I am trying to understand the relationship between the two. This topic came up because of arguments, debates, goads etc between myself and no1marauder.
My argument was if one were to play people of the same rating as oneself consistently, one would over the long haul receive approximately half wins and half losses. This seems reasonable enough. Marauder disagreed (obnoxiously, which shouldn't surprise anyone).
For the most part, I play people of approximately my own rating. Sometimes I play people somewhat higher, sometimes I play people somewhat lower, but most of my games are clan games in which my clan leader sets me up against people of about my rating. However, I have 92 wins and 39 losses (and 8 draws). Marauder has a record of 419W:115L, and I believe him when he says he doesn't bottom feed. So what's going on?
Let's suppose that a player joins the site. This player, if he were to play another random player rated 1600 on this site, would have equal chances of winning or losing. Therefore the player has a "real" rating of 1600. However, the player only plays one game at a time, and only starts games with people with exactly his own rating.
This player will win the vast majority of his games until his rating rises from 1200 to 1600. During this time, he will learn a little bit. Suppose during the time it takes him to get to 1600 his "real" rating actually has climbed somewhat. By the time he gets to 1650 his RHP rating will equal his "real" rating - that is, if he were to play a random 1650 at this time, he would have equal chances to win or lose.
At this point the player should win and lose approximately equally often, since he only plays one player at a time and only plays people of his own rating. Does this make sense?
Now, should my model be accurate? If this model is accurate, how does this model compare to reality? Well, people don't play one game at a time. How does this affect things? Also, different people learn at different speeds. How does this affect things? What else is different?
Now, my hypothesis was that every single player, assuming that each player generally starts games with people approximately his own rating (with a few much higher or lower maybe), should in the long run win the same number of games as he loses (approximately). There will be an initial string of wins (or losses) when the player joins RHP because the player has not reached his "true" rating yet, but once the player hits a high enough rating such that his competition is at his skill level, he should not win more games than he loses.
Is my hypothesis valid? If not, why not?