The below is a basic example of the equations we use, it does not include all the factores that the production model uses. In
the equations below Xi,j
are the number of goals scored by the home team(i) and away team (j) respectively, α represents a parameter
describing the ‘strength’ of the teams and γ represents a parameter
describing the home advantage of team i.
is augmented with the inclusion of total shot data. To achieve this we simple
extended the above equation with the assumption in equation below, where κ is a scaling factor.
are the total shots (on and off target) in a game by the home and away teams
respectively. In this model we are modelling a match as a combination of goals
scored in a match and the goals that should have been scored inferred from the
regression includes a weighting function (equation 2.2) which allows the model
to place greater importance on more recent matches. We have included the same
weighting function. In our model t=(fd-md) represents the
difference, in days, between the date the match was played (md) and the date
chosen to represent the “fit date” (fd). ξ is a
constant representing the strength of the decay
allow us to vary the relative importance of “goals” inferred by the shot data
to the actual goals scored we have included a further weighting function to fit
to those relevent elements. This constant, τ, is
fixed at 1 for elements representing goals and a lesser value for those
elements in the fit representing shots.