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Massey computations

mark

(10 pts)

In this problem, you’re going to perform Massey’s computation a given graph representation of the games, very much like we described in this Observable notebook or this converted Sage notebook. Once you get your graph, you should respond to this post with:

  • A picture of your graph,
  • The corresponding game matrix X and margin of victory vector \vec{y} typed out,
  • The computed ranking, and
  • A link to the Sage cell server code that you used.

You can generate your graph by choosing your name from the following list:

audrey

My graph looks like so:

graph

Here are my game matrix and margin of victory vector:

    X = Matrix([
        [1,-1,0,0],
        [1,-1,0,0],
        [1,0,-1,0],
        [1,0,0,-1],
        [0,1,-1,0],
        [0,1,0,-1],
        [0,0,1,-1],
        [0,0,1,-1]
    ])
    y = Matrix([[4,3,1,8,7,6,5,6]]).transpose()

My team ratings are:

A: [ 3.58333333333333]
B: [ 1.91666666666667]
C: [-0.416666666666667]
D: [ -5.08333333333333]

Here’s a link to my Sage code:

hgrant2

My graph looks like so:
graph

Here are my game matrix and margin of victory vector:

X = Matrix([
    [1,-1,0,0],
    [1,-1,0,0],
    [1,0,-1,0],
    [1,0,0,-1],
    [0,1,-1,0],
    [0,1,-1,0],
    [0,0,1,-1],
    [0,0,1,-1]
])
y = Matrix([[2,6,1,8,1,3,7,7]]).transpose()

my team ratings are:
[ 3.64062500000000]
[ 1.20312500000000]
[0.765625000000000]
[-5.60937500000000]

Here’s a link to my Sage code: Sage Cell Server

jnarehoo

My graph looks like this:

graph
graph549×512 10.9 KB

These are my X and y matrices based on the graph above.
X = Matrix([
[1,-1,0,0],
[1,-1,0,0],
[1,0,-1,0],
[1,0,0,-1],
[0,1,-1,0],
[0,1,0,-1],
[0,0,1,-1],
[0,0,1,-1]
])
y = Matrix([[8,5,3,3,4,1,1,5]]).transpose()

Team Rankings:
A = [ 3.62500000000000]
B = [-0.875000000000000]
C = [-0.625000000000000]
D = [ -2.12500000000000]

Here is my code on Sage.

tfields

graph
graph549×512 16.1 KB

These are my X and Y matrices based on the graph above.

X = Matrix([
[1,-1,0,0],
[1,-1,0,0],
[1,0,-1,0],
[1,0,0,-1],
[0,1,-1,0],
[0,1,0,-1],
[0,0,1,-1],
[0,0,1,-1]
])
y = Matrix([[6,7,3,2,8,1,2,7]]).transpose()

Team Rankings:
[ 3.58333333333333]
[-0.0833333333333333]
[ -0.916666666666667]
[ -2.58333333333333]

here is my sage cell:

jbrandy1

My graph looks like this:

graph

Here are my game matrix and margin of victory vector:

X = Matrix([
[1,-1,0,0],
[1,-1,0,0],
[1,0,-1,0],
[1,0,0,-1],
[0,1,-1,0],
[0,1,0,-1],
[0,0,1,-1],
[0,0,1,-1]
])
y = Matrix([[3,1,5,5,5,4,6,5]]).transpose()

My team ratings are:

A: [ 3.12500000000000]
B: [ 1.62500000000000]
C: [-0.625000000000000]
D: [ -4.12500000000000]

Here’s a like to my Sage code:
strong text Sage Cell Server (sagemath.org)

ssatterw

graph
graph549×512 12.7 KB

X matrix
\begin{bmatrix} 1 & -1 & 0 & 0\\ 1 & -1 & 0 & 0\\ 1 & 0 & -1 & 0\\ 0 & 1 & 0 & -1\\ 1 & 0 & 0 & -1\\ 0 & 0 & 1 & -1\\ 0 & 0 & 1 & -1\\ 0 & 1 & -1 & 0\\ \end{bmatrix} * \begin{bmatrix} r_1\\ r_2\\ r_3\\ r_4\\ \end{bmatrix} = Score Matrix\begin{bmatrix} 2\\ 5\\ 6\\ 2\\ 7\\ 7\\ 2\\ 3\\ \end{bmatrix}

X = Matrix([
[1,-1,0,0],
[1,-1,0,0],
[1,0,-1,0],
[0,1,0,-1],
[1,0,0,-1],
[0,0,1,-1],
[0,0,1,-1],
[0,1,-1,0]
])
y = Matrix([[2,5,6,2,7,7,2,3]]).transpose()

