re: How Salary Cap is Set

[jaywalkszzz]

In Larry Coon's CBA FAQ (http://www.cbafaq.com/salarycap.htm#Q13) he gives an example on how the salary cap is adjusted starting in 2013-2014: "If the league didn't pay the players enough the previous season, i.e., if they had to cut the players a supplemental check to make their guarantee, then the shortfall, divided by the number of teams in the league, is added to the cap. For example, in 2014-15 there was a shortfall of $57.3 million, which led to a $1.91 million increase in the cap"

I calculated the 2014-2015 shortfall to be $57,100,000 & the increase in cap should be $1,903,333 (https://docs.google.com/spreadsheets/d/1i6YHb0c-iVwbMma8iNuvzwTSQSfbyjdiaENRif8boC0/edit?usp=sharing)
Numbers are close to Larry Coon's, but the actual increase in cap was $6,935,000 from the 2014 cap to the 2015 cap, not $1.91 million as stated in the above quote.

Furthermore, the 2015-2016 shortfall was $130,495,000, (divide that by 30 teams) and the cap should increase by $4,349,833, but the cap increased $24,143,000 from 2015 to 2016.

The league most recently projected (http://heathoops.com/2016/07/nba-lowers-its-2017-18-salary-cap-projection-from-107m-to-102m/) a shortfall for 2016 to be $200,000,000 which means there should be a $6.7 million increase in the cap from 2016 to 2017. The cap increase is $7,857,000 from the 2016 cap to the most recent cap projection of $102 million. This implies the league is projecting a shortfall closer to $235,710,000 in 2016.

I understand the cap is calculated based on projected BRI, which is in turn is negotiated between the league and player's association, but I'm curious how the cap jumped mathematically from $63,065,000 (2014 cap) to $70,000,000 (2015 cap) to $94,143,000 (2016 cap) to $102,000,000 (2017 cap projection)?

The reasoning why it jumped is obviously due to the 24 billion 9 year TV deal. Any clue how the league got the new salary cap numbers/projections?

[DBoys]

You've misconstrued what Coon said. The shortfall adjustment is not the cap increase per se.

Instead, they first calculate the increase or decrease in the cap, due to change in the projected BRI from the prior year to the year ahead. Then, if there was a shortfall the prior year, they also add that amount on top of the prior calculation.

For example, in calculating the 2016-17 cap, they first calculated the projected BRI for the 2016-17 season, split it down to the players' portion and divided it per team according to the formula, and there was a jump up to about $90M team cap. Then they added the shortfall from [edit] 2015-16, and added another $4.xxM to get a cap of $94.xx for each team.

[jaywalkszzz]

You've misconstrued what Coon said. The shortfall adjustment is not the cap increase per se.

Instead, they first calculate the increase or decrease in the cap, due to change in the projected BRI from the prior year to the year ahead. Then, if there was a shortfall the prior year, they also add that amount on top of the prior calculation.

For example, in calculating the 2016-17 cap, they first calculated the projected BRI for the 2016-17 season, split it down to the players' portion and divided it per team according to the formula, and there was a jump up to about $90M team cap. Then they added the shortfall from 2014-15, and added another $4.xxM to get a cap of $94.xx for each team.

DBoys, thanks for the reply.

In your example, didn't you mean, "they added the shortfall from 2015-2016, and added another $4.xxM to get a cap of $94.xx for each team"?

What is known:

2016 cap: $94,143,000
2015 underage: $130,495,000 (how I got that number is highlighted in green in this doc: https://docs.google.com/spreadsheets/d/1i6YHb0c-iVwbMma8iNuvzwTSQSfbyjdiaENRif8boC0/edit?usp=sharing or in the last table in http://www.cbafaq.com/salarycap.htm#Q19)
2015 underage divided by 30 teams = $4,349,833 (what you refer to as "$4.xxM" I believe)

Thus working backwards,

$94,143,000 - $4,349,833 = $89,793,167 (2016-17 cap before underage adjustment)
$89,793,167 x 30 teams = $2,693,795,000 (2016-17 projected player's guarantee or designated % of BRI salaries not including non-salary benefits)

$2,693,795,000 x 9/100 = $242,441,550 (2016-17 non-salary benefits assuming 9% benefits relative to projected salaries)

$2,693,795,000 + $242,441,550 = $2,936,236,550 (2016-17 projected salaries + projected benefits)

$2,693,795,000 x 100/51 = $5,281,950,980 (2016-17 projected BRI since players can only earn up to 51% of BRI)

$2,936,236,550 x 100/50 = $5,872,473,100 (2016-17 projected BRI assuming 50% split)

So, somehow the league & players' association agreed/calculated a 2016-17 projected BRI of about $5,872,473,100 $5,281,950,980, even though the 2015-16 actual BRI was $5,289,000,000?
(http://www.cbafaq.com/salarycap.htm#Q18)

[DBoys]

1 Yes I meant 2015-16 and my post has been edited to read correctly. Sorry about that.
2 In your reverse calculations, something sizable is missing. You have not adjusted your various numbers for the cost of non-salary player benefits, which are a significant amount, and are part of the players' total 50% of the annual pie. (I don't have time to work through it in any more detail at the moment.)

