View Full Version : Okay Math and/or Excel wizards, help me out here calculating player salaries

Hicks

07-04-2012, 07:40 PM

I'm trying to add something to help me figure out new NBA contracts in detail as they get announced.

I used to have an Excel file from count55 that did this for me, but I don't seem to have it anymore, and I want to recreate it for myself.

I want to be able to use an Excel spreadsheet so that I can enter a value in a cell (the total amount of a new contract), enter the number of years in another cell, and have it spit out the year by year amounts of the contract under the assumption that the player gets X% of a raise each season (4.5% for one, 7.5% for another).

What do I need to do to make this work? I think a few years ago I was taught how to do something like this, but I've since forgotten.

Thanks!

rabid

07-04-2012, 07:49 PM

I don't know the new CBA rules well enough to do this, but given the formula I could probably make you a very basic template in excel or google docs. It's not that hard, you just put the equation you're using as the value of the cell instead of a number...

I'd be happy to do a basic version if you can give me the numbers and multipliers you're using...

EDIT: ahhh I see now why your problem is a bit more complicated. I put something together that, given the first year salary and the %increase per year, can calculate all the subsequent year salaries. But it's a bit more complex (for me anyway - and maybe beyond my immediate spreadsheet skills) to calculate all that when you only have the total amount to start with.

Plus I have some fireworks to attend.

Whoever knows how to do this, I'd be curious to see it as well.

Larry Staverman

07-04-2012, 08:17 PM

I'm trying to add something to help me figure out new NBA contracts in detail as they get announced.

I used to have an Excel file from count55 that did this for me, but I don't seem to have it anymore, and I want to recreate it for myself.

I want to be able to use an Excel spreadsheet so that I can enter a value in a cell (the total amount of a new contract), enter the number of years in another cell, and have it spit out the year by year amounts of the contract under the assumption that the player gets X% of a raise each season (4.5% for one, 7.5% for another).

What do I need to do to make this work? I think a few years ago I was taught how to do something like this, but I've since forgotten.

Thanks!

YR 1 salary - enter cell that has stating salary...ex:=1a or=b2

yr 2 salary - =yr1 cell * 1.075 or yr 1 cell * 1.045

yr 3 salary - =y2 cell * 1.075 or yr2 cell *1.045

etc

here is an example

10000000

=a1*1.045

=a2*1.045

=a3*1.045

=a4*1.045

Total - =sum(a1:a5)

rabid

07-04-2012, 08:18 PM

That's what I came up with too, but that only works if you know the first years salary...

xIndyFan

07-04-2012, 08:42 PM

here is a math formula that will calculate the beginning salary given the total amount of the contract and the years.

n = total number of years

x = total dollar amount of the contract

I = the interest rate [as a decimal .045 or .075]

x/{[(n(n-1)/2)*I] + n}

Hicks

07-04-2012, 08:46 PM

That's what I came up with too, but that only works if you know the first years salary...

Right. I'm having trouble calculating the first year salary, which is why I'd like an algorithm to do it for me if I can give it the total, the number of years, and the annual % raise.

Hicks

07-04-2012, 08:57 PM

here is a math formula that will calculate the beginning salary given the total amount of the contract and the years.

n = total number of years

x = total dollar amount of the contract

I = the interest rate [as a decimal .045 or .075]

x/{[(n(n-1)/2)*I] + n}

So let's take the reported salary for George Hill.

n = 5

x = 40,000,000

I = .075

x/{[(n(n-1)/2)*I] + n}

40,000,000/{[(5(5-1)/2)*.075] + 5}

40,000,000/{[(5(4)/2)*.075] + 5}

40,000,000/{[(20/2)*.075] + 5}

40,000,000/{[(10)*.075] + 5}

40,000,000/{[.75] + 5}

40,000,000/5.75

6956521.739130435

~ $6,956,522.

Nice!

So does it have to be that formula, or could it be simpler? I mean eventually it seems to have come down to the total dollar amount divided by the sum of the number of years plus 10*I. X / [N + (10*I)]

Just a coincidence in this case?

Hicks

07-04-2012, 09:04 PM

Hell, let's give it a look.

Roy's deal is apparently supposed to be worth 58,504,264 and start at 13,675,000 and go for 4 years.

n = 4

x = 58,504,264

I = .045

Let's try the shorter one first:

X / [N + (10*I)]

58,504,264 / [4 + (10*.045)]

58,504,264 / [4 + (.45)]

58,504,264 / [4.45]

13147025.61797753

~ 13,147,026. Close, but not right.

