Dann Corbit wrote: ↑Tue Jun 30, 2020 11:34 pm
Maybe we do have difficulty understanding each other. I guess my problem is that when something makes no sense to me, I don't believe it.
I could, of course, be wrong. I am wrong a lot. But when the outcome of a model says something stupid, I think the model is wrong.
So this thread becomes about trying to make LOS make sense to you.
First, let's talk about "Superiority". It is a thing that exists that tells you who is factually stronger.
Superiority is either 1 if it exists or 0 if it doesn't. Note 0 can exist on both sides if an engine plays itself (I won't say "identical", because 0 0 superiority is just self-play.)
Now, let's say there's these things:
10^100 entities called "A"
10^100 entities called "B"
As are factually superior to B. The LOS of A over B entities is 100%.
Now, we have them play 10^100 games. Whenever As play each other there's mostly draws, and whenever B plays each other there's mostly draws, otherwise As always have more wins than Bs when they play each other, but A could just be Superior to B by 0.000000...add a bunch of zeroes...00000001 ELO.
AFTER that's in place, you have this result:
(10^100)-8 games were drawn between ENTITY ONE and ENTITY TWO. ENTITY ONE won 8 games.
What LOS is trying to answer is what is the chance that ENTITY ONE is from the As and ENTITY TWO is from the Bs
That's all, and in most scenarios, it'll happen in fact that ENTITY ONE was A and ENTITY TWO was B.
LOS was right most of the time.
A single case where A plays A or B plays B and we get this result and LOS is wrong ignores all the other possible cases.
Hope this clears thing up, LOS is trying to guess the chance that superiority exists for one of the sides (which includes all these possibilities), and you don't need to include draws for this.