I looked mostly at the independence of results section. I mean I need to read a few of your posts back for the rest, but my curiosity is often about model assumptions explicit or not.
as a question, does assuming all games in a tier tournament are independent as outcome events to each other say that there was not tiered change of context? I might be ignorant of many known things about tournaments.. but my question may still be helpful to both of us in different ways.. (me side learning about the things to know that your response might include, as well as getting more involved in learning about your models, i.e. guide my reading of this series further, etc.. in ignorance, questions, or hypotheses guide us... as we don't know what we ignore).
Maybe there is something about the paired sampling not being itself modeled? so few games for each pairings possible.. seems like a tournament is not a very "dense" set of data.. (being vague).
By the games being independent, I just meant that the outcome of one game or the tournament situation is assumed to not influence the results of other games.
Tournaments and pairing sampling world. one tournament, has tiers right. sequential even, but possibly also total tournament initial population of individual to generate pairings from (excuse my inculture, but i think we can make such abstraction to correspond to something making sense to you at least).
So there might be the first tiering on the phase axis, where all results of the previous phase, that would be one kind of games outcome affecting or conditionnig the next phase pairing event sampling world.
Each phase might themselves have their own stratification or subgroup or subpools from average estimators of each individual rating from previous total experience in tournaments or other admissible game events.
And then within each of those 2 imagined "tiering" separations:
(or more in my ignorance as not part of this current model I am babbling about, kidding of sorts, playing on the concept of ignorance, and a reader only sampling of mine being inferable from my commited ramblings here.. lots of words in vain even and perhaps).
The very tree hierarchical tree of matching instanciated sample, tree structure itself containing its own path dependencies...
I guess I know only of the theory behind Lichess type of online chess, where the pairing hypotheses of Glicko seem to be denser type of sampling, from more diverse pairing distances in a non-tiered fashion, (if not onlin tournament). like a well stirred sampling model of the whole pool of chess players. even if there were sub pools having gated their expreience in ratings, the general population behavior might have "denser" or more "uniform" sampling model characteristics.
where using rating to find best player , obviously not a mediecal there can only be one on the top of hill competition, would really mean that previous games could be used to predict future games.. maybe not the one crisp champion..
So far, I've only looked at round robin tournaments, where all the pairings are known from the start. For other tournaments, one would also need to simulate the pairings to get a good prediction
I will reread carefully from the begginning of the series of article. and revise tournament set ups.. I am not sure to understand the probabililty space setup here. my problem (ignorance).
I looked mostly at the independence of results section. I mean I need to read a few of your posts back for the rest, but my curiosity is often about model assumptions explicit or not.
as a question, does assuming all games in a tier tournament are independent as outcome events to each other say that there was not tiered change of context? I might be ignorant of many known things about tournaments.. but my question may still be helpful to both of us in different ways.. (me side learning about the things to know that your response might include, as well as getting more involved in learning about your models, i.e. guide my reading of this series further, etc.. in ignorance, questions, or hypotheses guide us... as we don't know what we ignore).
Maybe there is something about the paired sampling not being itself modeled? so few games for each pairings possible.. seems like a tournament is not a very "dense" set of data.. (being vague).
I'm not sure what you mean by tier tournament.
By the games being independent, I just meant that the outcome of one game or the tournament situation is assumed to not influence the results of other games.
Tournaments and pairing sampling world. one tournament, has tiers right. sequential even, but possibly also total tournament initial population of individual to generate pairings from (excuse my inculture, but i think we can make such abstraction to correspond to something making sense to you at least).
So there might be the first tiering on the phase axis, where all results of the previous phase, that would be one kind of games outcome affecting or conditionnig the next phase pairing event sampling world.
Each phase might themselves have their own stratification or subgroup or subpools from average estimators of each individual rating from previous total experience in tournaments or other admissible game events.
And then within each of those 2 imagined "tiering" separations:
(or more in my ignorance as not part of this current model I am babbling about, kidding of sorts, playing on the concept of ignorance, and a reader only sampling of mine being inferable from my commited ramblings here.. lots of words in vain even and perhaps).
The very tree hierarchical tree of matching instanciated sample, tree structure itself containing its own path dependencies...
I guess I know only of the theory behind Lichess type of online chess, where the pairing hypotheses of Glicko seem to be denser type of sampling, from more diverse pairing distances in a non-tiered fashion, (if not onlin tournament). like a well stirred sampling model of the whole pool of chess players. even if there were sub pools having gated their expreience in ratings, the general population behavior might have "denser" or more "uniform" sampling model characteristics.
where using rating to find best player , obviously not a mediecal there can only be one on the top of hill competition, would really mean that previous games could be used to predict future games.. maybe not the one crisp champion..
So far, I've only looked at round robin tournaments, where all the pairings are known from the start. For other tournaments, one would also need to simulate the pairings to get a good prediction
I will reread carefully from the begginning of the series of article. and revise tournament set ups.. I am not sure to understand the probabililty space setup here. my problem (ignorance).