On to the other formula:

x/{[(n(n-1)/2)*I] + n}

58,504,264/{[(4(4-1)/2)*.045] + 4}

58,504,264/{[(4(3)/2)*.045] + 4}

58,504,264/{[(12/2)*.045] + 4}

58,504,264/{[(6)*.045] + 4}

58,504,264/{[0.27] + 4}

58,504,264/{4.27}

13701232.78688525

~ 13,701,233

Also not the right number based on what I've been told. What gives?

Pacers

07-04-2012, 09:19 PM

I miss count. :(

xIndyFan

07-04-2012, 09:20 PM

. . . On to the other formula:

x/{[(n(n-1)/2)*I] + n}

58,504,264/{[(4(4-1)/2)*.045] + 4}

58,504,264/{[(4(3)/2)*.045] + 4}

58,504,264/{[(12/2)*.045] + 4}

58,504,264/{[(6)*.045] + 4}

58,504,264/{[0.27] + 4}

58,504,264/{4.27}

13701232.78688525

~ 13,701,233

Also not the right number based on what I've been told. What gives?

either rounding error, calculation error or informational error.

the n(n-1)/2 is the number of 'raises' a player will get. In Roy's case yr 1 = no raise, yr 2 = 1 raise, yr 3 = 2 raises [the 1st one plus one more] and yr 4 = 3 raises. That gives you 6 raises @ .045 each ='s 27%. Plus the 4 yrs of the contract is 4.27.

the total value $58M is divided by the 4.27. That part is right.

do they compound under the new CBA? i didn't think so.

xIndyFan

07-04-2012, 09:24 PM

Hell, let's give it a look.

Roy's deal is apparently supposed to be worth 58,504,264 and start at 13,675,000 and go for 4 years.

n = 4

x = 58,504,264

I = .045

Let's try the shorter one first:

X / [N + (10*I)]

58,504,264 / [4 + (10*.045)]

58,504,264 / [4 + (.45)]

58,504,264 / [4.45]

13147025.61797753

~ 13,147,026. Close, but not right.

. . . Also not the right number based on what I've been told. What gives?

you're assuming 10 raises. that is true only in a 5 yr contract. a 4 yr contract is 6 raises.

docpaul

07-04-2012, 09:25 PM

Right. I'm having trouble calculating the first year salary, which is why I'd like an algorithm to do it for me if I can give it the total, the number of years, and the annual % raise.

I think you might be making an incorrect presumption here.

The first year of a multi-year contract's max value is set by the CBA, not by a regression of a total salary number.

Take a look:

http://www.cbafaq.com/salarycap.htm#Q16

In this case, the first year's salary would be: $12,922,194 for 2011-2012.

If you want to play with the numbers more, I've made a Google Spreadsheet (works like Excel, only online instead), try:http://pgb.me/pacercap

Hicks

07-04-2012, 09:29 PM

either rounding error, calculation error or informational error.

the n(n-1)/2 is the number of 'raises' a player will get. In Roy's case yr 1 = no raise, yr 2 = 1 raise, yr 3 = 2 raises [the 1st one plus one more] and yr 4 = 3 raises. That gives you 6 raises @ .045 each ='s 27%. Plus the 4 yrs of the contract is 4.27.

the total value $58M is divided by the 4.27. That part is right.

do they compound under the new CBA? i didn't think so.

But he doesn't actually get 6 raises. It's supposed to be Yr 1, then Yr 1 * 1.045 = Yr 2, then Yr 3 = Yr 2 * 1.045, then finally Yr 4 = Yr 3 * 1.045

Hicks

07-04-2012, 09:30 PM

I think you might be making an incorrect presumption here.

The first year of a multi-year contract's max value is set by the CBA, not by a regression of a total salary number.

Take a look:

http://www.cbafaq.com/salarycap.htm#Q16

In this case, the first year's salary would be: $12,922,194 for 2011-2012.

If you want to play with the numbers more, I've made a Google Spreadsheet (works like Excel, only online instead), try:http://pgb.me/pacercap

You've calculated Roy's new deal based off of last year's psuedo-salary cap figure, which was I believe 51.7m. It's not gone up to 54.7m (yes, despite the real cap being the same both seasons).

Good point though that Roy's is a little different being a max. In the case of a max, you figure the first year salary first, then use that to figure the other years and the total of the deal. Yet with non-max deals, it's the opposite (total and number of years, then figure the first year, then the others).

docpaul

07-04-2012, 09:35 PM

You've calculated Roy's new deal based off of last year's psuedo-salary cap figure, which was I believe 51.7m. It's not gone up to 54.7m (yes, despite the real cap being the same both seasons).

