One interesting thing about Elo is that the whole win probability thing doesn't accurately apply to any one individual player. Every player will have their own distribution of how well they do against each rank of opponent.
For example, a player may consistently stay at 500 Elo when they play against other 500 Elo opponents, because they win half of their games against them. But if that same player were to play for example against 200 Elo players, it's possible that their Elo would go well under 500, because they don't do as well against lower rated opponents as their Elo would suggest.
Conversely, someone may be best at securing wins against lower rated opponents, and thus reach 500 Elo while playing against those, but in the event where they were to face other 500 Elo players, they may drop lower because they don't do as well against top players.
This is interesting because it puts to light that Elo is not a fixed number, it's relative to many things and its number can vary depending on how you look at it and what sorts of opponents you put a player against.
The same phenomenon can be seen in sports. There are teams that are known for wavering against lower ranked teams, but will usually show up when playing against the big teams. And conversely, teams that do very well against smaller teams, but that fail surprisingly often when put up against higher ranked teams.
For example, a player may consistently stay at 500 Elo when they play against other 500 Elo opponents, because they win half of their games against them. But if that same player were to play for example against 200 Elo players, it's possible that their Elo would go well under 500, because they don't do as well against lower rated opponents as their Elo would suggest.
Conversely, someone may be best at securing wins against lower rated opponents, and thus reach 500 Elo while playing against those, but in the event where they were to face other 500 Elo players, they may drop lower because they don't do as well against top players.
This is interesting because it puts to light that Elo is not a fixed number, it's relative to many things and its number can vary depending on how you look at it and what sorts of opponents you put a player against.
The same phenomenon can be seen in sports. There are teams that are known for wavering against lower ranked teams, but will usually show up when playing against the big teams. And conversely, teams that do very well against smaller teams, but that fail surprisingly often when put up against higher ranked teams.
