would be very stiff on high spenders ! Basically, it gives a little room to go over the league's average salary mass but is too punitive to go way over it. The 1.01 factor is arbitrary and would be up for debate.

Here are some numbers to crunch. Let's assume AS = 1.55 (with a rollback). BM would be set at 34.1. All numbers are in millions.

SM ---- USM ---- LT ----- LT.75 --- LT.2
34.10 _ 34.10 ___ 0.00 ___ 0.00 ___ 0.00
40.00 _ 43.13 ___ 3.13 ___ 4.43 ___ 1.18
50.00 _ 61.26 ___ 11.26 __ 11.93 __ 3.18
60.00 _ 83.53 ___ 23.53 __ 19.43 __ 5.18
70.00 _ 110.74 __ 40.74 __ 26.93 __ 7.18
80.00 _ 143.80 __ 63.80 __ 34.43 __ 9.18

To compare, I've inlcluded what a .75/dollar and .2/dollar luxury tax over the first 34.1M would amount to. With a 1.01 "rise factor", we can see that my "non linear" luxury tax system approximates a .75/dollar luxury tax at 40M and 50M but starts getting more punitive at 60M. Obviously, the parameters of the equation are up for debate. Most notebly the raise factor (set a 1.01 for the example) and the BM which realy equates to how much the players are ready to roll back salary (I used the 24% figure in this example).

What do you people think ? Fire away !

2. ### Lexicon DevilRegistered User

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What's the point? To be more mathematically pure?

You might as well just take these numbers and do what the NHLPA did.

Or perhaps you should try a hyperbolic sine.

3. ### OrangeRegistered User

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1. To have a more restrictive system than simple linear fonction, which does not completly adresses the issue of the really really big spenders.
2. To have a system that indexes itself each year without the need for lenghty negociations.
3. Propose a system that is halfway between a cap and a "classic" luxury tax.

Last edited: Dec 11, 2004
4. ### ChemiseBleuHonneteRegistered User

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very good idea, but it still doesn't address the #1 need. That is controlling a player's value on the market. The problem isn't how much a team spends on their total salary mass, it's how much they wreck the market by giving too much to one player.

5. ### David A. RainerRegistered User

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So let me see here.

LT=USM-SM

USM=LT+SM

LT+SM=SM*1.01^([SM-BS]/AS)

LT=SM*1.01^([SM-BS]/AS)-SM

LT=SM(1.01^([SM-BS]/AS)-1)

This is just defining the Luxury Tax as an exponential function of the difference between the Salary Mass (or payroll) for a team and the Base Mass (or average payroll) of the league. So instead of establishing threshholds at certain levels (that is, a certain rate at \$40M, another rate at \$50M, etc), the tax just increases exponentially with every cent increased.

That's fine with me. The tax would not be linear, but it would be a continuous exponential function. That makes it more efficient. In demonstration, under a linear threshhold scheme, a team at \$40M would be taxed the same rate as a team at \$49M (presuming the threshholds are at \$40M and \$50M), which might seem a little unfair. But under an exponential scheme, a team at \$40,000,001 would be taxed marginally stiffer than a team at \$40,000,000 and not as stiff as a team at \$40,000,002. And the higher up you get, the more it hurts. If you want to make the curve steeper, increase the arbitrary 1.01. If you want to make it shallower, decrease the 1.01 (setting the limit at 1).

Again, that's fine with me.

Last edited: Dec 11, 2004
6. ### OrangeRegistered User

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