Cool - a mathematical analysis will be illuminating (I hope)
And just to note that when you say “you”, you don’t mean “me, GreenAsJade”, whch is the reason why I’m not responding to that question 
I, GreenAsJade, am not worried about rank pool distortion, but I do know that the reason why the rules are they way they are is to guard against it
GaJ
No I don’t mean you personally. I apologise, it’s just the way I address the issue.
This is a very important question that seems to have had little impact on the discussion. Yet, it points the way to a reasonable compromise on the issue. The current rule implies that the second undeserved win by timeout would have a terrible effect on the whole ranking system and therefore must be annulled. This seems extreme and unlikely, but we admittedly have no evidence one way or the other. It may be that the effect accumulates gradually, or that it becomes much more serious at some critical point—we don’t know. It is quite possible that several such wins are needed before they have a significant effect on the system. One way to test this would be to set up a model and input different timeout wins to see what the effect would be. Short of that, a compromise would be to raise the limit from the second serial timeout to, say, the third, or fourth, or fifth. This would make it much harder on the cheaters, while delivering a little more justice to the honest players. Not perfect, of course, but a compromise.
I have done the simulation.
Here is the background information
A club of 30+1 player. A total of 77 games played. 6 games in question.
The control player’s initial rating is 1500, deviation 78. Club players are from 1310 to 1600. Deviation is from 88 (for 1300) to 72(for 1600). I can change the initial ratings but I don’t think I can change the deviations.
I tested out 4 situations:
Normal play
Timeout lost
Timeout annulled
Cheater (only timeout losing games)
Games in question:
Result summary
Not surprisingly, player who would have lost (hi lighted yellow) is happy either way, and player who would have won (hi lighted green) is not happy when games are annulled.
A time out win boost to the original losing player takes longer to revert than I guessed a few posts above. From losing to winning is about a 40pt difference. Each subsequent games will correct itself for about 2-3pts. I will now guess it takes about 10-15 games to revert back to normal.
As for the question whether time out win is going to distort the rank POOL, here is the result. Had the games been played out till the end, the total score for all 31 players is 45061. If annulled, the total score is 45,065. When timeout wins, the total is 45,079. If we don’t count the 7 people involved, the total score is 34,883, 34886, 34887 respectively.
What this all mean is YES, time out win distorts the pool. But is this distortion significant? This is a subjective question and I personally I think NO, it’s not significant. I will compare it to a drop in a bucket. Is there more water? Yes. Does it mean anything? No. And keep in mind this is just 30 players and 77 games. OGS has a few thousand active players and over a million games.
A surprising observation is that cheating’s effect seems to be very little on the overall ranking of others.
I have uploaded the files if anyone is interested in checking the detail results.
https://nofile.io/f/aOT7OD9Ervz/ogs+cheated.xlsx
https://nofile.io/f/yYGVpQMNqvv/ogs+annulled.xlsx
https://nofile.io/f/mv81A9hkTp0/ogs+lost.xlsx
https://nofile.io/f/bqw1OhDygw5/ogs+normal.xlsx
https://nofile.io/f/EYzbbo3Fdkj/result+summary.xlsx
Very well, since we got something so interesting here let me jump back in 
Starting with a few clarifications. First, anything we are now discussing here goes WAY beyond what I talked about with the dev team, so this all just my personal understanding, nothing official. And second I very much enjoy good discussion with interesting arguments, but just a friendly warning - as stated above the dev team was clear about willigness to look at alternatives, but also that until one is found the rule stands. Now you might change their mind if you are REALLY compelling, but you might also be very much wasting your time, if having the rule removed is your only goal. Just so you know what the stakes are 
I am sorry, but to me this is completely inaplicable idea. As I was saying in the post just before yours, not all timeouts are the same. When luck has it, fifty timeouts against similarly paired players who might have been winning anyway would mean nothing. Should an unlucky streak happen just three timeouts (arbitrary number for illustrative purposes) against much weaker players who would surely lose can deal a severe blow. Not mentioning the issue of the original player coming back to play. Would you want to multiply this streak variable by something related to strength of opponents and further somehow detect and adjust if the original player comes back? And is that even all there is to it? I am sorry, but to me personally this seems way too simplistic approach to a complex issue and that can often lead to trouble. Not to mention it would be even more confusing than the current rule
Now that is something! 
