Trying to quantify how unfair these "retirement" contracts are (Kovalchuk and others)

Piggybacking on posts by Crabby Appleton and cobracg, and given that the NHL may be reconsidering a few other contracts, I wanted to try to put numbers to why many of these retirement contracts "feel" wrong.  I think Crabby was on to something good regarding how much cap-hit-savings is available for an early retirement.  Taking another approach, I'm going to apply the GINI coefficient, a standard measure of inequality in the social sciences, to compare these contracts.  At best it might suggest a bright line standard the NHL could use (e.g. "anything over .2 is an illegal contract") and at worst you might get exposed to some statistics.

First, a little math background.

I'm no stats whiz; I'll just give a few simple examples and let you figure out where to read more. The idea of Gini is to compare a set of data across time/space/people to a theoretical perfect in which everything is distributed equally.  To do that you have to rank everything or everybody (by dollars, let's say) and see how different that would be from perfect equality.  You wind up with a curve underneath a straight line, and the bigger the area difference between them, the more unequal:

For something like income inequality Brazil is at around .61, the US at .44, and Norway at .28.  There's a theoretical maximum of 1 (one person owns everything, billions of others nothing) and minimum of 0 (everyone makes exactly the same amount).

Let's shift to hockey contracts.  A 10-year contract where the player makes \$1.45M every year has a Gini of 0.  Another 10-year contract where he makes \$14.5M in year one and then zero for the next nine years has a Gini of .90 (it isn't 1 because it'd have to be infinite years out of making nothing to get that).  Obviously that contract doesn't fit any minimum salary rules; also you can see that Gini doesn't really approach 1 in practice.  How about the most fanciful spirit-of-the-CBA-breaking contract we can imagine: \$10M in year one, \$500k in years 2-10.  That would still be a cap hit of \$1.45M and a Gini of .59.  So that's a sorta-practical range from zero to .6.

Where would Kovalchuk have been? 17 years for \$102M structured his way is Gini of .425.  Definitely the worst in the league. His comrades:

1. Kovalchuk* - .425
2. Savard - .381
3. Pronger - .32
4. Hossa - .306
5. Luongo - .264
6. Keith - .237
7. Franzen - .218
8. Lecavalier - .214
9. Kiprusoff - .2
10. Zetterberg - .192
11. Richards - .154
12. Heatley - .115

I don't know that these are actually the 12 worst, just the ones that are commonly mentioned as fishy and a couple others that I saw and wanted to quantify.  And Richards and Heatley may well not be 11 and 12 given the way the numbers drop (.192 to .154 to .115).  For Pronger I think we all now know that Philly isn't getting any benefit of cap avoidance since he's an over-35.  But they were clearly trying for that and screwed up.  Also a few foolish people have tried to suggest Backstrom (.058) and Ovechkin (.026) belong in this fishy grouping.  Uhh, they don't.

Caveats - You would expect to see some fall-off in salary as a player reaches the end of his career.  Modano is about to go \$4.25M, 2.25, 2.25, 1.75 in consecutive years (Gini .179).  Of course that's over three contracts, to past age 40.  But Kiprusoff's drop-off (\$6M, 5, 1.5) seems more defensible than Lecavalier (\$8.5M, 4, 1.5, 1).  With a contract like Keith's it may be very defensible (from \$6M in '16-17 at age 33 gradually falling to \$1.5M in '22-23 at age 39).  But by throwing in so many of the potential retirement years it does look very fishy, and drives up the Gini score to 6th in this list. And I guess statistically Gini is much more useful for large datasets, or in this case, longer contracts.  Numbers can be thrown sharply higher by just tacking on an couple years to a short contract (ahem, Savard and Pronger).  But maybe that's why Gini is useful here, in making them stand out. Kovy had to add 6 fake years to get to number 1.

So this could be the basis for some NHL-approvable contract criteria.  Excluding .2 and above knocks off the 10 contracts many of us would call the most egregious.  Other bright-line criteria could include 1) maximum potential savings at any point in the contract, relative to cap hit (Crabby), 2) a maximum percent salary drop from year to year in the contract, 3) a maximum percent drop from the highest to lowest years in a contract, 4) maximum contract length based on age of the player.

* The Gini calculator I used is here.

If this FanPost is written by someone other than one of the blog's editors, the opinions expressed in it do not necessarily reflect those of this blog or SB Nation.

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