I mentioned before that IRT is basically an Elo for the game of responding correctly to benchmark questions. For Elo, here’s the win probability of player A vs. player B, given respective strengths Sa and Sb:
P(A wins) = 1 /​ [1 + 10^((Sb—Sa)/​400)]
Nitpick. I think the above is the probability of winning plus half of the probability of drawing.
Thanks Vasco, and you are right. How Elo and related systems ‘manage’ draws/​partial credit is something I didn’t explore, but as you say the commonest approach is to set ‘draw’ at 0.5. The equation above is still true for games which only have wins or losses (so P(A draws) = 0).
Hi Gregory. Great post.
Nitpick. I think the above is the probability of winning plus half of the probability of drawing.
Thanks Vasco, and you are right. How Elo and related systems ‘manage’ draws/​partial credit is something I didn’t explore, but as you say the commonest approach is to set ‘draw’ at 0.5. The equation above is still true for games which only have wins or losses (so P(A draws) = 0).