Good point though that Roy's is a little different being a max. In the case of a max, you figure the first year salary first, then use that to figure the other years and the total of the deal. Yet with non-max deals, it's the opposite (total and number of years, then figure the first year, then the others).

Absolutely, I put in the hypothetical caveats, and the fact that Hibbert's base year salary is based on this current year's figures. If you read the fine print of the Larry Coon FAQ, you see:

They use a different cap calculation to determine the maximum salaries, which is based on 42.14% of projected BRI rather than 44.74%. For this reason, the maximum salaries are not actually 25%, 30% or 35% of the cap, and instead are a slightly lower amount. For example, even though the salary cap for 2011-12 is $58.044 million and 25% of this amount is $14.511 million, the 0-6 year maximum salary is actually $12,922,194.

Hicks

07-04-2012, 09:36 PM

But that says for 2011-12. Aren't we now operating 2012-13?

docpaul

07-04-2012, 09:37 PM

But that says for 2011-12. Aren't we now operating 2012-13?

Yes, sorry... I've been trying to say this. I put in a hypothetical starting salary for 2012-2013 based on a flat BRI this next year.

Hicks

07-04-2012, 09:45 PM

Yes, sorry... I've been trying to say this. I put in a hypothetical starting salary for 2012-2013 based on a flat BRI this next year.

Right, but I'm being told the psuedo-BRI number they use to calculate max deals went up by $3m, so Roy's contract is supposed to be a little bit larger than what you have, no?

docpaul

07-04-2012, 09:58 PM

Right, but I'm being told the psuedo-BRI number they use to calculate max deals went up by $3m, so Roy's contract is supposed to be a little bit larger than what you have, no?

That's not what Coon has been saying, but who knows? It's not official yet. He's been saying on Twitter, that the salary cap numbers are going to stay the same next year most likely, which implies that projected BRI either stays the same, or goes down.

xIndyFan

07-04-2012, 10:12 PM

But he doesn't actually get 6 raises. It's supposed to be Yr 1, then Yr 1 * 1.045 = Yr 2, then Yr 3 = Yr 2 * 1.045, then finally Yr 4 = Yr 3 * 1.045

IIRC, the raise is only calculated once. it is .045 x starting salary.

yr1 = 100

yr2 = 104.5

yr3 = 109

yr4 = 113.5

that is way the last CBA was done. Have they changed it?

Hicks

07-04-2012, 10:18 PM

IIRC, the raise is only calculated once. it is .045 x starting salary.

yr1 = 100

yr2 = 104.5

yr3 = 109

yr4 = 113.5

that is way the last CBA was done. Have they changed it?

I don't know; I just thought it was the opposite.

xIndyFan

07-04-2012, 10:54 PM

you win, you made me look it up. :laugh:

raises are not compounded is the way larry coon (http://www.cbafaq.com/salarycap.htm)explained it. they are only figured once on the starting salary.

wintermute

07-04-2012, 10:55 PM

here is a math formula that will calculate the beginning salary given the total amount of the contract and the years.

n = total number of years

x = total dollar amount of the contract

I = the interest rate [as a decimal .045 or .075]

x/{[(n(n-1)/2)*I] + n}

I have it as :

starting salary = x*I/[(I+1)^n-1]

E.g. x = 58.5, I = 0.045, n = 4

-> starting salary = 58.5*0.045/[(1.045)^4-1] = 13.674 (a little rounding off error)

For Hill's (reported) deal, starting salary = 40*0.075/[(1.075)^5-1] = 6.89, assuming the higher 7.5% raises.

wintermute

07-04-2012, 11:03 PM

That's not what Coon has been saying, but who knows? It's not official yet. He's been saying on Twitter, that the salary cap numbers are going to stay the same next year most likely, which implies that projected BRI either stays the same, or goes down.

To quote from count55, who's apparently one of the guys who's read the actual CBA:

http://www.eightpointsnineseconds.com/2012/05/pacers-offseason-post-1-how-much-money-do-they-have-to-add-player/

“For purposes of this Section 7 only, the Salary Cap shall be calculated in accordance with Article VII, Section 2, except that the percentage of Projected BRI to be utilized for such calculation shall be 42.14% for all Salary Cap Years. Notwithstanding the foregoing, (i) the Salary Cap for the 2011-12 Salary Cap Year for purposes of this Section 7 only will be $51.689 million, and (ii) the Salary Cap for the 2012-13 Salary Cap Year for purposes of this Section 7 only will equal the greater of (x) the Salary Cap as calculated pursuant to this Section 7(f), and (y) $54.675 million.”

