Think of it like this... Rating is constantly fluctuating based on the performance of others. Winning just ensures you don't lose as many points from fluctuation as you would have without the game completing
As far as i know(you should be aware it could be complete bullshit:P)
In True-skill teorethically games doesn't expire. But your recent games have bigger impact on your rating than your old games Imagine situation - you have 10 win against highly rated player and then play against someone with low rating. You win, but your gain from beating weak player is not enough to cover losses caused by reduced significance of earlier wins - thus your rating decrease despite winning a game.
Is it not because if you win against a player who is very low rating your deviation increases but your true skill mean does not increase or does not increase by the same proportion thus your rating decreases?
deviation increases by a very small amount it dosen't matter if my SD goes from 50.61 to 50.82 cause that's a very small change and it does not compensate for the loss in rating points in turn i lose 1 rating point the increase in SD is not enough to taake back the lost point from the next game against a pro player and to add to that,it does not account for the fact that we can still lose the next game against strong opponent,which nulifies any profit we could have had by increase in SD
But even if your rating changes only upon game completion, the rating is not solely impacted by that game... it is also impacted by the performance of past opponents correct? (As well as the 'expiration' effect you mentioned previously)
(1) TS ratings (used in RT ladder) only depend on the games you play at the moment you play them. They do not fluctuate when others play games.
(2) The mean increases hardly when you beat a very weak player (and it decreases only slightly when you lose against a very good player). TS is actually better in this than BayesElo. In BayesElo, the mean (which is also your rating in BayesElo) may decrease much more from a win against a very weak team, in TS this is theoretically not possible!
The variance would technically decrease due to a larger number of games, but also increases to allow for change in skill.
Long explanation: when you consider the idea of the variance, you have to understand what the developers aimed for. Every additional game decreases the variance as the algorithm has more information on the skill of the player. However, if this is the only thing that happened, your variance would converge towards zero after many games. So instead, every game a small amount is added to the variance. The reason is that the player's skill is not assumed to be constant over time, but can fluctuate (very reasonable right?). Hence, every game played gives more information about the player's skill (decreasing variance), but at the same time also adds a bit of extra uncertainty as this player's skill is evolving (increasing variance). To capture this in the formula, the variance is calculated in a complicated way (see earlier posts for links to the mathematical algorithm or just search it in Google) which incorporates both the reduction and increase based on the difference in means (and the variances) of both players. If you play someone whose rank is very different from yours, the program hardly gets any new information on your skill (it was extremely likely you'd win/lose anyway), but at the same time it does still correct for the changing skill. The result would be an increasing variance and a slighly lower rating (as this is mean - 3*SD)
(3) I did some simulations on TS in the past and I never encountered a decreasing mean after a win. I reran an old simulation on this and got the following result: I let the highest ranked team (rating 2556.171 W 34 L 1 mean 2894.665 SD 112.831) play against the lowest ranked team (rating 95.632 W 2 L 31 mean 524.027 SD 142.798). After the game, the new results were: HR: rating 2555.839 W 35 L 1 mean 2894.665 SD 112.942 LR: rating 95.369 W 2 L 32 mean 524.027 SD 142.886 You can see clearly that both means remain constant up to 3 decimals. The standard deviation on the other hand increases for both players. As a result, both players end with a lower rating after this game.
(4) The "downweighing" of earlier games is complicated and difficult to explain. The whole set of information of all previous games is included in your mean and variance and it can not be decomposed anymore to see what exactly had how much influence. However, the last game will "pull" these numbers a little bit. So you could say that newer games have a higher influence although this cannot be quantified at all. So Krzychu's first post is both completely wrong (mathematically / formula wise) but also very much spot on if you really want to intuitively translate the workings of the algorithm to the results of single games.
@Math Wolf if Ryiro was to play against 1200 rated players with around 50 SD his rating would drop from 2050 to about 2000 and that too after winning 50 games in a row and without losing a single game
the way i see it only whose who have high SD can actually play in the ladder strong players make ladder runs by 50-60 games and then get 2200-2300 rating and leave with rank 1 without playing against any other player of their caliber cause as long as their SD is high they can afford to play against low rated players oldies don't get that opportunity and get stuck around a particular number for no reason
now explain why this system is not faulty?
Edited 5/1/2015 16:26:51
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