5

I'm trying to predict the outcome of a sports match between two teams. I have data on wins and losses for all teams in the league. I intend to use a Bradley-Terry model to find the relative rankings of each team and predict the probability of team $i$ beating team $j$. Before doing so, I'd like to better understand what assumptions are buried in the model.

Questions:

  1. Does this model only account for team $i$'s record compared to team $j$'s record or does the strength of a team's opponent come into play?
  2. Does it matter if teams have played a different number of games? i.e. team $i$ could have a record of 5-0 and team $j$ could have a record of 50-0. Both are undefeated but intuitively team $j$ should be favored against team $i$.
  3. Does the model care if team $i$ beat team $j$ in calculating the probability of team $i$ > team $j$, or is it purely based on their respective league-wide record?
kjetil b halvorsen
  • 63,378
  • 26
  • 142
  • 467
ilanman
  • 4,503
  • 1
  • 22
  • 46
  • 1
    Quick remarks: Bradley--Terry models are based on wins and losses but are *not* based on league-wide records except in special cases (e.g., perfect round-robin tournaments) and, even then, only some properties of the model are expressible in terms of overall record. So, (1) strength of opponents is implicitly a factor, (2) undefeated teams lead to infinite parameters in the model (without regularization), so all undefeated teams appear (equally) "invincible" and (3) any previous results between teams $i$ and $j$ would play a role in the parameter fits and, hence, in subsequent predictions. – cardinal Dec 10 '16 at 22:34
  • 1
    Thanks this is helpful. Any chance you could expand via example or mathematically on (3)? – ilanman Dec 11 '16 at 19:14

0 Answers0