Naive Bayes Match Predictor
Start from how often each result happens, then let every clue shift the odds. Switch between three separate clues and one combined clue to see what counting the same news twice does.
Each gap is points per game, home side minus away side: over the last five matches, over this season so far, and over last season. Positive means the home side has been better.
Clues
Try an example
- Home win
- Draw
- Away win
Clue by clue
| Home | Draw | Away |
|---|
Try the Rangers v Motherwell example with three clues, then one. Each clue repeats much of the last, so three separate clues push the forecast far too high. Motherwell won 3–2.
How it works
Each result starts at its base rate, and each clue multiplies in how typical that gap is of matches with that result:
$$\begin{aligned} &P(\text{home} \mid \text{clues}) \\ &\quad \propto P(\text{home}) \times P(c_1 \mid \text{home}) \times \dots \end{aligned}$$In plain football
- The base rates come from the 3,900 training matches, 2001/02 to 2020/21: home wins 43.8%, draws 23.4%, away wins 32.8%.
- How typical a gap is comes from a bell curve fitted to that gap in matches with each result. Home wins came with a this-season gap of +0.31 a game on average; away wins with −0.39.
- The strength clue is the average of the this-season and last-season gaps, the mix that scored best on held-back seasons. With it, naive Bayes scored a log loss of 0.951 on the five test seasons, level with logistic regression; with three separate clues, 1.020.
Where it goes wrong
- Three clues counted separately make it overconfident: when it said a home win was 80% likely or more, it averaged 92%, and 80% happened.
- It knows only results. Injuries, suspensions, transfers and new managers are invisible to it.
- It sees gaps, not teams, and it was fitted on the Scottish Premiership, where two clubs have usually been far ahead of the rest.
How it was built and tested: Clue by clue. Naive Bayes, and the danger of counting twice
These figures come from a statistical model and are for analysis and education. Football remains uncertain and model predictions will frequently be wrong.