Why do ranks change when stronger beats weaker?

Suppose an “10.0k” beats a “12.0k”.

I would have thought that the best you could conclude is that you are more sure that the 10k is 10k (and not a worse rank).

There is nothing about this result that tells us that the 10k might in fact be closer to 9k.

So why does that player get a rank increase? Surely just a reduction in uncertainty would be appropriate.

Similarly for the other player.

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First - there is some information missing in your post if one is to judge what should the result be, the rating system here tries to evaluate not only the rank, but also the uncertainty in ones rank. (whether it means there isn’t enough data to tell or if they play inconsistently for a player of certain rank)

Second - when you have rating for 10 kyu, it doesn’t mean you beat anyone < 10 kyu 100% of the time, it means you beat them more often than they beat you and the bigger the difference, the bigger the chance.

To give an example, if you start as a 10 kyu and consistently beat 11 kyu 100 times out of 100, you are not 10 kyu or they are not 11 kyu. The difference between your ranks is much more than one rank. Simple as that.

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I think you have nailed it. Thanks.

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I forget the exact numbers and I can’t put my hand on the website I saw this on but it goes something like this.
A person of rank X kyu will beat an X-1 kyu 70% of the time.
So a person of rank X kyu will beat an X-2 kyu something like 89% of the time (i can’t remember the exact numbers).
Similar stats exist for X kyu/dan vs an X-y kyu/dan for y=1:N
So if I am playing a 9dan pro, there is some non-zero chance that I will win

Back to your question. If a 10k plays a 9k we expect the 9k to win 70ish percent of the time. To see why we need to increase the rank of the 9k, imagine that the 9k plays a 10k 100 times and wins 95% of them. We know that the ‘9k’ is stronger than 9k because the 9k won way more games then we expected him to. (95% vs 70%)

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Those ranks should not be looked at as a hard, scientific evaluation of one’s skill at GO, but rather as an estimation of one’s prowess which can be affected by multiple factors both in and out of a player’s control. This is one of the reasons that I’m happy with the 3-rank spread used when I am looking for a game. My 17K is actually a level between 14K and 20K, inclusive. By playing with the 3-rank spread I am playing within my level. Given the myriad of circumstances (illness, clarity of mind, kibitzing by my cat, etc.) I could play at any one of those levels on any given day.