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Hero battle (PvP) ratings

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OP

by

Firefly

7 months ago


Listen up! I've created an initial algorithm for Hero Battle (PvP) rankings. It's an iteratively balanced weighted graph that should give a truly mathematically correct score for each player. In theory.

How does everyone feel about the top 10 distribution under this algorithm:

1. obi2002, score: 337, targets: 431, nemeses: 169
https://angeldu.st/en/players/14972/obi2002

2. Firefly, score: 218, targets: 242, nemeses: 227
https://angeldu.st/en/players/1652/Firefly

3. Alex makarov, score: 196, targets: 204, nemeses: 86
https://angeldu.st/en/players/150488/Alex+makarov

4. space is green, score: 154, targets: 172, nemeses: 102
https://angeldu.st/en/players/5/space+is+green

5. Tailsmancion, score: 109, targets: 128, nemeses: 87
https://angeldu.st/en/players/247785/Tailsmancion

6. LIL XXARDD, score: 79, targets: 256, nemeses: 45
https://angeldu.st/en/players/226121/LIL+XXARDD

7. ExcaliburGaming, score: 56, targets: 64, nemeses: 44
https://angeldu.st/en/players/266746/ExcaliburGaming

8. WertuXAN, score: 48, targets: 289, nemeses: 74
https://angeldu.st/en/players/107744/WertuXAN

9. trieuthien, score: 43, targets: 44, nemeses: 57
https://angeldu.st/en/players/5346/trieuthien

10. Pandegiri, score: 34, targets: 50, nemeses: 17
https://angeldu.st/en/players/229850/Pandegiri

You can see that the total score doesn't directly depend on any statistic, but is based both on your own performance as well as that of your targets. For instance, LIL XXARDD has a high target count, but those are all low-value empty accounts.


# 2

by

Hummm

7 months ago


I list that I don't even have a rank in ... that's quite an elaborate algorithm ;)


# 3

by

Firefly

7 months ago


Hey @Hummm :)! Turns out you're actually in 11th place:

11. Hummm, score: 34, targets: 238, nemeses: 37
https://angeldu.st/en/players/141192/Hummm

Your score is just slightly lower than Pandegiri, I rounded everything to the nearest integer, but internally it's stored with a few decimal places.


# 4

by

obi2002

7 months ago


Damn, turns out Alex isn't 2nd! Bravo Firefly!

Question 1: Since I am the highest value target, people get more points than from anyone else from killing me, yes? And I can't kill myself...therefore I cannot get the max possible score from one kill like others. I am at a disadvantage, right?

I have to go for you Firefly haha

Question 2: Does being exhusted decrease the score?


# 5

by

Firefly

7 months ago


@obi: the whole algorithm is new and I'm not sure how it works in practice. My first objective was to find a theoretically sound idea and figure out what kind of ranking it gave. The result is this list.

I was also surprised that Alex isn't in 2nd place. Looking closer, he's got a very impressive T/N-ratio, but I have almost 40 more 'targets' which pushes me a bit higher. I think Alex needs only 20 more targets to surpass my score value. So exhausting others is rewarded, as well as playing against other good players.

Answers: 1. I think you're definitely right that you don't get 'max score' for a kill since you're the top dog right now. The fairness here is that everyone is objectively worse than you so you can easily rack up your score :D

2. The algorithm is a directed graph of all exhaustions. It spreads out your score value to everyone who shot you. Everyone's scores are continuously rebalanced based on everyone's performance. So you don't really lose or win points in real-time, but you get more or less points based on what everyone has done. This also means that your score can increase or decrease based on what others have been doing, even if you didn't play yourself during that time.

The whole thing is as much of a surprise and discovery for me as it is for everyone here. I think the initial score list is very representative of the actual performance of players. I have no idea how the ranking dynamically evolves over time. That's something we'll have to see once it goes live. The first step is discussing this initial list—does it seem plausible?


