First, thanks for the great game - I've wasted so much time on it when I should have been doing better things!
I've noticed that the First Games Malus still seems to be based on 20 games rather than 30 (point 5 in the Ranking Algorithm), so it's inconsistent with what's described at the bottom of the ranking pages.
Also, I'd like to suggest a possible improvement to the algorithm - using an exponential weighted average rather than averaging over the last 100 games. With this method, a score n games ago gets weighted x^n, so the weighting of past games gradually decays rather than falling off suddenly after 100 games. This would mean that the change in a score won't be based on comparing the last result to the result 100 games ago. Currently, if you had a good run of results 100 games ago, you might be reluctant to play because that's likely to reduce your score.
Exponential weighting should be easy to implement too, because:
New exponential weighted average
= x * Previous exponential weighted average
+ (1-x) * Most recent game score
e.g. I'd suggest using a value of x like 98%, giving:
New exponential weighted average
= 0.98 * Previous exponential weighted average
+ 0.02 * Most recent game score
Then, as before, you can multiply by 100/6.2 to get a score.
I think this method would have a few more advantages over the current algorithm:
1) There would be no need for a First Games Malus, because, if all scores are initialised to 0 or a low number, you need to play a reasonable number to build up a decent score.
2) Scores move up or down depending on whether your previous result was better or worse than your weighted average.
3) Initial results get a lower weighting. Under the current system, it might be possible to get an inflated score by playing bingo on the first 2 games and setting up a new account if you lose. Once you win 2 games, you can then play the minimum number of games to overcome the First Games Malus, then your average will be about a point higher than it would otherwise be (I hope I'm not giving people evil ideas...). The exponential method prevents this strategy, however people might play bingo just to build up an initial score quickly. This could be avoided by setting the initial average to something greater than a bingo playing average - say 4 or 5 points.
4) There is no need for the 0,01% bonus for the first 500 games, because a similar effect results from the asymptotic transition from the initial score to the long term average under the exponential weighting method. The current bonus method is subject to exploitation - you can play bingo or just leave immediately for your first 400 games, then play normally for the next 100 (or even better play bingo until you get a good run of results, then start playing normally). Using this exploitative approach you will attain the full 5% bonus after your first 100 sensible games rather than having to wait for 500 games. This could be quite important for someone looking to gain a high ranking.
Anyway, thanks for reading this - hope it makes some sense; what does everyone think of this method?
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