We continue to train the brain. Add competitions

Six months ago, I wrote a post about my interest in exercises for brain training , the result of which was a small site with such exercises , created for everyone who wants to embark on the path of cognitive enlightenment. Since the site was made with an eye to desktop games and applications, it essentially turned out to be such an application only on the web. But recently it was decided to fix this small flaw and add some kind of interaction between the users of the site, in the hope that this can give someone additional motivation for training. The first thing that comes to mind is of course the competition system.

Horizontal separation

At first there were attempts to find a third-party service that could be fastened quickly, but all that I found was tailored for casual games with a simple system of a single table of results and a pinch of achievements. I would like that there would be a separation of users by skill out of the box (a fairly standard practice, for example, in games such as LoL and SC2), because if I participate a hundred people, then obviously someone will be in the hundredth place, and maybe it will not feel very comfortable , looking at the top ten with results many times greater than his. Therefore, we need a mechanism for dividing into smaller groups of equal strength. As a result, I had to write myself.
I did not become too philosophical and seek out some ingenious algorithms for this task. If you need to divide it into homogeneous groups, then we get the standard cluster analysis problem, take the k-means algorithm and get a partition. The only problem that arises here is that too good and too bad results can grab a whole group for themselves. We also go from simple and rank this problem as a known problem in statistics, the problem of detecting outliers, we take the simplest algorithm to find them, and before using clustering, we cut off these results and automatically assign them to the best and worst groups, respectively.
Total, we have a horizontal partition. Further, the system could be improved by adding a vertical partition, which would solve the problem of too many identical results. That is, instead of having one group with the results 1 1 1 2 2 2 3 3 3, it would be better if there were three equal groups 1 2 3, 1 2 3, 1 2 3. But since there are not so many participants, and the problem is not so acute, it was decided to postpone this modernization until better times.

Format

The static list from the top seemed less interesting to me than the constantly updated list, so the format of the weekly competitions was chosen. And since training is most useful for their regularity, it would be nice to somehow stimulate a person so that he would visit the site the next day and try again with renewed vigor, so it was decided to update their positions and leagues once a day.

In total, this is not such a tricky system. Take part and leave feedbacks.
ru.brainexer.com/contests.html
www.brainexer.com/contests.html