Who Takes a Discount in the NHL Salaries Part One: Taxes

NHL Salaries
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In the past few years, taxes have been brought up more and more when talking about NHL salaries and contracts. The theory is pretty simple in that teams like the Vegas Golden Knights and the Tampa Bay Lightning play in areas with relatively low-income tax rates. While teams like Toronto Maple Leafs and Montreal Canadiens play in high tax areas. As a result, players are willing to take discounts to play in Vegas and Tampa because they can make more money on a lower cap hit than they could in Toronto. There has always been reason to be skeptical of this, so we decided to see if players really do tend to take discounts to play in low tax cities. The results were not so simple.

NHL Salaries and Discounts

Defining “Value”

First we need to define players’ “worth” to estimate what is a discount. Luckily, Evolving Hockey (EH) produces well-calibrated player salary projections, and Matt Cane did it too back in 2018. 2020 contracts have not been included because of the external complications caused by COVID-19 this offseason. Given their data, the idea is simple. Taking term as a given, compare players AAV (average annual value) as a percentage of their expected AAV, and check the relationship of that number with the income rate. If tax rates are so meaningful, there should be a positive correlation. More simply, players should be more likely to earn below expectations when in low tax cities.

NHL free agent frenzy

So, for example, take Artemi Panarin‘s $11,642,857 per year contract last summer. EH forecasted Panarin’s most likely contract as an 8 year $11,172,683 per year contract. On a 7 year deal, they forecasted him at an AAV of $10,482,359, so that is the number we will work with. Given this forecast, take Panarin’s actual $11,642,857 AAV, divided by his projected $10,482,359. This shows us we see Panarin earned about 11% more than was expected, meaning his cap hit as a % of expected AAV is 111%. This is the number we will compare against tax data for each player.

Income Tax Data on NHL Salaries

After doing this with all the players from 2018 and 19 free agencies, it was time to pull up CapFriendly. Using their calculator, you can estimate the income tax rate for playing in each city given the size of the contract. What percentage of the contract is signing bonus changes the calculation slightly, but since that varies year to year I calculated each contract as a pure base salary. This has a small effect, but Nashville is still a low tax city, while Toronto is high tax.

Since the income tax rate in each city changes with the size of the contract, you can use “relative tax rate”. This is simply the Z-Score for each cities tax rate at a given AAV. For an example, imagine a $5,000,000 contract. Here are CapFriendly’s tax estimates for each NHL city.

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The estimated tax rate in Toronto would be 52.96%. Since the NHL average is about 46% with a standard deviation of 4%, Toronto’s relative tax rate for a $5,000,000 player is 1.67.  This calculation shows Toronto as an incredibly high tax city. Note the exact relative tax rate changes along with AAV, but the rough positions stay the same.

Does Relative Tax Rate Correlate With Discounts?

With tax rate data and the NHL salaries expectation data, it’s time to compare the two. Intuitively speaking, we should see cap hit as a % of expected AAV being positively correlated with the relative tax rate. In other words, it should cost more money to sign players in high tax environments. But is that actually the case? On the surface, it is not so simple. Note only skaters appear in all the graphs below.

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We can see there is no obvious correlation between AAV as % of expectation and income tax rate. So on the surface, skepticism seems justified.  If taxes mattered as much as some think, there would be a distinct upward trend in the graph above because contracts would become more expensive as the income tax rate rises. We could have easily stopped here and taken a victory lap. After all, the graph above seems to imply that income tax rates do not affect who takes a discount in the NHL. Better yet, when broken down between RFA’s and UFA’s, the same trend exists for each subsection of contracts.

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There is no correlation between the residuals of contract projections and tax rates. So, taxes don’t matter and everyone should stop using them to explain why players take discounts. Unfortunately for me, it’s not so simple.

Not all Contracts Are Equal

The two figures above treat all contracts equally. So Mitch Marner‘s 22% overpayment on a $65 million contract can be offset by Kyle Dubas signing an $850,000 player for $700,000. Of course, Marner’s overpayment is far more meaningful, so it is far more valuable information. The solution to this was to run a regression that tried to predict Cap hit as a % of expected as a function of the tax rate, but weigh the regression by the overall size of the contract.

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This regression shows us there is a “statistically significant” relationship between income tax rates and who takes a discount in the NHL. To put the regression output above into something meaningful, reimagine that $5,000,000 AAV contract. In a league average tax city like Columbus, the contract is expected to cost that $5,000,000. In a high tax environment like Toronto, that contract is expected to cost $5,225,000, a 4.5% premium above league average, plus or minus about 1%. On the contrary, in a low tax city like Tampa Bay, the same contract is expected to cost $4,785,000. A 4.3% premium below league average.

Why was this relationship not obvious without further digging? Well, I have been reading papers on this topic for school, and the literature suggests that high-income earners respond more to tax rates than lower-income earners. While every NHL player is a “high-income earner”, it looks like the same relationship exists in the NHL. Using a crude method of those who signed a $10 million contract, the relationship between cap hit as % of expected AAV and relative income tax rate is slightly(?) more obvious.

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All in all, early findings suggest two things.

First, I was probably wrong, players salaries do respond to different income tax rates after accounting for contract size. So teams like Tampa Bay and Las Vegas probably have some small edge over Toronto and Montreal when signing players. However, there is enough there to keep digging further. So, there will be a part two of NHL Salaries and discounts coming soon!

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