This provision hasn't been widely reported, but the 4 year/$58.5m number has, so I'm taking it as true until otherwise reported.

xIndyFan

07-04-2012, 11:31 PM

I have it as :

starting salary = x*I/[(I+1)^n-1]

E.g. x = 58.5, I = 0.045, n = 4

-> starting salary = 58.5*0.045/[(1.045)^4-1] = 13.674 (a little rounding off error)

For Hill's (reported) deal, starting salary = 40*0.075/[(1.075)^5-1] = 6.89, assuming the higher 7.5% raises.

think you're compounding the raises in your formula. aren't you?

raising the 1.075^5-1 is compound interest.

wintermute

07-04-2012, 11:36 PM

think you're compounding the raises in your formula. aren't you?

raising the 1.075^5-1 is compound interest.

Technically, yes I guess, but I'm just inverting the formula for the sum of a geometric series.

The reason you get a term like 1.075^5 is because you're adding: S + S*1.075 + S*1.075^2 + ... + S*1.075^4, where S is starting salary.

xIndyFan

07-05-2012, 01:28 AM

Technically, yes I guess, but I'm just inverting the formula for the sum of a geometric series.

The reason you get a term like 1.075^5 is because you're adding: S + S*1.075 + S*1.075^2 + ... + S*1.075^4, where S is starting salary.

but the salaries are not geometric series, they are arithmetic. at least that what I thought this said.

No. Raises are limited to a percentage of the first-year salary. Raises in extensions are based on a percentage of the first season of the extension. If a team signs another team's free agent (4.5% maximum raises) to a four-year contract starting at $10 million, the maximum raise is $450,000 each year. This player's four-year salary would be:

NBA CBA FAQ (http://www.cbafaq.com/salarycap.htm)

wintermute

07-05-2012, 04:54 AM

^ All I can say is that my interpretation is the same as others' in the thread (see Larry Staverman's post #3 and rapidpacersfan's post #4), and what's more the results are consistent with publicly known contracts.

Naptown_Seth

07-05-2012, 08:56 AM

IndyFan is right, they do NOT compound raises. You have your base and you have your per year raise in dollars, not PCT increase from the prior year.

So

Y1 = X

Y2 = (X) + 0.045*X => (prior year) + raise

Y3 = (X + 0.045*X) + 0.045*X => (prior year)+raise

Y4 = (X + 0.045*X + 0.045*X) + 0.045*X => (prior year) + raise

This gives you 4 "X" (base salary) as he said and then "6 raise packets", six 4.5% of base additions to the total. 6 * 4.5% is the 27%.

Thus 4.27 * X is the 4 year total using 4.5% raises. The formula IndyFan gave is just the progression so you can have other raise amounts and different year counts.

There isn't much/any wiggle room on this. If the 58m total doesn't seem to match what the expected first year salary should be by BRI, well then it means that what we think the BRI is going to be hasn't actually turned out to be that.

I haven't checked all the new CBA, but I assume they left in flat and front loaded options on deals too? Not that Roy or the Pacers would do that in this case since it wouldn't be a max deal.

IndyHoya

07-05-2012, 10:01 AM

There isn't much/any wiggle room on this. If the 58m total doesn't seem to match what the expected first year salary should be by BRI, well then it means that what we think the BRI is going to be hasn't actually turned out to be that.

I was wondering if the cap is indeed $58M. I say this because I saw this Indy Star article dated 7/3/12 indicating that $58M was the cap in effect for 2011-2012, but implying that the 2012-2013 cap was going to change with the change being announced sometime later this month."

http://tinyurl.com/6th54p8

Surely the Front Office has to know what the cap is. But I haven't seen any announcement of any new 2012-2013 cap figure and everyone seems to be using the old $58M cap figure. Did the Star get this wrong?

IndyHoya

07-05-2012, 10:19 AM

I found this at this website: http://tinyurl.com/75bnqh5

"The NY Post has reported that sources, presumably the Knicks, have informed it that economic projections say that the NBA salary cap will grow to about $60-$61 million for the 2012-13 season. The salary cap for 2011-12 was set at $58,044,000 in negotiations over the collective bargaining agreement. Remember that the exact number of the cap relies upon a projection of basketball related income and is not set until July before each season. I’ll use the $60M in this post as a nice square number."

Hicks

07-05-2012, 10:58 AM

but the salaries are not geometric series, they are arithmetic. at least that what I thought this said.

NBA CBA FAQ (http://www.cbafaq.com/salarycap.htm)

Ahh, okay. So with Roy, a max is 54,700,000 x .25 for a starting salary of $13,675,000, with annual raises of $615,375?