[jaywalkszzz]

1 Yes I meant 2015-16 and my post has been edited to read correctly. Sorry about that.
2 In your reverse calculations, something sizable is missing. You have not adjusted your various numbers for the cost of non-salary player benefits, which are a significant amount, and are part of the players' total 50% of the annual pie. (I don't have time to work through it in any more detail at the moment.)

Yea I think you're right.

I made some changes in bold/italics and striked through old calculations. I included non-salary benefits, which was estimated based on past years' numbers (~$200,000,000 between 2012-2015 http://www.cbafaq.com/salarycap.htm#Q19).

I tried to read through the legal verbiage in the actual CBA on how players get their benefit amounts and I quickly got bored.

[DBoys]

My quick eyeball test says you're probably still way off. The difference in projected BRI from last season to this season would have to be more than a billion before I trusted it might be right, and I'm hedging on the very low side (my very rough guesstimate puts projected 2016-17 BRI at somewhere approaching $7 B, not $5.3)).

The problem imo is going to be in how you derived your base line numbers, and the formula(s) you created using the relationship between those base line numbers, from which you extrapolated unknowns. I think the solution will be found by starting with simpler math and relationships and exprapolations, that then can be tweaked (if you wish) once you start landing in the right ballpark..

[jaywalkszzz]

My quick eyeball test says you're probably still way off. The difference in projected BRI from last season to this season would have to be more than a billion before I trusted it might be right, and I'm hedging on the very low side (my very rough guesstimate puts projected 2016-17 BRI at somewhere approaching $7 B, not $5.3)).

The problem imo is going to be in how you derived your base line numbers, and the formula(s) you created using the relationship between those base line numbers, from which you extrapolated unknowns. I think the solution will be found by starting with simpler math and relationships and exprapolations, that then can be tweaked (if you wish) once you start landing in the right ballpark..

Not sure if you noticed, but my updated calculations of projected 2016-17 BRI above was at $5,872,473,100 (This number was mainly obtained from your suggestions in post#2 and post #4, which I don't trust yet).

The 2015-16 actual reported BRI is undisputedly $5,289,000,000 straight out of http://www.cbafaq.com/salarycap.htm#Q18 (I assume you're confusing actual 2015-16 BRI vs. projected 2016-17 BRI when you said "$5.3")

Nonetheless, I agree that 2016-17 projected BRI should still be higher.

Without regard to the shortfall adjustment, I calculated projected BRI and projected benefits using two known formulas

Salary Cap = (.4474 x BRI - Benefits) / 30 (http://www.cbafaq.com/salarycap.htm#Q13)
Luxury Tax = (.5351 x BRI- Benefits) / 30 (http://www.cbafaq.com/salarycap.htm#Q21)

By using these formulas and solving for Benefits, I ended up with the following formula

Benefits = (13.422 x Luxury Tax - 16.053 x Salary Cap)/ 0.0877 (simple algebra below on how this formula was derived)


Math:
A= Cap, B= BRI, C= Benefits, D= Luxury Tax

A = (0.4474 x B - C)/ 30 (http://www.cbafaq.com/salarycap.htm#Q13)

D = (0.5351 x B - C)/ 30 (http://www.cbafaq.com/salarycap.htm#Q21)

A(30) = (0.4474 x B) - C
A(30)+C = (0.4474 x B)
(A(30)+C)/ 0.4474 = B

D(30) = (0.5351 x B) - C
D(30)+C = (0.5351 x B)
(D(30)+C)/ 0.5351 = B

(A(30)+C)/ 0.4474 = (D(30)+C)/ 0.5351
(30A + C) 0.5351 = (30D + C) 0.4474
30(0.5351)A + 0.5351C = 30(0.4474)D + 0.4474C
16.053(A) + 0.5351C - 0.4474C = 13.422(D)
0.0887C = 13.422(D) - 16.053(A)
C= [13.422(D) - 16.053(A)]/0.0877

Once Benefits is solved for, BRI can be calculated from either formula (A) or (D):
B= (30 x A +C)/ 0.04474 OR B= (30 x D+C)/0.5351

Plugging in known values 2016-17 Salary Cap ($94,143,000 for A) and Luxury Tax ($113,287,000 for D), 2016-17 Projected BRI should be $6,548,688,712, which is closer to your 7 Billion "guesstimate"/"eyeball test".

