Player rating for tournaments across all installments of Heroes.

The same problem exists here: in a tournament with 25 participants, the winner will receive significantly more points than the winner among 10 participants. I won't repeat why this isn't ideal; it has already been discussed.

If this is the only significant issue, it can also be balanced... For example, a maximum limit could be set – although in this case, with a large number of participants, too many will receive the maximum, which is also not ideal...

In short, the only task for today is to build a rating scale based on the placement achieved. Moreover, the lower placements should remain significant, and the top placements should not be "too unattainable"... :)

Option #1

The rating for participating in a tournament, as an option, is set within the range of [100; 20] inclusive. The number of points is not fixed but depends on the ratio of the winner's result and the result of the participant for whom the rating is being calculated. This is what IronAxe suggested in his rating system.

For example, after a speed tournament, five participants achieved the following results:

1. 8 days - 100 points
2. 11 days - 100*8/11=73 points
3. 32 days - 100*8/32=25 points
4. 48 days - 100*8/48=17 points=20 points (minimum for the game)
5. 63 days - 100*8/63=13 points=20 points (minimum for the game)

Almost all previously discussed nuances are taken into account here, except for one flaw: only one strong player can lower the bar for all participants in the tournament when the first player gets 100 points, and the second gets 50... The rest will get even less.

Option #2

The rating for participating in a tournament is set within the range of [100; 20] inclusive. The number of points is not fixed but depends on the number of participants and is distributed evenly:

After a speed tournament, five participants achieved the following results:

1. 8 days - 100 points
2. 11 days - 100-80/(N-1)*(R-1)=80 points
3. 32 days - 100-80/(N-1)*(R-1)=60 points
4. 48 days - 100-80/(N-1)*(R-1)=40 points
5. 63 days - 100-80/(N-1)*(R-1)=20 points

Where,
N - number of participants
R - player's position in the table

Here, there is a linear dependence, reflecting only the number of participants. The minimum is always 20 points, the maximum is 100.

Option #3

A synthetic parameter – the arithmetic mean of the two parameters mentioned above.

I strongly urge you not to dismiss this option if it seems inappropriate or unclear to someone. I will explain: essentially, we have obtained an oscillator that correctly smooths the results curve. On the one hand, we allow the leader to gain a non-linear advantage over competitors, which, I agree, is fair. If they achieved a very good result compared to the others, it should somehow benefit them. On the other hand, the oscillator takes into account the number of participants in the tournament and the number of players who performed better than you.

Agree, completing a map in 32 days and being in 3rd place (see example above) or, with the same leader's result, being in 8th place (more players performed better than you) is not the same and should be reflected in the final result...

1. 8 days - 100 points
2. 11 days - 76 points
3. 32 days - 43 points
4. 48 days - 30 points
5. 63 days - 20 points

That's all.
Let's discuss... :)

Example calculation for the "Best of the Best" tournament.

For comparison, two abstract "bots" are introduced, which change the tournament table. Note that the first rating option does not react to the appearance of two strong players at the top of the table; the second option reacts but does not reflect the leader's advantage, which is unfair. The third option takes everything into account quite correctly and is not complicated in the calculation. Moreover, changing the number of participants in the tournament also affects the result, as required by the problem... :)