# Determining the winner of a match given nothing but each team's winning percentage

Team A and Team B are playing a game against each other. This is the only information we have for each team:

• Team A has won 65% of their games this year
• Team B has won 59% of their games this year

We do not know how difficult their schedules were to achieve those results and we do not know any strengths or weaknesses the teams have against each other. It's a vacuum of information except for the win rate.

Given that, is the best approach to predict a winner done by normalizing their win rates so they add up to 1?

For example:

Team A odds to win against Team B = $$\left(\frac{0.65}{0.65+0.59}\right) = 0.524 = 52.4\%$$

Team B odds to win against Team A = $$\left(\frac{0.59}{0.65+0.59}\right) = 0.476 = 47.6\%$$

Or, is there a better method?

• You are going to have to make some additional assumptions, e.g. that their schedules are equivalent. (I just watched my U-6 grandson's soccer game, and regardless of their record they would have little chance against Arsenal). You're going to have to make a variability assumption, also. A win proportion of .67 could be 2 out of 3 (rather meaningless) or 20 out of 30. – zbicyclist Oct 27 '19 at 22:05
• You might also review rating systems, e.g. the Elo rating system in Chess. This allows good predictions of win proportions between opponents who have never faced each other. But, in the Elo system, eventually you have a way to link the two players to each other. – zbicyclist Oct 27 '19 at 22:07