So these are the real numbers:

$13,675,000

$14,290,375

$14,905,750

$15,521,125

Total: $58,392,250

?

Hicks

07-05-2012, 11:01 AM

So that clears up Roy's contract, but I'm not clear yet as to what formula I can use to find George's year by year numbers based only on knowing (presuming) a $40m total and 5 years on contract and 7.5% raise.

Naptown_Seth

07-05-2012, 11:02 AM

That's it Hicks.

Naptown_Seth

07-05-2012, 11:13 AM

So that clears up Roy's contract, but I'm not clear yet as to what formula I can use to find George's year by year numbers based only on knowing (presuming) a $40m total and 5 years on contract and 7.5% raise.

5 years to a total of 40.000

In millions:

6.9565

7.4782

7.9999

8.5217

9.0434

But that's for dead-on 40.000, obvious it's probably rounded to 40 for the press, like Roy. First year of 7m flat takes you to 40.250m.

When I play around with this in XL the quick simple version is to make A1 your base, B1 your raise PCT (.045, I turn on % formatting for viewing), make C1 = A1*B1 which is the per year raise.

Then I made A2 a formula of A1 + $C$1, the dollar signs make that reference fixed when you copy/paste. You can use F4 key with C1 highlighted to cycle through the 4 variations of "$" (which is handy). Then copy this cell and paste in A3, A4, etc. You only need 5-6 lines for current contract rules.

Then down farther I just put a =SUM(A1:A8) for the contract total.

This allows you to try different starting salaries and different raises very quickly, but it isn't the enter total and enter years and enter raise % formula. I can quickly add a years cell and then use a =ROW() check with an =IF to automatically calc the cells based on the number of years entered instead of doing the copy/paste/delete thing with the rows.

But that's overkill on this to me. ;)

edit, not overkill enough to avoid a nerd-out. I made the years cell D1

Then I turned cells A2 to A7 into this formula, using this as A2 and then copying

=IF(ROW(A2)<=$D$1,A1+$B$1,0)

I put the SUM in A8 =SUM(A1:A7)

xIndyFan

07-05-2012, 11:53 AM

So that clears up Roy's contract, but I'm not clear yet as to what formula I can use to find George's year by year numbers based only on knowing (presuming) a $40m total and 5 years on contract and 7.5% raise.

we're back to the [n(n-1)]/2 formula.

T = total amount of the contract

n = number of years

R = interest rate as a decimal [.045 or .075]

x = 1st years salary

The formula is: x = T/[n + [x(x-1)/2]*R]

This will generate the 1st years salary. Use it to find the raise. and add the raise repeatedly to find any years salary.

George Hill for example. 5 years/ $40M

x = 40,000,000/[5 + [5(4)/2]*.075]

x = 40,000,000/[5 + [10] * .075] -------> Hill has 10 raises @ 7.5% each

x = 40,000,000/5.75

x = 6,956,521.74 ------> this is the starting salary

6,956,521.74 * .075 = 521,739.13 -----> this is the raise

6,956,521.74

7,478,260.87 -------> 2nd year 6956521.74 + 521739.13

8,000,000.00 -------> 3rd year 7478260.87 + 521739.13

8,521,739.13 -------> 4th year

9,043,478.26 -------> 5th year

xIndyFan

07-05-2012, 12:57 PM

not an excel expert, but here goes.

A1 = Total amount of the contract

B1 = number of years

C1 = interest rate

A3 = the first years salary

A4 = the 2nd years salary

A5 = the 3rd years salary

A6 = the 4th years salary

A7 = the 5th years salary

A3 = A1/(B1 + (((B1*(B1-1))/2)*C1))

A4 = A3 + C1*A3

A5 = A4 + C1*A3

A6 = A5 + C1*A3

A7 = A6 + C1*A3

there, think that will work

edit: Have to use only parentheses in excel instead of brackets and braces

Hicks

07-05-2012, 11:12 PM

I always liked Math in school, but often was more of a B student than an A one. So I'm still trying to fully understand why that equation works in finding the first year salary. I understand how it technically gets used, but WHY does T/[n + [n(x-n)/2]*R] actually work out the way it's supposed to to get the right first year salary?

I understand why R is in there. It's more the [n + [n(n-1)/2] part I'm curious about. I understand what the variable mean, but why does that specific equation get you where you want to go? How do you know? I don't know if I'm asking the right questions; sorry.

Hicks

07-05-2012, 11:21 PM

not an excel expert, but here goes.

