A picture paints a thousand words....NEW STATISTICS TREE ICON!!!
I want to suggest that the duolingo team creates a new STATISTICS TREE ICON on the toolbar where people click on the icon and are brought to a page with a large tree for each language.
Each language tree would be multicoloured and the colours would represent percentages of people at specific levels. Each colour would be categorised e.g. Yellow = 0-40%, Green =40-60%, Blue = 60-80%, Red = 80-90%, Black 90-100%,.
In this way we could compare ourselves to other learners and aspire to move into higher colours/percentages.
We could also directly compare the success of other learners with other languages by comparing the percentages of people in the highest colours/percentages.
If there were no people at the higher levels then that colour would be narrow with wider bands for the filled lower levels.
Is it a good idea?
Quite interesting idea and I'd definitely give it a shot but probably in a little different way... Because mere level doesn't actually mean anything. You can get level 15 by just repeatedly practicing "Basics 1". Insane, yet possible.
But! Another way of comparing (points gathered within that tree, % of all words available in the specific tree, translator tier lvl for immersion, other?) could be more, I would say... reliable?
Perhaps have instead: Bronze = 100-60%, SIlver = 59-40%, Gold = 39-25%, Platinum = 24-10%, Diamond = Final 9%. This should give a more even distribution on the tree, since the vast majority of users probably never do more than ten lessons.
However, I think it would be more interesting to see the percentage of questions correct in particular sections of the tree by users that are friends with you. It would work with a different percentage scale, but the idea would be there.