# 6

by

obi2002

7 months ago


I think you should do some extensive pvp next stream(if there are enough people), and compare the score change. It might reveal more. Plus I won't be able to make it...so I wonder how much score I will gain or lose.

Having it fluent/dynamic like this is really interesting, makes it a completely different point system in comparison to the coin leaderboard.


# 7

by

Firefly

7 months ago


I thought it over a bit more. The 'score' is a balanced result (or sum) of what a player has achieved compared to others and gives a decent rating system I think.

You don't score 'points' interactively, but you can influence the entire point distribution of all players to your advantage by shooting someone. It does mean that you push the score of your nemeses up as you become a higher value target yourself.

Getting shot means you spread some more of your points back to your nemesis who in turn spreads it back to his nemeses and so on. This could also mean that you suddenly rate relatively higher to others if you also shot your nemesis in the past as you get more points for getting shot by someone who you also shot. It's score-ception from here on out.

Another ranking system would be 'score' divided by 'nemeses'. That is actually the indication of how many points you'd get for shooting someone. Kind of like the 'high value target' list.

The question then becomes: is the number one player the one who shot many equally skilled players, or is the number one player the one who has the highest value, disregarding the actual exhaustion counts?


# 8

by

obi2002

7 months ago


Thought: If I have a bunch of exhuastions on every person below me(or atleast more than they have of me), does that mean they can never go above me? Unless they exhuast me enough times to pull score from me? Beacouse, if they try and get more score by EX-ing other people...it will only bring my score up further.

For example: You(Firefly) Have EX-ed me 23 times, and I EX-ed you 33 times...if you get more score, it brings my score up by a 23/33 times the ammout of score I pull from you. If i understand how it works correctly, you're in a way getting score for me...?

Another thought: Hummm has the safest and most stable/fixated score...the people he EX-ed are 90% O T 0 N alt accounts. These accounts won't ever in any way change their score, so Hummm's score won't change?

Thought 3: If score is fluent-dependent on what other people do, it's a team effort...more score for you means more score for me? The smart thing to do, is going for everyone playing and get EX all around, so if they get more EX you pull their score.


# 9

by

Firefly

7 months ago


This is going to be math, possibly the clearest way to define what I'm doing so we can discuss more in-depth. Also, EX = exhausted.

Your score = Sum of ( Target score × Your EX% on Target )

So your own score is the sum/total of all your targets' scores weighted by the number of EX'es you got on them compared to their total EX'eds.

For calculating your score, it seemingly doesn't matter how many times you got EX'ed yourself (it does, but forget it for now). Consider this example:

Target A, score: 100, EX'ed in total: 50×, You EX'ed them: 10×
Target B, score: 300, EX'ed in total: 10×, You EX'ed them: 4×

Your own score would become:

From A: ( 10 / 50 ) × 100 = 20
From B: ( 4 / 10 ) × 300 = 120
Your score: 20 + 120 = 140

Ignore how A and B got their scores in the first place. You can see that even though you EX'ed A 10 times, you only get 20 points in total, because other players have EX'ed A a lot, too and A isn't worth much to begin with.

However, your 4 EX'es on B are worth a lot since B has a high score *and* you got 40% of their total EX'ed count.

And now you ask: but how do you get these score values in the first place? That's why the algorithm is recursive / iterative. After enough iterations averaging old and new score values, the entire distribution settles. So in the end result the above formula is always correct for all accounts and EX'es.

Here we find ourselves with (I think) a mathematically and theoretically correct and sound way of ranking players based on their all-time performance. I haven't run any tests however on what single EX'es do in the system.

On paper it'll result in another perfectly balanced and fair ranking. In practice it might mean that many players see their score (and ranking) shift around even though they didn't even play. Is this fair? I think it is. Feel free to discuss the mathematical model above or this interpretation.


# 10

by

obi2002

7 months ago


I think it is very fair and interestingly cool.

I'll post what I'll find out from the maths above in a bit :)


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