I won't provide numbers because I don't think they will convince you. I'll explain it simply, in words.
Let's take your situation as an example and imagine it's a 100-meter race.

I've already heard examples about motorcycle racing and ping-pong. Now it's come down to the 100-meter dash :) But we're not actually running. We're running in place.

What we see is that runner E reasonably takes third place in the second Competitive event, and he will be remembered not for being just a little behind the leader, but for the fact that another runner overtook him. That is, he is third.

But I see that player D simply entered the second Tournament, not the first. And the results of B and E are absolutely identical. If D had entered a different Tournament, the player rankings would have changed in the opposite direction, which shows that a player's rating depends on random factors and on the composition of the Tournament.

In Competitive events, what matters is not the leader's result, but how many people are between the leader and the runner. And how many seconds someone is behind the leader is of no interest to anyone (except, of course, the runner himself and his coach :D).

In Competitive events, the place does matter, and no one gives a runner 100 points and then compares the results of the others to that 100. But in our game, one of the main points of the system is that the leader is given 100 points for his wins.

Therefore, the place must be taken into account in the ranking.

Therefore, the place should not be taken into account in the ranking in the Heroes game at all.

Added 4 minutes ago

2IronAxe
Players A, B, C, D, and E received a zero rating in all systems because such Tournaments cannot be called ranking Tournaments.

There are still a lot of letters in the alphabet; I can create an example specifically for you where there will be a quorum. But I'll make it simpler. Both Tournaments were official. And according to the rules, a rating for an official Tournament is always awarded, even without taking into account the quorum. Let's calculate and see the results; don't make excuses. In this example, everyone will see how the systems with place taken into account mess up. With equal game results, players will receive different ratings. And this is not justified by anything. Neither by the 100-meter dash nor by motorcycle racing.

Added 9 minutes ago

to Iron
Your exaggerated example is not quite suitable, because I won't calculate the rating for two or three players :D

The example is called exaggerated because it does not take into account the quorum (consider it official Tournaments). It clearly shows how even in such a simple situation, the "place" parameter messes up.

And regarding the fact that E will get a lower rating than B, this is absolutely fair because he lost to more people.

But why should players receive DIFFERENT ratings for REAL IDENTICAL results, just because player D decided to enter the second Tournament instead of the first?

P.S. In my opinion, both the "place" parameter and the oscillator may reflect the rating more accurately, but only within the framework of ONE Tournament. And in order for them to continue to work without errors in other Tournaments, it is necessary that the composition of participants from Tournament to Tournament be CONSTANT, which is impossible in principle, especially for tracking a universal rating. Good luck to you in creating the formula; it's not going to happen until you realize that the "place" parameter needs to be removed from the formula. Why are people coming up with all sorts of bonuses and coefficients for the oscillator? Why doesn't anyone apply these things purely to the NON-LINEAR part of the formula?