Math question - hattrick & money related

[Alf]

OK, I found a study dealing with sponsor money and number of spokespersons. It also deals with how many guys you should retain towards weeks remaining before the next season starts (as there is a drop at that time).

The study only talks about 8 remaining weeks maximum, but my feeling is that the "correlation" should not be too difficult to do. Problem is, my maths have disappeared a long time ago... And I need some help here to find correlation for the following table.

This idea is to get values for the other remaining weeks (9,10,11, etc...). I have currently 4 spokespersons and my sponsor money has only increased 900$ this week, so I feel I should have one guy less (at least).

The link to the article

		Number of spokersons					
Weeks left	2	3	4	5	6	7
	2	6	8	10	12	14	16
	3	4	5,5	7	8,5	10	11,5
	4	3	4,2	5,4	6,6	7,8	9
	5	2,4	3,4	4,4	5,4	6,4	7,4
	6	2	2,86	3,71	4,57	5,43	6,28
	7	1,71	2,46	3,21	3,96	4,71	5,46
	8	1,5	2,16	2,83	3,5	4,16	4,83
	9						
	10						
	11						
	12						
	13						
	14						
	15						
	16

Crossreference the number of of spokespeople you presently have with the number of weeks left till the start of the new season (remember to take into account the break we have between seasons). The number is how many $1000 you need have your sponsors funding increase (that is "this week's sponsor income - last week's sponsor income") by before you need to fire a spokesperson. For example, say I have 5 spokespeople and there is 6 weeks left in the entire season (including the break). The result is 4.57, meaning that if the amount my funds from my sponsors increased by less than $4570 then I am going to lose money, and thus should fire one spokesperson (the cost of firing and rehiring next season is taken into account).

[Dawgfan1980]

Does anyone remember Calculus??? :-) The formula is going to end up being somewhere along the lines of x^2 = y where x is the data in the field... Who is in Calculus still??? (Been 5 years for me!)

[Alf]

bump - any maths master around here at FOFC anymore ?

[RonnieDobbs]

I'm going to give this a shot, but it's a two-variable problem.

From the article:

The number is how many $1000 you need have your sponsors funding increase (that is "this week's sponsor income - last week's sponsor income") by before you need to fire a spokesperson. For example, say I have 5 spokespeople and there is 6 weeks left in the entire season (including the break). The result is 4.57, meaning that if the amount my funds from my sponsors increased by less than $4570 then I am going to lose money, and thus should fire one spokesperson (the cost of firing and rehiring next season is taken into account).

So, this thousand dollar value is dependent on two variables, both weeks left in the season and number of supporters currently held. More than one variable makes this a little bit of a more difficult problem. Off to see what I can do.

[Franklinnoble]

And to think I slept through math in college when I could have paid more attention and been able to solve problems like this...

[Brillig]

I can't speak for the underlying math, haven't had a chance to study it yet. But a straight extension of the table is easy:

						Spokespersons					
		1	2	3	4	5	6	7	8	9	10
Weeks Remaining											
1		9.00	12.00	15.00	18.00	21.00	24.00	27.00	30.00	33.00	36.00
2		4.00	6.00	8.00	10.00	12.00	14.00	16.00	18.00	20.00	22.00
3		2.50	4.00	5.50	7.00	8.50	10.00	11.50	13.00	14.50	16.00
4		1.80	3.00	4.20	5.40	6.60	7.80	9.00	10.20	11.40	12.60
5		1.40	2.40	3.40	4.40	5.40	6.40	7.40	8.40	9.40	10.40
6		1.14	2.00	2.86	3.71	4.57	5.43	6.29	7.14	8.00	8.86
7		0.96	1.71	2.46	3.21	3.96	4.71	5.46	6.21	6.96	7.71
8		0.83	1.50	2.17	2.83	3.50	4.17	4.83	5.50	6.17	6.83
9		0.73	1.33	1.93	2.53	3.13	3.73	4.33	4.93	5.53	6.13
10		0.65	1.20	1.75	2.29	2.84	3.38	3.93	4.47	5.02	5.56
11		0.59	1.09	1.59	2.09	2.59	3.09	3.59	4.09	4.59	5.09
12		0.54	1.00	1.46	1.92	2.38	2.85	3.31	3.77	4.23	4.69
13		0.49	0.92	1.35	1.78	2.21	2.64	3.07	3.49	3.92	4.35
14		0.46	0.86	1.26	1.66	2.06	2.46	2.86	3.26	3.66	4.06

[RonnieDobbs]

Having seen that and not desiring to do regression analysis, I shall stop.

[Franklinnoble]

Originally posted by RonnieDobbs
Having seen that and not desiring to do regression analysis, I shall stop.

That'd be a GREAT excuse to use after being caught cheating on an exam.

[damnMikeBrown]

Ok, here's something that isn't accounted for in the above. Spokespersons give benefits such as keeping supporters & sponsors attitude up. That correlates to how many fans you get each week, which in turn, adds to your sponsor income & fan attendance.

This comes more into the equation if your team isn't successfull. The worse you're doing, the more effect (I think) the spokesman can have on keeping attitudes up. That is not reflected by weekly sponsorship gains alone.

[Alf]

Thanks Brillig. How did you do the extension of the table ?

[Brillig]

I just looked at it as a pure math problem, Alf - looking at the column for 2 spokespersons, it was clear that the values:

6
4
3
2.4
2
1.71
etc...

were

12/2
12/3
12/4
12/5
12/6
12/7
etc...

So the implication appears to be that for 2 spokespersons, the value is 12/(weeks reminaing in season).

Once that is determined, the change per spokesperson can be done similarly. For example, looking at the change from 2 to 3 spokespersons, by weeks remaing, from the original table, we have:

2
1.5
1.2
1
0.86
0.75
etc...

Again, this can be put in terms of a simple progression:

6/3
6/4
6/5
6/6
6/7
6/8
etc...

Having derived those two relationships, it's a simple matter to fill out the rest of the values in the table.

[Alf]

Thanks. Makes sense to me, and the graphic agrees with your explanation too !