# Eigenranking

edited March 21

(10 pts)

For this assignment, you'll use our Eigenranking technique to rank a small sports league. So here's your problem:

Use this webpage to generate some data for a league with five teams. Then, use this Python code to rank the teams. Report your results here.

• edited March 22

My matrix was:

matrix = [

[0,2,1,2,4],

[4,0,4,4,2],

[4,2,0,1,2],

[3,2,4,0,4],

[4,1,4,4,0]

]

The ranking for my league is:

Team 2: rating = 0.5165517842331686
Team 4: rating = 0.48670829470439997
Team 5: rating = 0.47767125643216296
Team 1: rating = 0.3784150823149017
Team 3: rating = 0.3534423380504801


Team 2 is the best.

• My team matrix: [

[0,3,3,2,2],

[4,0,1,3,1],

[1,4,0,4,2],

[2,1,3,0,2],

[3,1,4,2,0]

}

Team 3: rating = 0.4848807961654844
Team 5: rating = 0.47317429197368976
Team 1: rating = 0.4632070845269747
Team 2: rating = 0.4163867448282543
Team 4: rating = 0.39122624975897735


Team 3 had the highest rating at 0.48488.

• My matrix was:

[0, 1, 3, 1, 2],

[2, 0, 1, 3, 1],

[2, 4, 0, 1, 3],

[2, 3, 1, 0, 1],

[4, 2, 2, 2, 0]

My ranking was:

Team 3: rating = 0.5273129974036033
Team 5: rating = 0.5215157378625016
Team 1: rating = 0.4172591286356548
Team 4: rating = 0.3713873702087703
Team 2: rating = 0.3713873702087703


• My matrix is:

matrix = [

[0,3,4,1,3],

[4,0,1,3,4],

[4,3,0,4,4],

[4,1,4,0,2],

[2,4,3,4,0],

]

The ranking for my league is below. Team 3 is the highest ranked in the league.

Team 3: rating = 0.5176519293474793
Team 5: rating = 0.4613383888892107
Team 2: rating = 0.4237581736661745
Team 1: rating = 0.41451885767177027
Team 4: rating = 0.4096419141952378


• edited March 22

My team matrix

[0,2,0,1,2,1,0,2],

[1,0,1,2,1,0,2,2],

[2,2,0,2,2,2,2,2],

[2,1,0,0,1,2,2,2],

[0,2,0,2,0,1,1,0],

[2,2,1,1,2,0,2,2],

[2,1,1,0,2,1,0,2],

[0,1,0,0,2,0,0,0]

Team 3: rating = 0.5330684574735053
Team 6: rating = 0.44328808110881446
Team 4: rating = 0.3658903880213609
Team 2: rating = 0.3361884024157472
Team 7: rating = 0.3288985633701758
Team 1: rating = 0.2800826887310974
Team 5: rating = 0.27160622973048154
Team 8: rating = 0.10974860949549743


Team 3 is the best

• My matrix is

[0,4,2,2,4]

[3,0,1,4,4]

[1,2,0,1,2]

[2,2,4,0,1]

[4,2,4,3,0]

The ranking for the league is:

Team 1: rating = 0.5184926437130086
Team 2: rating = 0.5124889651579149
Team 5: rating = 0.5112730954121437
Team 4: rating = 0.3571588647222856
Team 3: rating = 0.28205993381697697


So team 1 is the best. Go team 1!!

• My matrix was : [

[0,1,2,3,1],

[2,0,4,2,4],

[1,2,0,4,1],

[4,3,2,0,3],

[3,4,3,4,0] ]

Team 5: rating = 0.5552749621639953
Team 2: rating = 0.493080305685833
Team 4: rating = 0.4796470095274982
Team 3: rating = 0.3560934619397378
Team 1: rating = 0.3027832907437918


Team 5 was the best.

• edited March 22

My matrix was:

matrix = [

[0,1,4,3,3],

[2,0,2,4,3],

[3,3,0,3,2],

[2,1,1,0,2],

[3,1,3,1,0]

]

and my ranking was:

Team 3: rating = 0.5054388063612655
Team 1: rating = 0.5016207712530641
Team 2: rating = 0.48157957363128245
Team 5: rating = 0.4108981576640922
Team 4: rating = 0.30356553355238997


Team 3 was the best.

