Table 2.

Summary of the simulation specifications differencing between the simulated reality and the simulated forecasting methods

Sports forecasting process	Simulated environment	Proposed methods
Step 1: Competition Network	18 competitors in a double round-robin competition during 10 seasons
Step 2: Rating procedure	Simulated rating $R_{\mathit{TRUE}}$ with $S\sim \text{N}\left(1000,0\right)$ $T\sim \text{N}\left(0,0.2\right)$ ${\mathrm{\Delta }}_d\sim N\left(0,2\right)$ And seasonal fluctuation drawn from $N\left(0,20\right)$	ELO rating $R_{\mathit{ELO}}$ with $k=14$, $c=10$, $d=400$ and a home advantage of 80 points
Step 3: Forecast method	Ordered Logistic Regression $OL{R}_{\mathit{TRUE}}$ with the covariate based on $R_{\mathit{TRUE}}$ and $C_0=-0.9$, $C_1=0.3$ and $\beta =0.006$	Ordered Logistic Regression $OL{R}_{\mathit{ELO}}$ with covariate based on $R_{\mathit{ELO}}$ and $C_0=-0.9$, $C_1=0.3$ and $\beta =0.006$ A forecast based on $OL{R}_{\mathit{TRUE}}$ with a ± 5% error $OL{R}_{\mathit{BM}}$ used by the bookmaker
Step 4: Evaluation	Rating accuracy Forecast accuracy Forecast profitability