Ladder maths

So we have this new ladder feature, but all the calculations are undone!

Ok, it is obvious, that a player sinks down the ladder, when not challenging (e.g. on vacation ). But what is the average sink speed?
The climbing speed on the other hand depends on how many challenging games a player wins and how many defending games he looses, so if a player moves faster in the challenging games than the others he will be climbing up, even if not better than the others.

Let's make the usual simplifying assumptions.
( Let p be a zero-dimensional chess player in a one-dimensional ladder-world ;-)
Lets take a 1-day-ladder of n=1000 players, all players of equal elo r=1500,
All move 2 moves per day and game, a game has 30 moves average, there are no draws, its 50:50 who wins.
1. What is the average sink speed for a player who is on vacation?
2. What is the average rising speed for a player p, who plays 4 moves per day and game?
3. How fast must a r=1300 player in this ladder play, to continuously improve his rank?

Originally posted by afx
3. How fast must a r=1300 player in this ladder play, to continuously improve his rank?

What is his winning chance? 50%? Or less?

Originally posted by Thomaster
What is his winning chance? 50%? Or less?

You can get that in the FAQ's here, the equation is given, so just make an assumption about the opponents rating, I.E.: If the player starts with a 1300 and plays a 1700, the max you can get from any one player, I think its 24 points. Have to look at the faq for sure but if he plays another 1300 player then the percentage would be 50%. If he played a 1700 player the percentage would be a lot lower, say 10%, meaning he could, in a long match, say 24 games, win two or three max. So you have to make assumptions or set up the situation where he plays a random set of ratings and do the calcs one by one and maybe come up with an average.