So I'm thinking about how to best design a global player ranking system. Lets assume you get a score 1-100 for for individual levels in you play in the game (e.g. a racing game where the score is based on the track time). How do you create a global player ranking - i.e. a ranking of the overall skill of the player? I'm not really aiming for the score to 100% accurately represent the skill of the player but rather have a ranking system that is enjoyable for the player (that may involve being accurate).

If for example a player gets the score 50 on one level and 75 on another. A few ideas to calculate the player score:

[indent=1]Add the scores for each individual level played. So the player score becomes 125 in this example. It encourages playing more levels but gives no incentive for the player to improve existing scores. The score does in no way reflect the skill of the player.

[indent=1]Take the average score. Total score / levels played = 62,5. Rewards the player for improving existing scores but gives no incentive to play new levels. It also gives poor indication of the current skill of the player as it becomes harder to improve the score the more games you play (I find lots of games makes this mistake when ranking players).

[indent=1]ELO-type ranking where you gain/lose points based on the difficulty of the level played and your current rank. You get a player score that very accurately shows the current skill of the player. The system punishes bad plays which makes it less enjoyable in my experience - you get defensive about your score and there is no rewards for trying/experimenting with new plays. Puts a lot of pressure on the player to perform well in every game - discourages casual play.

A few things I think are important:

• I want the the player feel like he is progressing i.e. I want the score to go up as the player plays levels (and not ever go down).
  
• There should be an incentive for the player to improve the score on existing levels - raising the score from 50 to 100 on a level should be rewarded more than playing another level and getting a 50 score.
  
• The ranking system should encourage the player to get better at playing - that involves incentivising playing more and making efforts to improve techniques/strategy in order to get higher scores on individual levels.
  
  
  Any ideas of how to implement such ranking system? Anyone know of any games that does something similar and does it well?
  
  Thanks

Hmm, good question. It's really got to be a compromise between fairness and player satisfaction. You want perfection to have a higher effect than levels played.

I'd suggest something like the following:
1. Get the best score achieved for each level and square them.
2. Add all those together.
3. Square root it.

Therefore someone who achieved 100 at 2 levels would get 141 (rounded), and someone who achieved 50 at 4 levels would get 100.

The pros:
- Score never goes down.
- Score goes up if you play levels you never played OR beat your high score at an already played level.
- Rewards perfectionists

The cons:
- Hard to understand the scoring system.
- Numbers aren't nice and round.
- Score doesn't move if you fail to beat your own high scores.

I'd suggest something like the following:
1. Get the best score achieved for each level and square them.
2. Add all those together.
3. Square root it.

Nice. Simple and at first glance it seems to work well.

Hmm, good question. It's really got to be a compromise between fairness and player satisfaction. You want perfection to have a higher effect than levels played.

Experimented with some numbers (scores between 1-1000):

[Score1, Score2, ...] = Player Score


[500, 500] = 707
[1000] = 1000
[1000, 1000, 1000, 500] = 1802
[1000, 1000, 1000, 500, 500] = 1870
[1000, 1000, 1000, 500, 500, 500] = 1936
[1000, 1000, 1000, 500, 500, 500, 500, 500] = 2061
[1000, 1000, 1000, 1000] = 2000
sqrt (1000^2*99 + 500^2) = 9962
sqrt (1000^2*100) = 10000
sqrt (1000^2*99 + 500^2*5) = 10012

I'd say it works pretty well. Improving an average score to a perfect score is worth about the same as adding 4 average scores. IMO doubling your score should be worth more so I'll try to tweak it.

Just need to understand the algoritm . So I found it's called RSS (root-sum square). What does it mean to take the RSS of the scores in this case? Any tips on how it can be tweaked?

I am planning to implement some kind of ranking for my game too. What I intend to do is to google for discussions about chess ranking systems. In my humble opinion, this topic should be pretty well discussed and researched in chess, and so it is the best place to "free ride".

I am planning to implement some kind of ranking for my game too. What I intend to do is to google for discussions about chess ranking systems. In my humble opinion, this topic should be pretty well discussed and researched in chess, and so it is the best place to "free ride".

Chess uses the ELO-rating system (and many other games). It works really well in PvP games with matchmaking - the rating is accurate in reflecting the players relative skill compared to other players. As I've stated in OP though, the ELO-rating system is not really what I'm looking for.

Any tips on how it can be tweaked?

Seeing [font=courier new,courier,monospace]sqrt(x)[/font] is the same as [font=courier new,courier,monospace]pow(x, 1/2)[/font] (i.e. the inverse of [font=courier new,courier,monospace]pow(x,2)[/font]), you can try tweaking that hard-coded 2 with different values, e.g. what you've got now is the same as this, so replace 2.0f with a variable and see what happens:int sum=0;
for( int i=0; i!=count; ++i )
sum += pow( scores, 2.0f );
score = pow( sum, 1/2.0f );I guess larger numbers give more weight to perfectionists, and smaller numbers are closer to a regular average.

[quote name='Opwiz' timestamp='1336810822' post='4939521']
Any tips on how it can be tweaked?

Seeing [font=courier new,courier,monospace]sqrt(x)[/font] is the same as [font=courier new,courier,monospace]pow(x, 1/2)[/font] (i.e. the inverse of [font=courier new,courier,monospace]pow(x,2)[/font]), you can try tweaking that hard-coded 2 with different values, e.g. what you've got now is the same as this, so replace 2.0f with a variable and see what happens:int sum=0;
for( int i=0; i!=count; ++i )
sum += pow( scores, 2.0f );
score = pow( sum, 1/2.0f );I guess larger numbers give more weight to perfectionists, and smaller numbers are closer to a regular average.
[/quote]

Thanks for the suggestion.

As Hodgman said, it can be tweaked by changing the powers involved, e.g. use cubes instead of squares to emphasize perfectionism.

The other thing to consider is that you can choose to use a similar formula for calculating the score for an individual level if you wish, e.g. sum((score(k=1..n)^p) / n) ^ (1/p). The higher p is, the closer it is to max(score(k=1..n)). When p=1 it's an average. The downside being that scores could go down if they do many bad replays. Or you could perhaps make it the sum of their best 3 scores so they can improve their score without beating their best score for a level.

There is still the question of how you translate time on a given level to ranking points.

I would recommend the system used in IPSC competition, where the best competitor gets max points per stage (= level in your game), and the rest get points scaled according to how well they did in comparison; this is robust and there is no need to estimate a theoretical "best" or "par" time.

This conflicts with your requirements in that points can go down. That said, it only happens when someone beats the track record, the negative effect on points is small and gets smaller over time (because the record can't be improved by that much). For example, when track record improves from 82 to 80 seconds on a level with 100 max points, someone whose personal record time was 94 seconds and had 87 ranking points from the level will still have 85 ranking points afterwards.