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There are two players A and B. They each play a game against a third player C. Player A has a 50% chance of winning, whereas player B has an 80% chance of winning.

I want to use a sentence to say how much better is player B at beating player C, compared to player A. I came up with:

Player B is __% better at beating player C than player A.

The problem is, I don't know what to put in the blank. Do I put 30 or 60?

If you look at the the difference between the probably of winning a game against C, it is 30%.

$$ 0.8-0.5=0.3 $$

But the percentage difference between 50% and 80% is 60%.

$$ \dfrac{0.8-0.5}{0.5}=0.6 $$

So should I use the percentage difference or just the difference in the above sentence?

If the sentence is actually ambiguous, how can I unambiguously compare players A and B without mentioning their actual probabilities?

Note: I didn't post this o ELU.SE because I am specifically asking about unambiguous, mathematical language.

Sweeper
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  • It really depends on what you desire I think. For example, using the former method (the one that gives you 30%), you'd be saying that if A wins 11% of the time and B wins 1% of the time, then A is equally better than B as if A wins 90% of the time and B wins 80% of the time. Would you be happy with saying this? – Minus One-Twelfth Feb 22 '19 at 09:41
  • Hard to tell. Let's get one point for each game one player wins and minus one point if a player loses a game. The the average of player A is zero whereas the average of player B is $0.6$. If one point was a Dollar, player B eventually gets a millionaire and player A gains nothing. – Michael Hoppe Feb 22 '19 at 11:21

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