XT = X.transpose()
M = XTX
n = M.dimensions()[0]
for i in range(n):
M[n-1,i] = 1
p = XTy
p[n-1,0] = 0

r = M.solve_right(p)

pretty_print(“M=”, M)
pretty_print(“p=”, p)
pretty_print(“r=”, r)

ratings are:
\begin{bmatrix} A: \frac{49}{12}\\ B: \frac{5}{12}\\ C: \frac{-3}{4}\\ D: \frac{-15}{4}\\ \end{bmatrix}

My Sage Cell :Sage Cell Server

jcoumarb

This is my graph:

graph
graph549×512 13.5 KB 

X = Matrix([
    [1, -1, 0, 0],
    [1, -1, 0, 0],
    [0, 0, 1, -1],
    [0, 0, 1, -1],
    [1, 0, 0, -1],
    [0, 1, -1, 0],
    [1, 0, -1, 0],
    [0, 1, 0, -1]
])
y = Matrix([[4,3,5,6,8,7,1,6]]).transpose()

My team ratings are:
A [ 3.58333333333333]
B [ 1.91666666666667]
C [-0.416666666666667]
D [ -5.08333333333333]

Sage cell server code

bking4

graph

Here are my game matrix and margin of victory:
X = Matrix([
[1,-1,0,0],
[1,-1,0,0],
[1,0,-1,0],
[1,0,0,-1],
[0,1,0,-1],
[0,1,-1,0],
[0,0,1,-1],
[0,0,1,-1]
])
y = Matrix([[8,7,5,4,2,3,1,2]]).transpose()

My team ratings are:

A[ 4.58333333333333]
B[-1.08333333333333]
C[-1.41666666666667]
D[-2.08333333333333]

Sage Cell

asword

My graph looks like this

graph
graph549×512 18.6 KB

Here are my game matrix and margin of victory vector:
X = Matrix([
[1,-1,0,0],
[1,-1,0,0],
[1,0,-1,0],
[1,0,0,-1],
[0,1,-1,0],
[0,1,0,-1],
[0,0,1,-1],
[0,0,1,-1],
])

    y = Matrix([[7,1,2,6,7,5,1,4]]).transpose()

My team ratings are:

A: [3.5]
B: [1.5]
C: [-1.5]
D: [-3.5]

Here’s a like to my Sage code:

wcshamblin

graph
graph549×512 11 KB

X = \begin{bmatrix} 1 & -1 & 0 & 0\\ 1 &-1 & 0 & 0\\ 1 & 0 & -1 & 0\\ 1 & 0 & 0 & -1\\ 0 & 1 & -1 & 0\\ 0 & 1 & 0 & -1\\ 0 & 0 & 1 & -1\\ 0 & 0 & 1 & -1\\ \end{bmatrix}

\vec{y} = \begin{bmatrix} 3\\ 8\\ 2\\ 4\\ 7\\ 3\\ 5\\ 1\\ \end{bmatrix}

Ranking:
A: (7/2)
B: (1/2)
C: (-7/6)
D: (-17/6)

Sage cell server link

jtweeten

My Graph looks like this:
graph

//This is my Game Matrix 
X = Matrix([
    [1,-1,0,0],
    [1,-1,0,0],
    [1,0,-1,0],
    [1,0,0,-1],
    [0,1,-1,0],
    [0,1,0,-1],
    [0,0,1,-1],
    [0,0,1,-1]
])


//This is my Y Vector
y = Matrix([[7,3,4,7,5,6,1,8]]).transpose()

My Team Ratings are:
A: [4.41666666667]
B: [1.08333333333]
C: [-0.91666666666]
D: [-4.58333333333]

Here’s a link to my Sage code

echou

My graph looks like:

graph
graph549×512 16 KB

\begin{equation*} X = \begin{pmatrix} 1 & -1 & 0 & 0 \\ 1 & -1 & 0 & 0 \\ 1 & 0 & 0 & -1 \\ 1 & 0 & 0 & -1 \\ 0 & 1 & -1 & 0 \\ 0 & 1 & 0 & -1 \\ 0 & 0 & 1 & -1 \\ 0 & 0 & 1 & -1 \end{pmatrix} \end{equation*}
\begin{equation*} Y = \begin{pmatrix} 1 \\ 4 \\ 28 \\ 4 \\ 1 \\ 28 \\ 7 \\ 2 \end{pmatrix} \end{equation*}
\begin{equation*} M = \begin{pmatrix} 4 & -2 & -1 & -1 \\ -2 & 4 & 1 & 1 \\ -1 & -1 & 4 & -2 \\ 1 & 1 & 1 & 1 \\ \end{pmatrix} \end{equation*}
\begin{equation*} P = \begin{pmatrix} 37 \\ 24 \\ -20 \\ 0 \end{pmatrix} \end{equation*}
\begin{equation*} r = \begin{pmatrix} 8.70833333333 \\ 6.54166666667 \\ -5.875 \\ -9.375 \end{pmatrix} \end{equation*}

Below is my code:

