If we're gonna revise the ladder, this is where its going to happen.

p=current rank
p2 = other player's rank
p -= 1/2p2

Look at that simplicity. Look at it STARE AT IT. ROLL IT OVER IN YOUR BRAIN. DO IT. NOW.

What's wrong? well, it goes negative. If you are the 8th player, and you beat someone who is 17 places below you, that somehow puts you in 1st place? So clearly, further revision is needed. So... um... why don't we just use that for positive? Let's come up with a negative now. If you beat someone who is below you:

0 1 2 3 4 5 6 7 8 9 10
^ ^
Your Rank Their Rank

p += -p2 + p

So what does this do? Well, in example above, you are player 3 and they are 8. So, replacing all the variables in the equation...

3 += -8 + 3

Thus, you would be in first place. That really doesn't seem legit, however. Look at it on a bigger scale...

238 += -300 + 238

That would take you down 62 places. Granted, that's not too bad... so that's when we start using fractions! Yes, Fractions! (fractions speak louder than words)

bad at writing with mouse. p(mod) = Pmod = -Popp/4 + Pold/4
Let's try this:
Your rank: 238
Their Rank: 300

238 += 1/4(-300) + 1/4(238)

so that will make our new place:

222.

the quarter system looks good- however, it might be necessary to replace the 1/4 with 1/p or something. tell me what you guys think. But just to make sure this crap works, lets do another example.


Your Rank = 600. Their Rank = 200. That's pretty damn good for you.

600 -= 1/4(-200) + 1/4(600)

Pmod = 100, Pold-Pmod = 100

New Rank: 500.

What's the problem with this, you ask?

It doesn't account for if you are in 10th place, and you beat someone in 600th, you shouldn't be in first.

So, two equations are necessary- one if you beat someone below you, one if you beat someone higher than you.

I have created a small console program that you can find here that will allow you to input two values and return them.

@squishypon3 @igncom1 @cptconundrum @KillerKiwiJuice I think you guys will have some fun with this

What's wrong with the current system? =o

it makes me sad

Well why's that? It is a formal ranking system after all... Glicko was it called? Bah I can't remember, I have a terrible memory. x3

You made a mistake, logging a larger/lower skilled number for the opponent's rank will increase your rank tremendously in the program.

Err wait I guess that's what you're trying to show. That can't be correct.

I was thinking that if the rank is lower than you, it would get how far the other person is from lat place and do something with that.

Something else- in the program, if you are in second place, no matter how many times you face the king, you will never become the king. I will have to change that.

Well, Glick doesn't work on ranks. It uses a number to depict the estimated strength of the player. For example 1560,3 or 1488,1 (the initial value is 1500 in Glicko 2). Ranks a simply derived by sorting according to the strength estimate.

So if you look at the first and second player, the rank itself does not tell you how far they are away from each other in terms of estimated strength. And this is part of the reason for the situation, where the second player beats the first, but the rank does not change.

http://www.glicko.net/glicko/glicko2.pdf

Well, honestly, if you beat someone 1 rank above you, their place should be assumed... that's just an example of humans forgetting to give a thoughtless machine common sense.

I don't think so, it's not because you beat someone that you are necessarily better than that person. It could be that your way of playing counters theirs quite well, or that you just got lucky in some way. I think the current system (or at least it should) takes into account all the people you have beaten, and those who have beaten you. Would it be fair to take someone's place because you beat them this one time, when they have overall defeated players of a higher skill level than the ones you have defeated?

You can theoretically have a situation where, between three players, there's never a situation where one player is better than the other two.

http://en.wikipedia.org/wiki/Voting_paradox

Throw in a few thousand players and it's guaranteed to happen. I don't know why we have to get so scientific about coming up with math heavy ranking systems, when we're really just trying to feed someone's ego.

Well, in the current ranking system math is WAAAAAAAAAAAAY more complex than this.

Complex math is needed because statistics takes into account your chance of winning and your skill level to calculate your loss/winning points. It further allows intelligent matchmaking. You have to add some statistical values to your calculation, like rating, confidence of rating and winning chance otherwise it is inferior to the current system.

I have a question. If I lose to someone who is above me (closer to 1st place) does that negatively affect my rank?

Look into how the glicko rating system works. Once you have done that you will have a better understanding on why the current rating system is good.

To answer your question you will always lose points if you lose. You will not lose many points if they are much higher on the ladder than you. They will also not gain many points by beating someone much lower than them.

Err... umm... what's with these curly braces?

Ugh. I would guess that's normal braces. He just used curly ones to distinguish the term of losing from the others. Well, or he isn't used to LaTeX
Later on in the example (page 5) the braces are normal again.

Braces? I've never heard them called such a thing, normally brackets. Admittedly I'm from the US, though I have lived in Britain... Is this the norm there? Haven't heard it before.

Brackets are [] and curly braces are {} to me.

I thought {} were only used to make weird faces......