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Mentioned option by quarague in comments
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Zizy Archer
Zizy Archer
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You can use the same 1/x function you are using to calculate your score in a level to weigh score of your levels. You get 100% for your best level, then 50% for the next one and so on. This means that starting your 100th level will only net you 1/100 points you could get - so, you don't lose points no matter how bad you did, but you barely gain any new ones even if you are as high as in your other levels. Once you add levels, yup, score will keep increasing, but slowly. First 100 levels will give you 5.2x points (of a single level) while levels 101-400 - 3 times as many - will only improve your score by 1.4x - 1/3 of the first 100 levels.

Note that this combination of functions (scoring per level and weighing level score) means that rank 2 in 3 levels is still worse than rank 1 in one level - meaning if you want to be the best on the main leaderboard, getting to rank 1 in some levels matters the most - top players are going to be those that manage to be the best in some levels, even if they compete in (and completed) only 10 levels out of say 500.

Also, aA side note: I wouldn't make a cutoff for level points at top 100 players (unless you have some specific reason for that) - I would simply calculate score as 1/x as you are already doing, without any cutoff - yeah, your poor run that gives you only rank 20000 for that level only nets you 0.5 points, but that's still an improvement to your score, making you feel your level run wasn't a complete waste of time. Additionally, this should help for retention of non-top players. Yeah, you are fighting for spot around 1000 instead of top players battling for the top ones, but you still get a feeling of improvement as you climb up the ranks. When paired with 1/x function for level scoring, getting those 0.5 points, divided by say 100, means you don't actually improve your score meaningfully. But you still don't regress by trying new levels.

As mentioned by @quarague in comment, you can also change proposed function from 1/x (= x^-1) to something steeper or slower - steeper means fewer levels matter, slower means more matter. I believe sensible range for the exponent is between 0 and -2. 0 means that all levels matter the same, so you reward griding of all levels. -2 means the best level is worth more than all the rest combined and you shouldn't really bother with more than few. I believe you should probably try -1 or -1/2 first.

You can use the same 1/x function you are using to calculate your score in a level to weigh score of your levels. You get 100% for your best level, then 50% for the next one and so on. This means that starting your 100th level will only net you 1/100 points you could get - so, you don't lose points no matter how bad you did, but you barely gain any new ones even if you are as high as in your other levels. Once you add levels, yup, score will keep increasing, but slowly. First 100 levels will give you 5.2x points (of a single level) while levels 101-400 - 3 times as many - will only improve your score by 1.4x - 1/3 of the first 100 levels.

Note that this combination of functions (scoring per level and weighing level score) means that rank 2 in 3 levels is still worse than rank 1 in one level - meaning if you want to be the best on the main leaderboard, getting to rank 1 in some levels matters the most - top players are going to be those that manage to be the best in some levels, even if they compete in (and completed) only 10 levels out of say 500.

Also, a side note: I wouldn't make a cutoff for level points at top 100 players (unless you have some specific reason for that) - I would simply calculate score as 1/x as you are already doing, without any cutoff - yeah, your poor run that gives you only rank 20000 for that level only nets you 0.5 points, but that's still an improvement to your score, making you feel your level run wasn't a complete waste of time. Additionally, this should help for retention of non-top players. Yeah, you are fighting for spot around 1000 instead of top players battling for the top ones, but you still get a feeling of improvement as you climb up the ranks. When paired with 1/x function for level scoring, getting those 0.5 points, divided by say 100, means you don't actually improve your score meaningfully. But you still don't regress by trying new levels.

You can use the same 1/x function you are using to calculate your score in a level to weigh score of your levels. You get 100% for your best level, then 50% for the next one and so on. This means that starting your 100th level will only net you 1/100 points you could get - so, you don't lose points no matter how bad you did, but you barely gain any new ones even if you are as high as in your other levels. Once you add levels, yup, score will keep increasing, but slowly. First 100 levels will give you 5.2x points (of a single level) while levels 101-400 - 3 times as many - will only improve your score by 1.4x - 1/3 of the first 100 levels.

Note that this combination of functions (scoring per level and weighing level score) means that rank 2 in 3 levels is still worse than rank 1 in one level - meaning if you want to be the best on the main leaderboard, getting to rank 1 in some levels matters the most - top players are going to be those that manage to be the best in some levels, even if they compete in (and completed) only 10 levels out of say 500.

A side note: I wouldn't make a cutoff for level points at top 100 players (unless you have some specific reason for that) - I would simply calculate score as 1/x as you are already doing, without any cutoff - yeah, your poor run that gives you only rank 20000 for that level only nets you 0.5 points, but that's still an improvement to your score, making you feel your level run wasn't a complete waste of time. Additionally, this should help for retention of non-top players. Yeah, you are fighting for spot around 1000 instead of top players battling for the top ones, but you still get a feeling of improvement as you climb up the ranks. When paired with 1/x function for level scoring, getting those 0.5 points, divided by say 100, means you don't actually improve your score meaningfully. But you still don't regress by trying new levels.

As mentioned by @quarague in comment, you can also change proposed function from 1/x (= x^-1) to something steeper or slower - steeper means fewer levels matter, slower means more matter. I believe sensible range for the exponent is between 0 and -2. 0 means that all levels matter the same, so you reward griding of all levels. -2 means the best level is worth more than all the rest combined and you shouldn't really bother with more than few. I believe you should probably try -1 or -1/2 first.

Source Link
Zizy Archer
Zizy Archer
  • 459
  • 2
  • 5

You can use the same 1/x function you are using to calculate your score in a level to weigh score of your levels. You get 100% for your best level, then 50% for the next one and so on. This means that starting your 100th level will only net you 1/100 points you could get - so, you don't lose points no matter how bad you did, but you barely gain any new ones even if you are as high as in your other levels. Once you add levels, yup, score will keep increasing, but slowly. First 100 levels will give you 5.2x points (of a single level) while levels 101-400 - 3 times as many - will only improve your score by 1.4x - 1/3 of the first 100 levels.

Note that this combination of functions (scoring per level and weighing level score) means that rank 2 in 3 levels is still worse than rank 1 in one level - meaning if you want to be the best on the main leaderboard, getting to rank 1 in some levels matters the most - top players are going to be those that manage to be the best in some levels, even if they compete in (and completed) only 10 levels out of say 500.

Also, a side note: I wouldn't make a cutoff for level points at top 100 players (unless you have some specific reason for that) - I would simply calculate score as 1/x as you are already doing, without any cutoff - yeah, your poor run that gives you only rank 20000 for that level only nets you 0.5 points, but that's still an improvement to your score, making you feel your level run wasn't a complete waste of time. Additionally, this should help for retention of non-top players. Yeah, you are fighting for spot around 1000 instead of top players battling for the top ones, but you still get a feeling of improvement as you climb up the ranks. When paired with 1/x function for level scoring, getting those 0.5 points, divided by say 100, means you don't actually improve your score meaningfully. But you still don't regress by trying new levels.