Thank you for the time put into this!
I, however, have nagging questions
How did you measure the player’s happiness? 
It seems to me you only measured players of similar strength. While the result is still interesting, it seems obvious that the changes would be minimal. What would happen if one (or god forbid two) of the losing players were significantly weaker? And what happens if the original player whose rank just got destroyed comes back and plays enough games to rank up to his original rank again?
I think much more adequate question would be: Is there any force to push this change back? Because while singular random wins and losses are normal noise, they usually cancel each other out. But is there similar, but opposing force to twenty sudden undeserved wins? Do they really dissolve among the normal noise, or will it just snowball? Because in that case the seeming small scale of the change does not matter if you are introducing a constant grow in only one direction.
If the games are annuled? Of course it is
I’m not Adam and I don’t have any concrete numbers to offer either. However, the problem is not with one player timing out and giving a few players an undeserved boost - that will regulate itself after a while and the rating system will converge to some new equilibrium.
I think the problem that OGS is worried about is the collective effect of MANY players timing out of hundreds and thousands of games, which leads to an overall shift in what ranking points mean in the whole player population, e.g. 9k now and 9k in a few months might not refer to the same level of play.
Rating systems experience a drift in what points mean anyway, but usually it is quite slow. While I obviously don’t have the numbers to know how significant that effect is, speeding possible shifts up is obviously undesirable.
Whether this goal is more important than not being able to game the system is up for debate. But again, this is not about a few players getting undeserved boosts - it is about the collective effect on the whole system.
My simulation above already shows that even 6 games out of 77 (that’s like 8% of total games played) have very little effect on OTHER PLAYERS rating. How many game in real life time out? Maybe admin can give us the data on that figure. I expect it to be significantly less.
Yes, I agree. Other noise tends to cancel out each other but time out win is a one way trip. For the moment I cannot think of any means to reverse that.
But if I may use the analogy of the drop in bucket again. How big of a drop would it become significant? If one guy’s time out bumps up everyone score by 20, of course its a problem. But if it only bumps 0.5 or 0.05, given all the grievance expressed in this thread, that could be an option.
I don’t know, if every correspondence player’s “won/lost games by result”-distribution looks anything like Tongue’s and unstable’s (~60% win by timeout, <3% loss by timeout) there’s bound to be the occasional 2 losses in a row by someone. I don’t know how many people play correspondence here or how prolific they are, but unless I see a mathematical argument that shows it’s better to count all the losses, I’ll have to support the current system based on the argument of good faith and the few if compelling “win/loss by result”-distributions I’ve seen so far.
This is interesting.
Maybe I’m going to have to eat a little humble pie!
So this evening pwxn timed out on me. Normally I wouldn’t even look at a timed out game, I would just carry on with games where it’s my turn.
Given that I’ve been taking part in this thread I decided to check out the game.
Well, it’s end game and it looks like I’m winning. I’m currently at 11K (started the game at 14K) and they are at 9k (started at 8k I think). They’ve timed out a few times here and there but nothing serial I think.
I’ve been looking at my graph and can’t work out if my rank has gone up because of this??
While I was trying to work this out (thinking hell I’ve been cheated!) I noticed that pwxn had timed out again.
Looks like an even game, possibly a loss for them.
Looking at pwxn’s graph I can’t tell if they’ve had a drop in rank??
Looking at their game history it lists them as 9k against my timed out game and 10k against the subsequent timed out game.
Apologies if this querying about the effect on rank has been discussed but it’s a long thread and my brain sometimes doesn’t work.
Question is, are they using time out to avoid a drop in rank?
Am I upset? Initially yes, but now, I think not.
Despite this I still believe that the rule to not count time outs is correct.
Edit: pwxn has now set vacation on…
for the record, the mathematical argument that you are looking for is exactly 5 posts above yours.
is it conclusive or compelling? that’s an open topic. but if you are looking for the math, then is there.