X = Matrix([
[1,-1,0,0],
[1,-1,0,0],
[1,0,-1,0],
[1,0,0,-1],
[0,1,-1,0],
[0,1,0,-1],
[0,0,1,-1],
[0,0,1,-1]
])
y = Matrix([[1,4,28,4,1,28,7,2]]).transpose()

XT = X.transpose()
M = XTX
n = M.dimensions()[0]
for i in range(n):
M[n-1,i] = 1
p = XTy
p[n-1,0] = 0

r = M.solve_right(p)

pretty_print(“M=”, M)
pretty_print(“p=”, p)
pretty_print(“r=”, r)

esalzber

My graph looks like so:

graph
graph549×512 18.8 KB

Here are my game matrix and margin of victory vector:
X = Matrix([
[1,-1,0,0],
[1,-1,0,0],
[1,0,-1,0],
[1,0,0,-1],
[0,1,-1,0],
[0,1,0,-1],
[0,0,1,-1],
[0,0,1,-1]
])
y = Matrix([[5,2,3,2,2,7,4,8]]).transpose()

My team rankings are:
A: [ 2.58333333333333]
B: [0.916666666666667]
C: [0.583333333333333]
D: [-4.08333333333333]

Here is a link to my Sage code:

papplega

My graph looks like:
graph

X = Matrix([
[1,-1,0,0],
[1,-1,0,0],
[1,0,-1,0],
[1,0,0,-1],
[0,1,-1,0],
[0,1,-1,0],
[0,0,1,-1],
[0,0,1,-1]
])
y = Matrix([[6,3,7,5,3,8,3,8]]).transpose()

The computed rankings are:
A: 4.458333333
B: 1.291666666
C: -0.79166666
D: -4.95833333

Here is a link to my Sage cell server code:

asmith42

My graph looks like so:

graph
graph549×512 13 KB

Here are my game matrix and margin of victory vector:

X = Matrix([
    [1,-1,0,0],
    [1,-1,0,0],
    [1,0,-1,0],
    [1,0,0,-1],
    [0,1,-1,0],
    [0,1,0,-1],
    [0,0,1,-1],
    [0,0,1,-1]
])
y = Matrix([[3,5,6,2,3,1,5,8]]).transpose()

My team ratings are:

A: [ 3.16666666666667]
B: [-0.166666666666667]
C: [ 0.166666666666667]
D: [ -3.16666666666667]

Here’s a link to my Sage code: Sage Cell Server

jfennimo

My graph looks like so:

graph

Below is my game matrix and margin of victory vector:

X = Matrix([
    [1,-1,0,0],
    [1,-1,0,0],
    [1,0,-1,0],
    [1,0,0,-1],
    [0,1,-1,0],
    [0,1,0,-1],
    [0,0,1,-1],
    [0,0,1,-1]
])
y = Matrix([[4,6,2,5,4,2,4,7]]).transpose()

My team ratings are:

A: [ 3.37500000000000]
B: [-0.125000000000000]
C: [ 0.291666666666667]
D: [ -3.54166666666667]

Here’s a link to my Sage code.

chooke

My graph looks like so:
graph

Here are my game matrix and margin of victory vector

X = Matrix([
    [1,-1,0,0],
    [1,-1,0,0],
    [1,0,-1,0],
    [1,0,0,-1],
    [0,1,-1,0],
    [0,1,0,-1],
    [0,0,1,-1],
    [0,0,1,-1]
])
y = Matrix([[4,8,4,6,2,4,4,4]]).transpose()

My computed rankings are as follows:
A: [4.333333333333333]
B: [-.333333333333333]
C: [-.333333333333333]
D: [-3.666666666666667]

Here is the link to my code

hzoppoth

My graph looks like so:
graph

Here are my game matrix and margin of victory vector:
X = Matrix([
[1,-1,0,0],
[1,-1,0,0],
[1,0,-1,0],
[1,0,0,-1],
[0,1,-1,0],
[0,1,0,-1],
[0,0,1,-1],
[0,0,1,-1]
])
y = Matrix([[6,7,8,3,8,5,2,1]]).transpose()

My team ratings are:
A: [ 5.00000000000000]
B: [ 1.00000000000000]
C: [-3.16666666666667]
D: [-2.83333333333333]

Here’s a link to my Sage code: Sage Cell Server

csabb

My graph looks like this:

graph
graph549×512 14.9 KB

Here are my game matrix and margin of victory vector:

X = Matrix([
    [1,-1,0,0],
    [1,-1,0,0],
    [0,1,-1,0],
    [0,1,0,-1],
    [0,0,1,-1],
    [0,0,1,-1],
    [1,0,0,-1],
    [0,1,0,-1],
])
y = Matrix([[4,8,2,4,4,4,6,4]]).transpose()

My team ratings are:

A: [ 4.60000000000000]
B: [-0.200000000000000]
C: [-0.600000000000000]
D: [ -3.80000000000000]

Here’s a link to my Sage code: