Introduction to the fundamentals of a rank system based on number of completions (full rank system model! very close at least)
Also I expect this to be my last post for a very long time on this subject lol.
(for surf only and maybe bhop as well. in other games stuff can get confusing because of the skill set requirement is more varied [and then you have to adjust for skill set popularity i guess and all kind of werid shit], but these concepts are still essential for all # completion based rank systems)
First of all, I don't necessarily support this type of rank system.
I believe Momentum is the best alternative among other surf platforms and offering a proper rank system is important because at least 1/3 of all players are playing for points.
Maybe I rather want an inaccurate total flat point system (because it is inaccurate in an ordered way and we maybe can't make a rank system that is accurate enough yet and that is guarded against psychopaths and manipulators, e.g., alt accounting), but Momentum has chosen this, so I will comment on this.
I'm not obsessed with tier either! I use tier because Momentum talks about # completion based rank system where tier is inherently connected. If it was time distribution rank system etc., tier wouldn't matter. In general, tier doesn't make maps more competitive or less competitive, that's what the current rank system asserts sadly!
Your competitive rank is your percentile, and to calculate the amount of points you get for a rank, percentile will be used as an indepedent variable in some function. Your absolute rank is not. So if you're rank50 out of 100, you are in top50%, if you're rank500 out of 1000 as well (same competitive value).
The competitive value for a rank can be described as this 1/percentile for example. e.g. 1/1%=100 points. You don't necessarily need this function, you just need a function that takes the percentile as an independent variable.
Problem is that we don't know the true percentiles on high tier maps because they exclude the part of the population with a highest tier achieved lower than the tier in quesiton.
So we have to estimate the size of the top100% on high tier maps.
In the simple version (more later about the advanced!), you do that by looking at the average number of completions on a t1 map.
You apply this top100% directly on maps of a higher tier map with an average number of completions according to the tier it belongs (maybe sounds confusing)
For example.
If the average number of completions on a t3 map is 500. And if the average number of completions on a t1 map is 1k, then rank500 on an averagely completed t3 map is top50% (so the last rank lays in top50%!)
If the number of completions on a t3 map is below the t3 average, then you adjust the top100% accordingly. Maybe there is only 400 completions on that t3 map.
Then you do this.
(400/500)*1000=800. So the the unknown top100% is estimated to be a size of 800 in that case.
If the number of completions on a t3 map is above the t3 average, for example 600. Then you do this.
(600/500)*1000=1200. So the unknown top100% is estimated to be a size of 1200 in that case.
This is all good.
But we have an issue that I described in the posts above. Let's look at t3 stage map. It consists of 10 stages. To clearly illustrate this issue, we will say it is a non-progression stage map.
All stages are equally hard (so the last stage is just as hard all the other stages).
The surfers with a highest tier achieved of t3 will have to grind his limit performance 10 times in a row! So obv. this stage map is not going to get so many number of completions.
But this will not be due to lack of popularity - but what you could call "horizontal tier". Just like you have to adjust for tier (vertical tier) in a # completions based rank system, you also have to adjust for horizontal tier.
If all maps were linear (starting from the very beginning whenever you fail in surf), horizontal tier wouldn't be a problem. Progression stage maps make this problem less severe.
Non-progression stage maps should be banned!!!
Because of horizontal tier, these maps get less number of completions from the group of people whose highest tier achieved is t3 especially, otherwise they don't affect it so much (length obv. affects number of completions but that will correlate with lower competition so that's no problem).
It is a complicated issue.
But my solution is like this, it's too simple tbh. But it's well, ok lol.
To estimate the top100% on tier n map I said that you start with the average number of completions on a t1 map. And then you look at the average number of completions on the tier n map.
But we will change this a bit.
To estimate the top100% on the tier n map, you take the average number of completions on a t1 map EXCLUDING the number of completions from the people whose highest tier achieved is t1. And then you look at the average number of completions on the tier n map EXCLUDING the number of completions from the people whose highest tier achieved is tier n.
What about t10? Good question for now lol.
Everything I have said here can directly be used to make a point system. It just lacks groups. The groups can be based on the same principles of tier.
I can't comprehend for now how horizontal tier could affect it or if it affects it all, so I will just use the simple model for now.
E.g., I said a t3 map with an average number of completion has 500 completions. t1 1k completions. So to join the t3 group, you need to be in top50% on any map (which is merely completing a t3 map).
So as you go up in tier, the low tier groups would dissapear. So no, you can't have all groups in all maps cross tier as the current rank system wants it. It's impossibru!
The horizontal tier complicates shit. You can also make a system that goes more in depth and looks a how many players from each group of highest tier achieved have beaten a map.
But I believe such a system is more vulnerable to manipulation etc. E.g., if all t10 players choose to beat a map which are very few, they can very easily boost the competitive value of the top ranks of a map.
e: It was not so fleshed out my adjustment for horizontal tier shit. That's because I don't understand it properly. We can maybe use the info from the linear maps to adjust for this (because linear maps don't have horizontal tier IN SURF ... e.g., in KZ linearity works differently ...). I think progression stage maps can get noobs hooked into a map, so appropriate horizontal tier can also attract noobs weirdly. So maybe progression stage maps can be ignored? I don't know. It's very complicated ... On KZ it's a bloody mess. A linear KZ climb map is not really a linear map, but a weird mix between stage and linear. A stage climb KZ map is some weird mix between stage and just what I said inside each stage lol (sub stages and sub linearity). And then there are all sort of KZ categories ...
I think my comment introduces the basic issues of # completions rank system. An estimated percentile is used as independent variable which is put into some arbitrary function that reward points for a map rank, that, that was the new thing in this post, summed up with everything else. Other people must do the remaining work now ...