A1 = Total amount of the contract

B1 = number of years

C1 = interest rate

A3 = the first years salary

A4 = the 2nd years salary

A5 = the 3rd years salary

A6 = the 4th years salary

A7 = the 5th years salary

A3 = A1/(B1 + (((B1*(B1-1))/2)*C1))

A4 = A3 + C1*A3

A5 = A4 + C1*A3

A6 = A5 + C1*A3

A7 = A6 + C1*A3

there, think that will work

edit: Have to use only parentheses in excel instead of brackets and braces

That's great to have! Thank you.

xIndyFan

07-06-2012, 11:02 AM

I always liked Math in school, but often was more of a B student than an A one. So I'm still trying to fully understand why that equation works in finding the first year salary. I understand how it technically gets used, but WHY does T/[n + [n(x-n)/2]*R] actually work out the way it's supposed to to get the right first year salary?

I understand why R is in there. It's more the [n + [n(n-1)/2] part I'm curious about. I understand what the variable mean, but why does that specific equation get you where you want to go? How do you know? I don't know if I'm asking the right questions; sorry.

Let me try. The question makes sense. Now lets see if the answer makes sense. :laugh:

George Hill's salary basically consists of the starting salary, S, and raises, R. The NBA does not compound their raises. The raise is 7.5%, or 4.5%, of the starting salary. That makes all the raises the same. For example, if George Hill signed a contract of 5 years starting at $10 million, his years salaries would be $10,000,000, $10,750,000, $11,500,000, $12,250,000 and $14,000,000. The important point is the raises are all 7.5% of $10M or $750,000.

The fact at all the raises are the same means the yearly salaries consist of a starting salary and one or more raises.

yr1 = 10M

yr2 = 10M + 750K

yr3 = 10M + 750K + 750K

yr4 = 10M + 750K + 750K + 750K

yr5 = 10M + 750K + 750K + 750K + 750K

There are 5, 10M's in a 5 year contract. 4 in a 4yr contract. etc. The number of starting salaries always equals the number of years. The raises, the 750K's, form a bowling pin pattern except they start with 0 pins. 0,1,2,3,4, etc.

In the interest of making things easier for me, I'm going to switch to algebra instead of numbers. S = 10M and R = 750K

The formula n + [n(n-1)/2] counts the number of S's and R's. the first n counts the number of S's, since there are always the same number of starting salaries as there are years in the contract.

The [n(n-1)/2] counts the total number of raises. It is just an algorithm that generates a bowling pin pattern starting at 0.

n=1 -----> 1[0]/2 = 0

n=2 -----> 2[1]/2 = 1

n=3 -----> 3[2]/2 = 3 [1 raise the 2nd yr and 2 raises the 3rd yr = 3 total]

n=4 -----> 4[3]/2 = 6 [0 + 1 + 2 + 3]

n=5 -----> 5[4]/2 = 10

the n[n-1]/2 formula is multiplied by the interest rate. That generates the total value of all the raises. In GH's case it is 5[4]/2 = 10 x .075 = .75 or 75%. The total value of all the raises is 75% of the starting salary. Add to that the 5 starting salaries and that makes the total value of the contract equal to 575% of the starting salary. So in GH's case, divide $40M by 575% to get the starting salary of year 1.

Example 2] Roy's contract. 4 years @ 4.5% would be

4 + [4[3]/2]*.045 = 4 + 6*.045 = 4 + .27 = 4.27, so RH's $58M contract will be 427% of his starting salary. so divide $58M by 427% to find the starting salary. or $13,583,138.17

This is where things get murky. Trying to explain why the n[n-1]/2 works. How it generates the bowling pin pattern, using a pattern of rectangle shapes. The x's are the bowling pins, the o's are blank spaces to make seeing the pattern easier.

[o] - length=1, width=0

xo - length=2, width=1

xxo - length=3, width=2

xoo

xxxo - length=4, width=3

xxoo

xooo

xxxxo - length=5, width=4

xxxoo

xxooo

xoooo

The number of x's and o's in each rectangle is length x width. The width is one less than the length That is where the n-1 comes from. So the length x width becomes length x length -1 or n[n-1]. To count just the x's, you divide by 2. That is where the n[n-1]/2 comes from.

Hope that made sense. There are other ways to explain the formula, but this seemed the easiest.

Hicks

07-06-2012, 01:33 PM

Let me try. The question makes sense. Now lets see if the answer makes sense. :laugh:

George Hill's salary basically consists of the starting salary, S, and raises, R. The NBA does not compound their raises. The raise is 7.5%, or 4.5%, of the starting salary. That makes all the raises the same. For example, if George Hill signed a contract of 5 years starting at $10 million, his years salaries would be $10,000,000, $10,750,000, $11,500,000, $12,250,000 and $14,000,000. The important point is the raises are all 7.5% of $10M or $750,000.

