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Why not use percentile as rating?

Wouldn't it be more telling to see that we are, say, 68.82 (meaning better than 68.82% of the players) rather than "1750"? Why show these arbitrary numbers when you can show less arbitrary and more meaningful ones?
Because percentile depends on rating, not rating depends on percentile
Another reason is if you show only the percentile, you are more limited on representation, you can't show 99,99999 and more 9's
Why is one more meaningful than the other? They both measure the exact same thing, your strength vs other players.
> Because percentile depends on rating, not rating depends on percentile

Even if we stick with the current way of calculating relative strength, in which case what you say would be true, why not showing the percentile rather than the rating. We don't perform the glick calculations ourselves anyway.

> Another reason is if you show only the percentile, you are more limited on representation, you can't show 99,99999 and more 9's

You can limit yourself to 4 digits. The same is done with ratings, and many people have the same one.

> Why is one more meaningful than the other? They both measure the exact same thing, your strength vs other players.

The rating gives you an indication of your strength vs. individual opponent you might consider with their rating, like the guy you're about to play. Percentile gives you that as well, but it also gives you an indication of your strength relative to the whole pool. That's why it's provided in the stats: people don't only want to know if they are better or worse than any individual player they might consider, but also how they fare generally. That's why it's more meaningful. You can add 100 points to everyone's rating, and nothing has changed. You can't do that with percentile. That's why it's less arbitary.
Look at the ratings of people with more than 2400, they have almost all 99.99 or 100% percentile, how do you know if someone has 2400 or 2800? The creators of this algorithm are clever, using efectivity and eficiency, is not randomly, they think in all cases
percentile will fluctuate without the player playing any game
Percentiles (or any means of ranking players) are less informative than ratings! Consider this hypothetical rating distribution:
1000, 1100, 1200, 1300, 2000

Even if player 4 increases their rating, somehow creating this distribution (or something similar):
1000, 1100, 1200, 1600, 1700

player 4's rating is still in the 80th percentile!
Indeed I have thought about that when reading jugando90. Percentile is strictly rank-based, and so it doesn't account for the "distance" betwen players, only their order. The best player in the pool may be slightly better than the 2nd one, or vastly better. And this is reflected in the rating while it would be lost in the percentile (or rank). In this sense the rating has an information that is lost in the percentile, even if on the other hand it lacks the information about strength relative to the whole pool.

I guess that's the best reason for not using percentile as the main indication of strength, though percentile (and rank when you get at the top) will need to be used at the same time to provide a usable picture of someone's strength.

The fact that percentile would change even without play doesn't seem to be a problem on the other hand.

Thanks for your comments :)

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