I don't understand
The first player loses a half point for having more turns than player two.
Shouldn't the stats separate out games where first player actually took an extra turn? E.g., you have the global stats, and then you have games where P1 and P2 took the same number of turns, and then you have games where P1 took an extra turn. You'd probably want to split the games where P1 took an extra turn into those where P1 won and where P1 lost, and then you could look at how much P1 usually wins by when the extra turn matters.
Because otherwise, what I think ends up happening is, you have the global median, and you say, let's bid this amount. But in reality, it just favors P2 whenever P1's extra turn doesn't matter, and it isn't enough for P2 when P1's extra turn does actually matter.