porkenbeans wrote:Yesterday, I spent the better part of the day compiling this list. It was very exhausting. I have therefor decided to enlist some help with the next edition. If I could get some volunteers, We could do it in an hour or so. And, it would be more accurate as a result, because we could put in some redundancy to compensate for players bouncing on the scoreboard. I am ready and willing to do this right away. And, I will be lowering the threshold, so that the list contains all the top players that are NOT Noob Farmers. Anyone interested in helping out on this project can respond here or by pm.
That is an excellent suggestion. I can provide moral support but I would rather not invest that kind of time in compiling a list until I get a tool that calculates:
Geometric mean RR of last 1000 opponents (or just all opponents if a player has not played 1000)
This is because, as Fruitcake, you, FabledIntegral and myself have all pointed out, it would be possible to cheat a system that computes RR on a rolling basis. I have calculated that using a window of the last 1000 opponents would ensure that an inflated farmer would lose about 3000 points.
I arrived at this number by extending the kind of calculations Fruitcake had posted.
Take a guy who farmed to get to 4000. Then he starts working on his RR to get it down to sqrt(1/2) = 0.71 (a number I like so far in theory because it means half your opponents are peers and half are guys 1/2 your score). If RR is computed on last 100 games, he could do it by playing 75 guys that have 4500 (25 opponents of ratio 1/4's - the noobs - and 75 of ratio 1.125's - the guys with 4500 - gives geometric mean of 0.73).
I used a win rate of 1/3 instead of 1/5 just to be conservative and because I think its conceivable if they are semi-decent. I calculated that in those games, he would win 562 and lose 888 points = -326 points. I think the highest that any player in the current scoreboard is inflated by is about 3000 points, so in order to ensure that an inflated farmer loses 3000 points, the window would need to be multiplied by ten and so extended to 1000 games.
AND as an afterthought, I calculated it for a guy who gets 5800 points and plays against a guy with 4500 in order to get his RR up to acceptable levels. He would get totally hammered, losing 1141 points in a mere window of the 100 last opponents. So using the 1000 opponent window, he will lose even more points than the 4000 point farmer, given equal skill levels, because the conqueror farmer lost about 800 more points than the 4000 point guy in the first 100 opponents of the window.
He would need to play that guy 95 times to get his RR up to 0.72. If the 5800 point guy won 1/3 of the time, he'd win 491 points and lose 1633 points, coming out minus 1141.
I extrapolated the last calculation so the amount actually lost would be somewhat less, because as you sink the amount you lose decreases.