Trophy Hunter Ranking System Help

[Goat King]

Hey everybody so recently I've been trying to create a system/mathematic way to rank on a scale of 0-10 that reflects how good of a trophy hunter a player is and not just a ranking based on the point scores like the ones already present on PSNProfiles. 

Unfortunately I am terrible at math and no equation I come up with works with what I want to include in the rank.

 

The factors I wanted to include that affect the ranking include:

- The number of completed games over the number of games played

- Overall trophy completion 

- Average game completion

- Average trophy rarity

 

If anyone is a math wiz I would appreciate any help in creating an equation that works, or if you think something else that should be included in the ranking I would appreciate input. 

 

[DaivRules]

What database will your average trophy rarity be based on and how will you account for it changing over time? 
 

The rest are calculations that are easy enough to figure out but how will you weigh them?

[Goat King]

Just now, DaivRules said:

What database will your average trophy rarity be based on and how will you account for it changing over time? 
 

The rest are calculations that are easy enough to figure out but how will you weigh them?

I was going to use PSNProfiles for gathering of stats.

 

I only wanted the equation to rate the player based on the account at time of viewing said account, if the player was updated later the equation could be rerun to calculate a new rank. 

 

I wanted to trophy rarity to weigh heavily. And I wanted that offset by average game completion or overall trophy completion but couldn't decided what is more important (I want both included though). I also felt completed game (100%s) over total games play would be good to include as to not give players just played more games a heavy advantaged to higher rank

[Mitsuru Kirijo]

Few things here:

1) Your first criteria will need to be reconsidered, it's too close to average game completion to be meaningful by itself

2) Worry about scale later, as you can normalize for scale at any stage.

3) Might want to adjust factor 4 to be average plat/100% rarity

 

The way that makes the most sense to me here is to combine factors 2-4 into a single metric with weights, then do a percentile among all players in the database.

 

An example formula you could use:

 

Rank Points = (Total Trophies Earned) * (Average game completion) * (1 - Average Platinum/100% Rarity)

 

EDIT: you can change the weights of things by using powers of each factor.

So, for example, if you wanted to increase the weight of Average Game Completion, you could use (Average Game Completion)^2 instead.

Or, if you wanted to decrease the weight of total trophies earned, you could do sqrt(Total Trophies Earned)

Edited May 23, 2020 by Mitsuru Kirijo

[Goat King]

7 minutes ago, Mitsuru Kirijo said:

Few things here:

1) Your first criteria will need to be reconsidered, it's too close to average game completion to be meaningful by itself

2) Worry about scale later, as you can normalize for scale at any stage.

3) Might want to adjust factor 4 to be average plat/100% rarity

 

The way that makes the most sense to me here is to combine factors 2-4 into a single metric with weights, then do a percentile among all players in the database.

 

An example formula you could use:

 

Rank Points = (Total Trophies Earned) * (Average game completion) * (1 - Average Platinum/100% Rarity)

I could see your point on the first criteria as 100%s would be reflected in the average game completion.

 

I still want to find a control so that rank is not effected by pure quantity of trophies (why I was using average rarity of all trophies over total trophies earned) 

 

Also a if I could request some clarification, when you say Average plat/100% Rarity. Do you mean a the average rarity of all a player platinums over the rarity of their 100%s? 

 

 

[Mitsuru Kirijo]

Just now, GoatKillham said:

Also a if I could request some clarification, when you say Average plat/100% Rarity. Do you mean a the average rarity of all a player platinums over the rarity of their 100%s?

 

So I just mean consider rarity of platinums and rarity of 100%s

 

1 minute ago, GoatKillham said:

I still want to find a control so that rank is not effected by pure quantity of trophies (why I was using average rarity of all trophies over total trophies earned)

 

The issue here is if you don't have some metric that relies on total trophies in some way (you can lower weight if you want) then the ranking system rates a person with 1 100% that 1% of people have and nothing else played the same as someone with 100 100%s with 1% rarity.

 

Basically, you want to find a way to encourage people to earn more trophies, while penalizing low completion rates and easy platinums.

[Goat King]

11 minutes ago, Mitsuru Kirijo said:

Basically, you want to find a way to encourage people to earn more trophies, while penalizing low completion rates and easy platinums.

Yes, and that's why I want wanted average game completion (penalizes low completion) and average trophy rarity (penalizes easy platinums) as factors.

 

11 minutes ago, Mitsuru Kirijo said:

The issue here is if you don't have some metric that relies on total trophies in some way (you can lower weight if you want) then the ranking system rates a person with 1 100% that 1% of people have and nothing else played the same as someone with 100 100%s with 1% rarity.

 

That's why I wanted to include number of games played as a factor in the first criteria perhaps I use that and leave of number of games completed (as it is reflected in average completion as you pointed out) that might be closer solving that problem.