• edited March 22

My team matrix: [

[0, 1, 1, 3, 1],

[2, 0, 2, 2, 2],

[3, 4, 0, 1, 4],

[1, 4, 1, 0, 2],

[4, 3, 2, 3, 0]

]

The ranking for the league was:

Team 3: rating = 0.5616064344284055
Team 5: rating = 0.5279808500356232
Team 2: rating = 0.4002177984108782
Team 4: rating = 0.3946242396754421
Team 1: rating = 0.29988640866168415


Team 3 was the best.

• Here is my Matrix:

M=[

[0,4,1,2,3],

[4,0,2,1,4],

[3,4,0,4,4],

[1,3,2,0,2],

[3,4,3,1,0]

]

And here is my team ranking:

Team 3: rating = 0.5621626778711195
Team 5: rating = 0.45596356825094614
Team 2: rating = 0.4451535544402384
Team 1: rating = 0.40012824676275205
Team 4: rating = 0.34322885535517655


• My matrix: [

[0,4,1,1,4],

[1,0,1,2,3],

[1,3,0,1,4],

[2,3,1,0,1],

[1,1,1,4,0]

]

Eigenranking:

Team 1: rating = 0.5312098699110835
Team 3: rating = 0.4855376577979557
Team 4: rating = 0.408991251670405
Team 5: rating = 0.39800103471102516
Team 2: rating = 0.39546250061814175


Team 1 is the best.

• edited March 22

My matrix is:

matrix = [

[0,4,2,1,4],

[4,0,2,3,1],

[3,1,0,3,2],

[1,1,1,0,4],

[4,4,1,2,0]

]

Team 1: rating = 0.5079982820145703
Team 5: rating = 0.5032938392103756
Team 2: rating = 0.4485785148338271
Team 3: rating = 0.4101302319490532
Team 4: rating = 0.34525869395863085


That means Team 1 was the best but doesn't look like it is by too much.

• My matrix:[

[0, 4, 2, 2, 1],

[1, 0, 4, 4, 1],

[1, 3, 0, 4, 4],

[1, 3, 2, 0, 1],

[2, 1, 4, 1, 0]

]

Team 3: rating = 0.5317387251068555
Team 2: rating = 0.4743664736534873
Team 1: rating = 0.43963279846587106
Team 5: rating = 0.41258201033241837
Team 4: rating = 0.3587888852214044


Clearly, team 3 has the advantage. However, since this is bling archery, you can never tell who will pull out on top.

• edited March 22

My matrix is

matrix = [

[0,1,3,2,4],

[2,0,2,2,2],

[3,1,0,1,3],

[4,4,3,0,3],

[2,4,4,4,0]

]

Team 5: rating = 0.5369571232846212
Team 4: rating = 0.5349109263288253
Team 1: rating = 0.4288594144453331
Team 3: rating = 0.35096444755792117
Team 2: rating = 0.34416697668415475


Team 5 was the best, followed very closely by team 4.

• edited March 22

My Matrix was ;

matrix = [

[0,2,1,3,3],

[3,0,4,3,4],

[1,1,0,1,4],

[1,2,2,0,2],

[4,1,3,2,0]

]

Eigen Ranking ;

My best team being Team 2 by far.

• My matrix was

matrix = [

[0,   4,   4,   4,   2],

[2,   0,   3,   4,   4],

[3,   1,   0,   3,   3],

[2,   1,   1,   0,   1],

[2,   3,   2,   2,   0]

]

The eigenranking was

Team 1: rating = 0.5676428888501164
Team 2: rating = 0.5140250259852949
Team 3: rating = 0.4266803335123048
Team 5: rating = 0.4096681506358447
Team 4: rating = 0.25234048971012685


And team 1 was the best.

• My matrix was matrix = [

[0,2,4,1,1],

[1,0,3,2,1],

[3,4,0,1,2],

[1,3,3,0,4],

[4,3,1,4,0]

]

The eigen ranking was:

Team 5: rating = 0.5351649756702808
Team 4: rating = 0.516996248452163
Team 3: rating = 0.43493231817629663
Team 1: rating = 0.3710347855055461
Team 2: rating = 0.3456593618764917


Team 5 was the best team.