Transfer Market Optimizerby

Colton Freund and Zachary Krepps

Soccer

Each team has 11 players

Attacker

Midfielder

Defender

Goalkeeper

Two 45 minute halves

Field size

Length is between 100 yards and 130 yards

Width is between 50 yards and 100 yards

Player Transfers

Transfer windows for England

Pre-Season July 1 - September 1

Mid-Season January 1 – January 31

Recent transfer prices from English Premier League

Raheem Sterling, Midfielder, from Manchester City to Liverpool, 69.4 ME

Josh Vickers, Goalkeeper, from Swansea to Arsenal, Free

Transfer values are not player wages

Players can be transferred between leagues

How do they work?

Option 1

Club A has a player

Club B wants said player

Club A and Club B work out a price to let said player out of his contract

Club B and the player work out a wage

The player is transferred

Option 2

The player’s contract for Club A expires

Club B works out a wage for said player

The player is transferred

Formal Problem Statement

Formally, we are looking to predict player transfer fees using a backpropagation algorithm, topological sort and averaging algorithm to compare the algorithms efficiency and accuracy to correctly predict player transfer fees for future seasons. The constraints to be factored in these algorithms will be:

Inputs

Age

Position

# of yellow and red cards

Appearences

Minutes

Tackles

Interceptions per game

Fouls

Offsides

Clearances

Dribbles

Own goals

Goals

Assists

Shots per game

Key passes

# of times fouled

Average passes per game

Passing %

Crosses

Backpropagation

Create Neural Network

Set Random Weights

Create test set

While Error is too large

Run in puts through network

Sum Inputs X Weights

Output through sigmoid function

Compute Error

Use error to re-adjust weights

Backpropagation Implementation

O(n^2) with respect to the number of neurons

28(inputs) -> 30(hidden) –>60(hidden)->40(hidden) -> 1(output, between 0, 1)

Neuron objects stored in list

Neuron objects responsible for

Taking inputs

Keeping track of all its weights

Computing its error

Computing its output

Updating its weight

Backpropagation Results

Network has output between 0 and 1

Output = (value)/(max transfer value for season)

Value = (Output)*(max transfer value for season)

Currently training on all players transferred in 14/15 transfer window

Once network is trained:

Run stats for players transferred in 15/16 to predict value

Compare to their actual transfer value

Determine accuracy of this trained network

Topological Sort

Split the data of players up into four different groups

Keeper

Defender

Midfielder

Attacker

Take a specific player and compare each statistic with the comparable statistic of the players in the data.

Find the player with the closest statistical match on the 26 different parameters and insert them into the list.

Use the surrounding players to match a transfer fee with the specific player

Average Algorithm

Split the data of players up into four different groups

Keeper

Defender

Midfielder

Attacker

Take a specific player and compare each statistic with the comparable statistic of the players in the data.

For each statistic find the closest player(s) and add there fee onto a stack.

Average all the fees together for the specific players transfer fee.

Findings

The percent difference

Percent Difference = abs(actual fee – proposed fee)/mean * 100

The Average Algorithm and Topological Sort are between 7% to 200%

The Average Algorithm is always better than the Topological Sort

Questions

Why is there such a wide range of error?

More data

Outliers

Others that have tried fee prediction

What does the term Backpropagation refer to?

The re-adjusting of weights in a neural network based on the output/output error.

What is the complexity of the Neural Network? Why?

O(n^2) with respect to number of neurons in the largest layer. For each additional neuron, it is O(n) to iterate through its respective layer list. After it is selected within its own layer you calculate the output by iterating through all the inputs (same as number of outputs or Neurons from the previous layer) O(n) and multiplying them by their weights . Hence the complexity of O(n^2).

Questions?