The fact at all the raises are the same means the yearly salaries consist of a starting salary and one or more raises.

yr1 = 10M

yr2 = 10M + 750K

yr3 = 10M + 750K + 750K

yr4 = 10M + 750K + 750K + 750K

yr5 = 10M + 750K + 750K + 750K + 750K

There are 5, 10M's in a 5 year contract. 4 in a 4yr contract. etc. The number of starting salaries always equals the number of years. The raises, the 750K's, form a bowling pin pattern except they start with 0 pins. 0,1,2,3,4, etc.

In the interest of making things easier for me, I'm going to switch to algebra instead of numbers. S = 10M and R = 750K

The formula n + [n(n-1)/2] counts the number of S's and R's. the first n counts the number of S's, since there are always the same number of starting salaries as there are years in the contract.

The [n(n-1)/2] counts the total number of raises. It is just an algorithm that generates a bowling pin pattern starting at 0.

n=1 -----> 1[0]/2 = 0

n=2 -----> 2[1]/2 = 1

n=3 -----> 3[2]/2 = 3 [1 raise the 2nd yr and 2 raises the 3rd yr = 3 total]

n=4 -----> 4[3]/2 = 6 [0 + 1 + 2 + 3]

n=5 -----> 5[4]/2 = 10

the n[n-1]/2 formula is multiplied by the interest rate. That generates the total value of all the raises. In GH's case it is 5[4]/2 = 10 x .075 = .75 or 75%. The total value of all the raises is 75% of the starting salary. Add to that the 5 starting salaries and that makes the total value of the contract equal to 575% of the starting salary. So in GH's case, divide $40M by 575% to get the starting salary of year 1.

So we know 40,000,000 = 5.75X , in other words. Therefore 40,000,000/5.75 = X , and that means X = 6,956,521.74 rounded to the nearest 100th. The starting salary.

I'm probably making this needlessly complicated, but to make it work for my brain:

So the 'easy' formula is F = T/X%

F is the first year salary of the new contract, what we're trying to figure out.

T is the given total salary of the entire contract that we already know.

X% is the percentage of F that equals the sum amount of all of the raises that will be paid to the player over the entirety of the contract.

We already know T, so before we can solve, we need find X%.

To find X%, the formula is, as you said, X% = (N + (N(N-1)/2)*R%)

N is the number of years of the contract.

R% is percentage of the player's raise (it will either be 4.5% or 7.5%, which in decimal form is .045 or .075)

So working my way back through George Hill's alleged 40m deal:

X% = (N + (N(N-1)/2)*R%)

X% = (5 + (5(5-1)/2)*.075)

X% = (5 + (5(4)/2)*.075)

X% = (5 + (20/2)*.075)

X% = (5 + 10*.075)

X% = (5 + .75)

X% = 5.75

F = T/X%

F = 40,000,000/5.75

F = 6,956,522 (when you round to nearest whole dollar)

So the only thing left to lay out there is what each individual raise is actually worth.

To get that, I use the formula R = .075F

R is the individual raise.

F is the first year salary.

R = .075F

R = .075*6,956,522

R = 521,739

Hill will get paid like this:

Year 1: F

Year 2: F + R

Year 3: F + R + R

Year 4: F + R + R + R

Year 5: F + R + R + R + R

Therefore, I plug in the numbers I've calculated like this:

Year 1: 6,956,522

Year 2: 6,956,522 + 521,739

Year 3: 6,956,522 + 521,739 + 521,739

Year 4: 6,956,522 + 521,739 + 521,739 + 521,739

Year 5: 6,956,522 + 521,739 + 521,739 + 521,739 + 521,739

Therfore, Hill's contract looks like this:

Year 1: $6,956,522

Year 2: $7,478,261

Year 3: $8,000,000

Year 4: $8,521,739

Year 5: $9,043,478

God, I'm spending way too much time on this. :laugh:

Speed

07-06-2012, 01:40 PM

Are the raises all based on the first year, not each previous year? :) Just seeing if I can get your head to explode.

Hicks

07-06-2012, 01:49 PM

I'll admit your xo boxes didn't really do it for me. :laugh:

Hicks

07-06-2012, 01:52 PM

Are the raises all based on the first year, not each previous year? :) Just seeing if I can get your head to explode.

If I'm understand your question, the answer is yes.

Year 1: F

Year 2: F + R

Year 3: F + R + R

Year 4: F + R + R + R

Year 5: F + R + R + R + R

That's the way it works. You figure out the first year salary, you figure out if the contract gets a 4.5% raise or a 7.5% raise, and then use that with F to figure out R.

