Optimal Contract Structuring: “Taking It To The Logical Conclusion”

Last February I was fortunate enough to attend the Sloan Sports Analytics Conference (mostly due to the excellent work of the ever-amazing Ryan Stimson). One of the marquee events was a panel titled “Moneymind: Overcoming Cognitive Bias“, which featured 4 of the best known “Money[sport]” GMs (Daryl Morey, Sam Hinkie, Farhan Zaidi, and Billy Beane) talking about how they make decisions and what makes their  respective management styles different from most executives in their sports.

While the whole panel was endlessly informative and extremely entertaining, one thing Daryl Morey said about the Rockets approach to implementing strategies really stuck with me:

“One thing I think all of us have done is more take the lessons that are sort of obvious that everyone has agreed to and taken them to the logical conclusion. Which is, for example us, it’s better to make 3 than 2 on a shot…genius, right…taking it to it’s logical conclusion, which is shoot 50 of them a night.”

Basically what Morey was saying is that if all the work you’ve done has shown that a strategy is beneficial, don’t hedge your bets and only go half-in on it. It’s this idea that’s been floating around in my head for the last 2 days since I wrote about optimizing contract structure – if GMs could theoretically save cap space by setting up contracts to pay more money to players upfront, how much total cap room could they create simply by structuring their contracts in the most efficient way possible?

The answer, of course, depends on the assumptions you make (since no one has been foolish enough to let me run my crazy experiments on an actual NHL team). First and foremost is the impact of the discount rate – higher discount rates make this a more effective cap optimization strategy, while lower discount rates have less total benefit. But this is easy enough for us to test out – we can simply run our analysis using various discounts and observe the range of impacts the each discount rate gives us.

There’s also the question of what the optimal contract structure is. While the ideal contract from a player’s point of view would be something like 99.9% of the money in the first year with the remaining cash spread out over the last N-1 years of the deal, the CBA has certain rules to prevent this kind of cap circumvention. Specifically, there are 2 major criteria that all contracts have to meet with regards to when payments occur:

  1. The difference in total salary from year-to-year can be no more than 35% (Edit: the ever insightful Petbugs points out that the 35% limit on YTY difference in contract value is 35% of the value of the 1st year of the contract); and
  2. The difference in total salary between the most and least-expensive years in a contract can be no more than 50%.

We can add 2 other criteria that are necessary to ensure that the NPV is maximized while minimizing the actual dollars spent:

  1. The total salary in year i should always be greater than or equal to the total salary in year i + 1. This is simply to ensure that the largest payments are pushed as far forward as possible.
  2. The total salary in year 1 should be double the total salary in the last year. Ideally we want the last year value to be as small as possible and the first year salary to be as large as possible, and this is the largest difference we can have without violating rule #2 above.

While these rules give us a general sense of what the best structured contract looks like, they don’t give us an exact answer as to what the optimal contract structure is. When the length of the contract is 1 or 2 years, the optimal structure is easy enough to define. For a 1 year deal, the AAV is the total salary in the first year, so we don’t have anything to do – there’s no way to actually optimize it. For a 2-year deal, the optimal structure is to pay in year 1, and 0.65P in year 2 – that’s the biggest drop you can get, and we want to move as much money forward as possible.

But for contracts that are 3 years or longer, there are actually many ways to structure a contract that meet the rules we established above, but that aren’t necessarily optimal. For example, if we call the salary in the first year of a contract P, we could simply decrease the salary of contract in a straight line until we hit 50% at the end of the contract (and then solve for the value of P that makes the NPV equal to the NPV of the actual contract signed). While this seems like a logical solution in theory, in practice it’s actually not aggressive enough in front-loading contracts, and many current deals are actually better structured as they exist already.

One method of structuring that’s mostly optimal[1] goes like this:

  1. In years 1 to N/2 (rounding down), pay P
  2. In year N/2 (rounded down) + 1, pay 0.65P
  3. For the remaining years, pay 0.5P

This won’t always give us the most optimal contract structure, but it will generally be a non-trivial improvement over how contracts are currently structured. We can solve for P in the same way we described above: simply find the value of that makes the NPV of our optimal contract the same as the NPV of the actual contract. We can then find the AAV as:

AAV (Optimal) = 1/N * [P * floor(N/2) + 0.65 * P + (N – floor(N/2) – 1) * 0.5 * P]

As a simple example, let’s look at P.K. Subban’s most recent contract that he signed with the Montreal Canadiens. That deal has an AAV of $9M per season, but is structured in far from an optimal manner: the bulk of the payments occur in the middle of the deal. In theory, the Habs could have offered to pay him more in the first 4 years in order to knock down the total cost (and with it the AAV). But what would the optimal way to structure it be?

If we assume a discount rate of 5%, the NPV of Subban’s deal was $60.9 million dollars when he signed it. Using the structure we described above, he could get the same value if he signed a deal that paid roughly $11.3M in years 1-4, $7.3M in year 5, and $5.65M in years 6-8. The AAV of that deal would have been ~$8.7M, saving the Habs Preds $300k per year – not a bad chunk of change just for rearranging some payments.

If we repeat this exercise for each player who has signed since July 1, 2014 and total up the savings by team, we can get a reasonable estimate of what optimizing each contract’s structure could be worth to a GM.[2]

Discount Rate Min Cap Hit Saved Per Team Average Cap Hit Saved Per Team Max Cap Hit Saved Per Team
2.5% $0.06M $0.38M $0.83M
5.0% $0.12M $0.75M $1.62M
7.5% $0.18M $1.11M $2.37M
10.0% $0.24M $1.45M $3.07M

As we noted above, the impact is highly dependent on the assumptions you make about the time value of money, but it seems to me that there could be some value to this strategy, particularly if you’ve got an owner with deep pockets. The average team would save nearly $400k under the most conservative of assumptions, an amount which could be the difference between adding that marquee player at the deadline and sticking with your current roster.

Now there are obviously a few caveats to this analysis that could reduce the potential impact. First, as we mentioned above, you’d need to have a very nice owner to give you the financial flexibility to structure deals like this. This may be a challenge in cash-strapped markets, but this strategy could actually be a good way for teams whose potential spending is being restricted by the salary cap to flex their financial muscle a bit.

Second, as I noted in my last piece, the savings from front-loading need to be weighed against the potential additional costs if you need to buyout a contract or if a player retires.  If we exclude players who are 30 or older when they signed, the expected cap savings tends to drop by $50k-200k, depending on the discount rate. That’s not enough to remove all merit from the strategy, but it does knock away some of the benefit that we noted above.

Third, it’s not necessarily clear that players would be willing to accept a lower cap hit, even if it was in their best interest financially. Players may be more concerned with their cap hit than the actual financial details of their contract, and may be reluctant to accept a deal that makes them look worse than one of their peers.

Nevertheless, it does look like there could be some cap benefit to a team with an open-minded owner who’s willing to take a risk. While correctly evaluating a player’s future performance will always be more important than these kind of accounting tricks, finding new ways to squeeze a bit of extra value out of your limited cap space may give team’s just enough room to add that piece that pushes them over the edge.


[1] There are only 3 contracts that are “more optimal” in their current state than this one, so I feel pretty safe saying this is pretty close to being optimal.

[2] Excludes contracts under $1MM and the Vegas Golden Knights.

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Posted in Salary Cap

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