Kestas

Your post mentioned several points and I will address them in order:

InflationYou should consider reassessing your position on this.

The only benefit of inflation is to promote more activity so players don't fall behind.

The biggest problem with this is apathy. At some point even the good players will not care about their rank any more because it's simply too much effort to keep up with the inflation, which is at least linear. The last thing you want is apathy towards ranks as this is the mechanism that defines your incentives.

I do not get rid of inflation completely, but merely where it hurts us. See below.

Zero-sumI actually mentioned this already. It is indeed not zero-sum. I said at the beginning that it may be a mistake to restrict ourselves to zero-sum functions as there are many interesting incentives one can define when we choose other functions. The fixed point was designed to do precisely what it does in your simulation.

If you have already made a simulation, I would like you to try the following:

Assume that the total population is growing. This is after all the desired scenario.

New population of course starts at rank 0.

And assume that population skill distributes normally in some sense. This is important, as with a larger population you will see stronger players.

I think you will observe some interesting phenomenon:

1) The average rank of the population should converge to just below the fixed point, depending on your rate of growth.

2) The top rank will indeed grow, despite the negative sum on high-ranked games. This negative sum is in fact hardly noticeable, it only curbs the inflation of the entire population.

What really stops the point race is the penalty for playing against lower ranks, and not so much the negative sum.

I see this as getting the best of both worlds. Good players can take a rest knowing that they won't fall behind too far, while active players know that with some work they can get to the top.

PPSC"P=0,W=.55,S=0 is a good approximation of PPSC"

That is the winner takes 55% and the rest divided PPSC.

This is even better than PPSC. It has all the same benefits as PPSC, but removes the horrible flaw that is the incentive to maximise your win.

All wins are equal.

I think you misunderstood the parametrisation.

There is Participation bonus, Winner portion and Survival* bonus, and the rest goes Per SC to survivors* (*minus the winner).

Game valueThere is a good reason that the minimum value is not far from the initial value.

Only 10% of the points were invested when we set G=.1

Players can optionally change G.

I don't see a problem here.

The default merely tries to keep the system stable so that players' ranks don't jump erratically.

The total game value doesn't add up by design.

That was the whole thing about not being zero-sum.

It has a strong positive sum for low ranks and weak negative sum for high ranks.

This achieves:

1) an incentive to participate for new players

2) fast convergence to appropriate rank

3) zero total inflation

4) negligible harm to higher ranks

ComplexIndeed.

It can be simplified tremendously either via interface or redesign.

By interface you can simply set some basic settings for the parameters and players choose (perhaps with an options to tweak).

The only parameter that is chosen freely by the players is G = % points invested.

Interfaces can range over (Default, WTA, "PPSC") X (Unranked,Friendly,Serious) giving 9 basic settings for the parameters that the players don't even have to know about.

Alternatively, we can go back to the basic principle, and redesign elements that you don't like.

The basic idea was to have a function that was globally "zero-sum", but locally that depended on the game rank, giving a boost to low ranks and a slight hindrance to high ranks. Also, I had other incentives in mind when I design the point distribution function. There are limitless variations.

Not sure what you mean by magic numbers.

Ultimately I think my system is at least as good as the current system.

There are some important differences however, and the real question is if these differences justify the effort of coding.

This is not for me to decide.

You understand the efforts of coding. It might be useful to gauge the importance of these differences to active players.

Here are the important differences to consider:

Pros:1) No inflation at the average rank, creating a reliable gauge of player strength.

2) Some inflation at the top ranks in a growing population, affording all the benefits of the current system's inflation.

3) Stopping the phenomenon of rank by quantity. A player cannot rise to high ranks by playing only weaker players, because the function is weighted, not because of the skewing.

4) 2 & 3 together should reduce the apathy of veterans to the ranking system, while still maintaining a spirit of competition.

5) Extra incentives for new players, participation, and survival.

6) Better differentiation of win/loss/survival.

7) Fast convergence to correct rank.

Cons:1) Marginally more complex for players

2) Significantly more complex for admin

If you don't see how these pros are achieved I can elaborate. I just don't want to make the post too long. It's already heavy.