The BCS ranking system was more complicated in 2001 than in 2008. The table belo

Question

The BCS ranking system was more complicated in 2001 than in 2008. The table below gives the BCS rankings at the end of the regular season. (A lower BCS Index gave a higher rank.) AP and USA gives the rank of each team in two opinion polls of writers and coaches, respectively. SS stands for strength of schedule ranking, with 1 being the most challenging. L is the number of losses during the season. CA (Computer Average) is the average of computer rankings from various sources. middotQW (Quality Wins) gives a measurement of the number of victories over highly ranked teams. Find the 2001 BCS ranking formula. BCS Index = (AP) + (USA) + (SS) + (L) + (CA) + (QW)

Explanation / Answer

Let Coefficients are ----- a,b,c,d,e,f.

BCS Index = a(AP) + b(USA) + c(SS) + d(L) + e(CA) + f(QW)

Now,

For team Illinois -->

16.08 = 7a + 7b + 37c + d + 9.7e _____ (1)

For team Maryland -->

19.75 = 6a + 6b + 75c + d + 11.09e _____ (2)

Doing eq.(2) - eq.(1) --

19.75 - 16.08 = (6a + 6b + 75c + d + 11.09e) - (7a + 7b + 37c + d + 9.7e)

3.67 = - a - b + 38c + 1.39e ________ (3)

For team Oklahoma -->

19.48 = 10a + 10b + 36c + 2d + 8.93e + f ______ (4)

For team LSU -->

23.58 = 12a + 12b + 10c + 3d + 13e + f _______ (5)

Doing eq. (5) - eq.(4) -----

23.58 - 19.48 = (12a + 12b + 10c + 3d + 13e + f) - (10a + 10b + 36c + 2d + 8.93e + f)

4.10 = 2a + 2b - 26c + d + 4.07e ______ (6)

For team Florida -->

13.48 = 5a + 5b + 19c + 2d + 5.78e + 0.8f _______ (7)

For team Nebraska -->

7.13 = 4a + 4b + 14c + d + 2.12e + 0.8f _________ (8)

Doing eq.(7) - eq.(8) -----

13.48 - 7.13 = (5a + 5b + 19c + 2d + 5.78e + 0.8f) - (4a + 4b + 14c + d + 2.12e + 0.8f)

6.35 = a + b + 5c + d + 3.66e __________ (9)

Doing eq.(6) - eq.(9) ------

4.10 - 6.35 = (2a + 2b - 26c + d + 4.07e) - (a + b + 5c + d + 3.66e)

- 2.25 = a + b - 31c + 0.41e _______ (10)

Doing eq.(1) - eq.(6) -------

16.08 - 4.10 = (7a + 7b + 37c + d + 9.7e) - (2a + 2b - 26c + d + 4.07e)

11.98 = 5a + 5b + 63c + 5.63e _______ (11)

Doing eq.(3) + eq.(10) -------

3.67 + (-2.25) = ( - a - b + 38c + 1.39e) + ( a + b - 31c + 0.41e )

1.42 = 7c + 1.8e _______ (12)

Doing eq.(11) + 5*eq.(3) -------

11.98 + 5*(3.67) = (5a + 5b + 63c + 5.63e) + 5*(- a - b + 38c + 1.39e)

30.33 = 253c + 12.58e _____ (13)

Doing eq.(12) - (7/253)*eq.(13) -----

1.42 - (7/253)*(30.33) = (7c + 1.8e) - (7/253)(253c + 12.58e)

1.42 - 0.84 = 7c + 1.8e - 7c - 0.35e

0.58 = 1.45 e

e = 0.58/1.45 = 0.4

Now, put value of e in eq.(12) ------

1.42 = 7c + 1.8 * (0.4)

1.42 = 7c + 0.72

7c = 0.70

c = 0.1

Doing eq.(9) - eq.(10) ------

6.35 - (-2.25) = (a + b + 5c + d + 3.66e) - (a + b - 31c + 0.41e)

8.60 = 36c + d + 3.25e

put the value of c and e ------

8.60 = 36*(0.1) + d + 3.25*(0.4)

8.60 = 3.60 + d + 1.3

8.60 = 4.90 + d

d = 3.7

Now put value of c and e in eq.(10) ------

- 2.25 = a + b - 31c + 0.41e

-2.25 = a + b - 31*(0.1) + 0.41*(0.4)

-2.25 = a + b - 3.1 + 0.164

-2.25 = a + b - 2.936

a + b = 0.686 _________ (14)

Now from eq.(4) --------

19.48 = 10a + 10b + 36c + 2d + 8.93e + f

19.48 = 10*(0.686) + 36*(0.1) + 2*(3.7) + 8.93*(0.4) + f

19.48 = 6.86 + 3.60 + 7.40 + 3.572 + f

19.48 = 21.432 + f

f = -1.952

Now, For team Washington ---->

38.27 = 18a + 24b + 21c + 3d + 14.97e + f

38.27 = 18a + 24b + 21*(0.1) + 3*(3.7) + 14.97*(0.4) + (-1.952)

38.27 = 18a + 24b + 2.10 + 11.1 + 5.988 - 1.952

38.27 = 18a + 24b + 17.236

18a + 24b = 21.034 _______ (15)

Doing eq.(15) - 18*eq.(14) -----

(18a + 24b) - 18 * (a + b) = 21.034 - 18 * (0.686)

18a + 24b - 18a - 18b = 21.034 - 12.348

6b = 8.686

b = - 1.4477

Now, a + b = 0.686

a - 1.4477 = 0.686

a = 2.1337

So overall -------

BCS Index = 2.1337(AP) - 1.4477(USA) + 0.1(SS) + 3.7(L) + 0.4(CA) - 1.952(QW)

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