However, this still doesn't answer my original question in post#1 on how the 2015 cap jumped from 70,000,000 to the 2016 cap of $94,143,000 with regard to the shortfall adjustment of $4,349,833.

If I get a hold of Larry Coon, either via Basketball Insiders Chat or Twitter I'll forward his answer in this thread.

[DBoys]

Not sure of the number, and haven't really worried about it. In any event, I think this puts to bed your puzzlement over how the projected BRI could be essentially the same as prior BRI. As it turns out, it's nowhere close to staying the same, with a jump in excess of 20%.

[jaywalkszzz]

You've misconstrued what Coon said. The shortfall adjustment is not the cap increase per se.

Instead, they first calculate the increase or decrease in the cap, due to change in the projected BRI from the prior year to the year ahead. Then, if there was a shortfall the prior year, they also add that amount on top of the prior calculation.

For example, in calculating the 2016-17 cap, they first calculated the projected BRI for the 2016-17 season, split it down to the players' portion and divided it per team according to the formula, and there was a jump up to about $90M team cap. Then they added the shortfall from [edit] 2015-16, and added another $4.xxM to get a cap of $94.xx for each team.

You were right. Kudos.

Below is Larry Coon's (The Salary Cap godfather) answer to my question (http://www.basketballinsiders.com/chat/nba-chat-with-larry-coon-8112016/):

"The $1.91 million was the extra bump from the adjustment you quoted. So think of setting the cap as occurring in two steps: 1) Set a cap amount based on projected revenues and projected benefits; 2) Adjust the cap amount from step 1 upward or downward based on what happened with salaries the previous season.

SO if the $6.935 million cap increase, $1.91 of it came from step 2, and the rest came from step 1.

The other way to think about it is this — collectively, the players are guaranteed to receive a specific amount. We won’t know what that amount is until next July, because it depends on revenues generated in the upcoming season. So the target is nebulous. The arrow is nebulous as well, because it’s the sum of all the contracts in the league, some of which were signed years ago, and some of which are yet to be signed.

The idea is that they want to get to the end of the year with the arrow hitting the target as closely as possible. A perfect season is when the aggregate salaries & benefits exactly hit the players’ guaranteed amount, and no adjustments are needed either way. The rules are set up so that the salaries hit the target as closely as possible.

This is why the cap is based on 44.74 percent of projected BRI, when the players are guaranteed 50 percent, plus or minus a percent. It’s the multiplier that gets them close to the target when benefits and the fact that most teams end up over the cap are factored in.

And from there, they adjust based on previous results. If they gave the players too much last year (i.e., escrow money was returned to the owners), then they pull back on the reins a little the following year by lowering the cap & tax amounts. If they gave the players too little last year (and had to give the players a supplemental shortfall payment), then they let loose on the reins the following year by raising the cap & tax amounts.

But just to be clear — most of the change in the cap from one year to the next is based on the projected revenues. A relatively smaller percentage of the change is due to the adjustments."

[jaywalkszzz]

1 Yes I meant 2015-16 and my post has been edited to read correctly. Sorry about that.
2 In your reverse calculations, something sizable is missing. You have not adjusted your various numbers for the cost of non-salary player benefits, which are a significant amount, and are part of the players' total 50% of the annual pie. (I don't have time to work through it in any more detail at the moment.)

Yea I think you're right.

I made some changes in bold/italics and striked through old calculations. I included non-salary benefits, which was estimated based on past years' numbers (~$200,000,000 between 2012-2015 http://www.cbafaq.com/salarycap.htm#Q19).

I tried to read through the legal verbiage in the actual CBA on how players get their benefit amounts and I quickly got bored.

Per Larry Coon (http://www.basketballinsiders.com/chat/nba-chat-with-larry-coon-8112016/):

"Projected Benefits are one of those “black box” numbers to me. They’re based on the league projections for all of the individual benefit amounts, and there’s not enough information available (to me) to project it with any degree of accuracy.

That said, the things that qualify as benefits are listed in the CBA. The actual (rather than projected) benefit amounts are just the aggregate of those items."