I commend your effort, but writing a simulation is not the same as a mathematical argument, because it rests on assumptions you made in your methodology, validity of the code you wrote and flawless-ness of the program you ran to arrive at the numbers … and I’m not inclined to check/review/validate any of these as it would be quite time-consuming.
Perhaps I should have said mathematical proof, to be clear.
The problem seems to be that there is no mathematical argument, let alone proof, for the rule as it exists. One win by timeout in correspondence, followed by a string of annulments, seems to be an arbitrary standard. Why not two or more wins before the annulments kick in?
As I understand it, and would argue, two timeouts in a row suggest someone isn’t playing because, well, for some reason they can’t play. In order to prevent this unintended break from further producing a string of incorrect results by default, these successive timeouts don’t count. Losses by timeout seem to be very common in correspondence games (otherwise we wouldn’t be seeing 60% win by timeout), despite being uncommon to occur in a row (otherwise we would see figures way beyond the 3% losses by timeout that I’ve observed).
First I produce Arguments.
Then someone said they want Math.
Then I produce Math .
And someone else says that’s not REAL Math.
I hope you do realize that Glickman wrote his “Glicko” system for his Harvard PHD, and I had no bloody idea what his REAL MATH means:
(for the record, I did not write the excel simulations above. I just plug in the numbers)
So I don’t have any more real math to show and I rest my case.
And I suggest that when someone else bring this topic up again in the future, whoever is in charge will just cut the cxxp and go straight to the heart:
“Look kid, we are not gonna change whatever you say so don’t even bother wasting your time.”
I don’t really get it.
OGS let newbies join at 13k, they lose again and again, so other people get points and get pushed up
OGS let good players join at 13k and they play and win and win so they can get their rank. Other people get pushed down
Players come and go all the time. Or make new accounts, still starting at 13kyu.
Why are we discussing if time out’s CAN distort rankings, when the actual system is supporting a ranking distortion, which seems way bigger to me than some Time Outs?
Very good point indeed.
I can only say that those in charge are incoherent and stubborn people who base their decision on speculations.
While I don’t like the timeout rule, this is silly and not true. It appears to be an attempt to goad someone “in charge” into responding directly to you by calling them names.
Actually the person in charge is very civil, and very busy taking care of many things, and quite sensibly letting other people explore and discuss the issues, acting only when the time is right.
The whole reason for this is to keep the rank pool in balance. IE it is for the same reason as the timeout rule, not contradictory to it.
The premise is that people who join OGS will span the range of ranks. So they are given a rank in the middle of the range. On average, some of those will actually be stronger, and will go up quickly, taking rank from people on the way up. Some will be weaker than 13k, and will go down quickly, giving rank to people on the way down. Note that at this time, the new person’s uncertainty in rank is high so their effect on other people’s rank is small.
That premise is incorrect.
You may or may not agree with the logic, but the reason behind the 13k starting rule is the same as the reasoning behind the timeout rule: to keep the rating pool steady.
so just to clarify:
A system where new players can start at 25k and good players at their current rank is not as good as a standard 13k rank because
“the 13k is to keep the rating pool steady?”
Sorry, i do NOT understand at all.
I can’t find even a bit of logic behind that.
You get a wrong rank, so of course rank distortion will happen. And it will happen with EVERY new player that is not 13k, with EVERY new account an old player makes.
So, how many timeouts are there every day?
Is the amount really much more than the new players/accounts?
If so:
How many timeouts should have been won / lost instead?
If it’s close to 50/50 it makes no big difference to close the abuse of the timeout rule - as per logic to “keep the rating pool steady”
If it is in favor of the Abusers - just kill this system already. The rank distortion will be less than before. (no data = wrong data in this instance)
PS:
The system, even if it works, is only good if it is fair to the players.
If you play a game with certain time settings, they are part of the game.
This line of debate - how and whether the 13k default works to achieve its goal - has a separate thread.
It would be unfortunate to derail this disussion about the timeout rule with that discussion about a different rule.
Suffice to say that there are arguments presented in that thread, and if you ‘don’t understand it at all’, you’d best read those in that thread and see if it helps.
The point here is that both that rule, and this one, are based in a premise about the maths of keeping the rank pool stable. They are not contradictory, as asserted.
