A new skill level

Some people complain about the removal of the skill level. That skill level was malfunctioning for a lot of time, was quite complicated, and wasn't very accurate with specific kinds of players. But people want it back. It was hinted that if some good, reliable stat was found relevant, it could be added to the profiles. So I open this thread to discuss potential ideas for a new stat which reflects how good a player is.

Most relevant is the rating for me. But it is supposed to stay secret. Points earned per games played would be also interesting. But then one can pretty easily calculate the rating knowing the number of games played.

I have an idea, but it may have needed to have been implemented in the code from the start of the site. It is a decimal system of 1000 becoming 1.000 for simplicity, where the program would start every player at 1000 (and only display it as 1). 2 points (0.002) are added for every player you beat with more points. 0 added for every player you beat with less points. 1 point deducted for every player you lose to with less points (this should account for suicides, favouritism, buddies, revenge attacks, rank attacks and crazy lucky dice). 0 deducted for those you lose to with more points. The program should only ever display the integer. So to move up to Skill Level 2 you would have to beat 500 players with more points than you (at that time). That's 1.000 + (500 X 0.002) = 2.000 To go all the way down to 0, you'd have to lose to 1000 players with less points than you (virtually impossible unless you are an awful player). The fact that you'd have to beat 500 good players for a skill point means you would have to play more multiplayer games which prove skill more than 2 player games and 2p Players would find it very difficult to increase this number, whereas anyone who won 1/3 of 500 4p+ games would have (probably) beaten 500+ players with more points than them and earned a skill point. It might then be very rare to see anyone on skill 7 or 8 unless they have been here winning for a very long time. Seeing someone on skill level 2 would be a warning of what you are up against. It appears to not move for a very long time, possibly years, but that surely is the point of true skill, the ability to win over a wide variety of games against a wide variety of players. Once you hit the top of the skill ladder, you won't necessarily be the player with most points and can still increase the rating, because as we know a lot of Same Time players and 2p Players have high points. Unfortunately, I can't think of a way to include players that have already played 1000's of games and already ranked up.

I believe that that rating would be too slow. Optimally you should be able to reach 100 in a few months on whatever thing we figure out or otherwise many players won't be able to even see changes!

Did it spring to mind that if we want a good and effective way to measure someones skill and make it public, then that is pretty much the same as making your rating publicely visible? Otherwise the best one would be the number of games you won / number of games played I guess.

Yes that's what I said. But it's the same thing of showing your rating, you just need to multiply.

Yes of course. I was suggesting something which can be adapted in any way to take into account multiplayer games. 1 point, 10 points or 100 points, whatever way suits. e.g. a SameTime Player can notch up 20 wins per day against low rankers and gain skill points... something I think that should be factored at lesser increments. Anyway, I dare say that there are more pressing matters than this, so I just chipped in, but probably won't involve myself in this discussion.

[quote=Matty]Otherwise the best one would be the number of games you won / number of games played I guess.[/quote] This needs to be normalised against the amount of players you play with. So for [i]k = 2..9[/i] you calculate the win percentage over all games with [i]k[/i] players. Then we calculate the difference with the expected number of games to win. So for 2 player that would be 50%. If you win 7 out of 10 games, that means you get +20%. This probably still has to be normalised again for variance, but you get the idea. The problem is that this number does not increase over time nor takes into account the skill of your opponents. Matty's point is valid though: why don't we just make the rating public instead if people are so inclined to have a measure for skill?

Oh wait sorry. I did read Matty's message wrong, I thought he was saying points earned / games played, but actually he talked about games won / games played. @Cireon, I agree with your "k" parameter in that case. It's absolutely required. Even more simple: you gain P points every time you win a game with P players. I don't mind if it is not a very good measure because it doesn't keep into account the rating of the players you beat. People just want a second rate that is quite relevant and possibly something that always grows, so although they get frustration for not ranking up at least they are happy to see their "winning points" growing. I think it is the reason why people liked the skill level, in practice was a rate that always growth, the more you play the more it raises.