If the starting salary happened to be exactly 10,000,000, and you knew the raise % was 7.5%, then R is .075 times 10,000,000, which is 750,000.

Going into year 2, the player gets another 10,000,000 PLUS an additional 750,000.

Going into year 3, the player gets another 10,000,000 PLUS an additional 750,000 PLUS YET ANOTHER 750,000.

It keeps stacking like that every year of the contract.

Gaucho.Don

07-06-2012, 02:12 PM

Here is a google spreadsheet of what I think you are looking for:

https://docs.google.com/spreadsheet/ccc?key=0Atrojwv-ZRfjdEJwY2dFVUlPSFU0NWRUczBzTnhaYnc

xIndyFan

07-06-2012, 08:06 PM

I'll admit your xo boxes didn't really do it for me. :laugh:

ok, let's try this. Imagine a room with one guy in it. He shakes everyones hand. Zero handshakes.

room with 2 guys in it. A shakes B's hand. B shakes A's hand. but only one handshake really happens because it takes 2 people to shake hands. That is how we get the divide by 2.

3 guys. A shakes B's and C's hand. B shakes C's and A's. C shakes A and B's. looks like 6 handshakes, but is really only 3 because it takes 2 to make one hand shake. Notice the 6=3*2

4 guys. A shakes B, C and D. B shakes A, C and D. C shakes A, B and D. D shakes A, B and C. 4*3=12 but again divide by 2 because it takes 2 people to make one handshake. 4*3=12/2=6

so 5 guys means each guy shakes 4 other hands. but divide by 2 because each handshake needs 2 guys. 5*4=20/2=10

n guys means each guy shakes n-1 hands divided by 2 so n[n-1]/2 = the number of handshakes. or in our case the number of raises.

Does that make more sense? :laugh:

xIndyFan

07-06-2012, 08:09 PM

Are the raises all based on the first year, not each previous year? :) Just seeing if I can get your head to explode.

yes, it makes the raises all the same. The reason the NBA does it that way is to keep down the effect of compound interest. It makes the raises smaller in the last years of the contract. Not as important now, but when JO signed his contract, the raise on the 7th year would be much larger than the first one and makes the contract total amount a lot larger.

surprise, surprise it is a cost control measure.

xIndyFan

07-06-2012, 08:11 PM

Yes, this is correct. :cheer:

So we know 40,000,000 = 5.75X , in other words. Therefore 40,000,000/5.75 = X , and that means X = 6,956,521.74 rounded to the nearest 100th. The starting salary.

I'm probably making this needlessly complicated, but to make it work for my brain:

So the 'easy' formula is F = T/X%

F is the first year salary of the new contract, what we're trying to figure out.

T is the given total salary of the entire contract that we already know.

X% is the percentage of F that equals the sum amount of all of the raises that will be paid to the player over the entirety of the contract.

We already know T, so before we can solve, we need find X%.

To find X%, the formula is, as you said, X% = (N + (N(N-1)/2)*R%)

N is the number of years of the contract.

R% is percentage of the player's raise (it will either be 4.5% or 7.5%, which in decimal form is .045 or .075)

So working my way back through George Hill's alleged 40m deal:

X% = (N + (N(N-1)/2)*R%)

X% = (5 + (5(5-1)/2)*.075)

X% = (5 + (5(4)/2)*.075)

X% = (5 + (20/2)*.075)

X% = (5 + 10*.075)

X% = (5 + .75)

X% = 5.75

F = T/X%

F = 40,000,000/5.75

F = 6,956,522 (when you round to nearest whole dollar)

So the only thing left to lay out there is what each individual raise is actually worth.

To get that, I use the formula R = .075F

R is the individual raise.

F is the first year salary.

R = .075F

R = .075*6,956,522

R = 521,739

Hill will get paid like this:

Year 1: F

Year 2: F + R

Year 3: F + R + R

Year 4: F + R + R + R

Year 5: F + R + R + R + R

Therefore, I plug in the numbers I've calculated like this:

Year 1: 6,956,522

Year 2: 6,956,522 + 521,739

Year 3: 6,956,522 + 521,739 + 521,739

Year 4: 6,956,522 + 521,739 + 521,739 + 521,739

Year 5: 6,956,522 + 521,739 + 521,739 + 521,739 + 521,739

Therfore, Hill's contract looks like this:

Year 1: $6,956,522

Year 2: $7,478,261

Year 3: $8,000,000

Year 4: $8,521,739

Year 5: $9,043,478

God, I'm spending way too much time on this. :laugh:

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