Not sure that I've seen this addressed, but I view Elo as an approximation to a PageRank-like stationary distribution. Have others thought about this more formally?
Incidentally, TrueSkill is implemented in Infer.NET, which IMHO doesn't get the attention it deserves. An open-source state-of-the-art factor graph engine with amazing performance. When dealing with many kinds of problems, including those involving discrete variables, I haven't found anything that compares in terms of speed and covergence.
[1] https://www.microsoft.com/en-us/research/uploads/prod/2018/0...
I also rated the whole season simultaneously as it's my opinion that a ranking should be based on the performance in a season versus a power ranking of who is best now. By my calculations, the people choosing teams for the playoffs are either stupid or corrupt in the sense of not treating all teams fairly. It's a popularity contest.
Capitalism sometimes leads to stupid outcomes as this big issue with "what is property".
Imagine if physicists patented their equations, forcing universities, books, movies, wikipedia, etc.. all to pay for the privilege of using their equations. The world would still be in the dark ages with just a privileged social class with access to advanced knowledge.
Not to mention this will bar a totally valid shot of others human beings of getting into the same result while trying to solve this problem, giving they are using a math toolbox that is generally available to anyone.
Corporations should have the right to explore something they worked on, of course, but look at this example where Microsoft already implemented and still profit from their invention/discovery.
Using the legal system and not creativity to stop everyone else to progress using not just their knowledge, but the knowledge that can come from everywhere its pure stupidity as its not serving towards a collective good.
We are in the middle of the COVID outbreak right now, imagine if this sort of adversarial view were prominent in the world, how many more people would die if basic techniques about making vaccines were patented?
This is just utterly stupid and it's another proof that the system is broken.
https://www.doctorswithoutborders.org/what-we-do/news-storie...
> So far, pharmaceutical corporations and other manufacturers of products needed to combat COVID-19 have not shown any willingness to take a different approach during the pandemic to ensure the necessary broad access to needed products
I hope there someone with enough intelligence out there to understand that if there's a time to rethink the rules, the time is now.
Even for people that are only thinking in terms of profits and economy, if too many people die, there will be no economy at all..
People on top of social structures: government, corporations, etc, are working like pavlovian dogs unaware that the rules of the old normal doesn't apply to the new normality. Or its just a matter of a corrupt system that is organically formed over power and money that is completely oblivious about the values they should all stand for.
So, in practice, stuff like PageRank is fairly brittle, and ELO tends to work better.
I also don't think PageRank is approximation to ELO. PageRank are just eigenvectors so (I believe) rankings are proportionate to each other. This happens with ELO but to a lesser degree because you aren't necessarily looking at all the results for all other teams at all times. A lot of information is embedded into an ELO rating but you are updating match-by-match (I believe, I have done a lot of work with ELO and learned how to modify it so understand it well...I have far less experience with the matrix-based methods). So the practical advantage of ELO is actually a theoretical one, imo.
The best way to think about ELO is Bayesian updating: you start with a prior about team skills, you use this to create a forecast, and then update your ratings based on the actual result. Comparisons are Kalman filters, Markov Chains or MCMC, etc.
I will add ELO is very powerful. Yes, Glicko is better, ELO is a special case of Glicko but ELO is also far simpler than Glicko. Simple ELO models beat complex regression most of the time, it is remarkable.
Imo, it is the Bayesian-esque updating that works so well. And, if you understand what ELO is at this level, you can split this part of the model off and use it with regression or whatever you want. It is truly amazing though.