Or also Aero's method, but maybe 1000 points required to move up 1 level are a lot. Or maybe not, I don't know. I can propose a small change like this: +2 for beating higher than you player [b][u]+1[/u][/b] for beating lower than you player -0 for losing higher player -1 for losing lower player

[url=https://youtu.be/s1TcnQxV4BE?t=7]I have come here to talk maths and chew bubblegum[/url] First my thoughts: 1) I'm entirely opposed to having a number that perpetually increases if you call it skill level. Maybe call it e-peen? Or just look at number of games played go up. 2) I agree with Matty that having a number that correlates to skill is what rating tries to do 3) But I disagree that rating measures skill. First of all, skill at what kind of game? I'm pretty sure we wouldn't be able to agree on what skill IS, let alone come up with an algorithm that measures it. MATHS! The best number I can think of that would correlate with skill level is the percentage of wins, normalised to x number of player games. 2 player games would make the most intuitive sense. So the number would be: <Cool Number Name> = Percentage win / (Average number of players per game / 2) Where <Percentage win> = games won / total wins Here are some things this number has going for it: 1) It's intuitive. A person who wins half the time at duels will have a 50% number. Likewise a person who wins a quarter of the times in 4p games, will also have a 50% number. 50% is what you'd expect. Average. When you win more than your fair share of games, the % will go up. 2) It doesn't suffer from the caveats of rating of having to avoid most of the player base. Many high-ranked players play only with other high ranked players, knowing that playing with low rated players will end up hurting their rank. For this number, victories against anyone count. However, this number doesn't differentiate between wins against higher rated or lower rated individuals. So to achieve that, here is a new number: <Improved Rating> = <Cool New Number> + (or minus) x Where x would be a small number (not sure what would work, would need to run some numbers - I'd guess it it would be in the order of .01%? Just a wild guess though) that would work like rating currently does. When you defeat someone with higher (improved) rating, you get more of it, when you defeat someone with lower improved rating you get less of it. Thoughts?

Interesting Machiavelli...

I like it. I would have an objective X value taking into account just the games played, and a Y value which takes into account the "game quality", ie how well rated/skilled your opponents are normally. The difference is that I would give a decent weight to that Y value, so a player with X=50% against newbs is ranked visibly lower than a player with X=50% against high ranked players, weighing X by 2/3 and Y by 1/3 for example. The good thing though about the old skill level is that you could always increase it by winning against new players. I would like to make the skill value unlimited and take into account this fact too. That is different of having a skill level that only goes up, though, because that would still use tallies.

@Machiavelli: You are very vague in the last part of your post. And that's exactly the part that deals with my problem with your rating. Winning a game against newbies is quite easy (provided none of them suicides). Winning a game against experienced players is very hard. There should be a big difference there. There is another problem with your rating as well - the 'average number of players per game' thing. Let's say I play 10 two-player games and 10 nine-player games. Now if I win all the 9-player games and lose all 2-player games, should I get the same rating as someone that won all the 2-player games and lost all the 9-player games?

[quote=Matty]There is another problem with your rating as well - the 'average number of players per game' thing. Let's say I play 10 two-player games and 10 nine-player games. Now if I win all the 9-player games and lose all 2-player games, should I get the same rating as someone that won all the 2-player games and lost all the 9-player games?[/quote] You’re right here. I was trying to come up with a hand-wavy number which would work with the publicly available data. This could work as a potential quick and dirty replacement for the old skill level, but falls short of being able to replace the rating in the form I presented it. [quote=Matty]@Machiavelli: You are very vague in the last part of your post. And that's exactly the part that deals with my problem with your rating. Winning a game against newbies is quite easy (provided none of them suicides). Winning a game against experienced players is very hard. There should be a big difference there. [/quote] You’re absolutely right. So I’ve made a new stab at the issue, this time with the more ambitious goal to come up with an improved rating system, without the vagueness. Another post incoming...