From the Blizzard formula for Arena points:

X = Team Rating, Y = Arena Points
If X>1500: Y = 2894/(1+259*e^(-0.0025*X))
Else: Y = 0.206*X+99



1st Derivative



2nd Derivative


Take a rating of X=2500, you get Y=1929. If you do this twice, you get ~4000, but you can only hold 5000 at a time so in 2weeks you are maxed nearly. However, if you are X=1500, you get Y=408 so it takes it takes 12 weeks to max. So going from X=1500 to X=2500 saves you 6x time. But from X=2500 to X=3500? You get 2779/week so in two weeks you'll get 5.4K (and if you dont spend at least 400 after first week, you'll lose them) so you get only 1.25x time saved from going from 2500 to 3500. Essentially, players who are looking to optimize their pvp rewards from arena points, but have some other time restriction like pve, irl activities, etc. face harsh devaluations of their time before the 1500 rank and after 3600.

I constructed these graphs using maple 10 (classic template). It's pretty straight-forward. The input is below:

The mathematical expression
piecewise(X<1500,0.206*X+99, 2894/(1+259*exp(-0.0025*X)) );
Expression
plot(Y,X=0..5000);
1st Derivative
plot( diff(Y,X), X=0..5000, style=point);
2nd Derivative
plot( diff(Y,X$2), X=0..5000, style=point);

Derivative curves are in point style because they are not continuous.

At least some sanity for those who rank well (or expect to) and don't feel the need to be in the top 1% - the top what... 15% will do something like 95% as well.

What is the "parity" point? In Magic: The Gathering, everybody starts with 1600. Getting beyond 1900 is near impossible unless you rarely lose and almost NOBODY is below 1400 unless you lose every game. Obviously I do not expect this system to be the same - but these numbers, while useful to give us a conceptual view of how they intend the arenas to work, are meaningless without some number data. If everybody starts at 0 for example, (is that even possible in a modified ELP system?) then the players who manage to get 4000 would be in the top .000001 percent vs those who are able to get say 3000 and are in the top .0001 percent.

All of this seems unlikely of course, it seems like they are rewarding the average players with 80-90% or more of the rewards of the top 5% but man oh man if you lose 10 games in a week talk about never being able to get arena gear.

I would argue that most hardcore teams are only going to play 10 matches a week of actual ranked games. Why chance losing? You don't even get honor points. And yes, the low end is going to be harshly devalued but the high end this is a boon. It means that you dont have to beat ass and take names all week long for 16 hours a week to get the leet rewards. 10 solid games, assuming you win what? 6? 7? of them will be enough to get you gear 85% as fast as teams winning 10/10 every week.

The compensation for winning 10/10 each week for a season? You get armored flying mounts! Ooooo exact same as regular flying mounts BUT ARMORED. Holy shit in a handbasket. Hold me back.

So...lets say you got stuck on a noob sucky team and went 0/10, would that get you anywhere at all?

double post

Not necessarily. 10/10 means you are placed against teams of similar win rates, an implied cost not accounted for. So being placed in the top bracket means your win rate will assumedly go down. So it might be optimal in the short-run, but in the long-run you might be able to maintain a higher average win rate with less effort by throwing a game or two depending on the variance of penalties associated with different tiers.

Then again, if you're the assured top-spot and average of 100%, that's obviously the best scenario. =p

You're assuming ratings of 3000+ are even realistically possible. Given unlimited opponents, unlimited games, always winning every game, and always playing games against people higher rating than you, sure. But eventually if your rating is that high, everyone elses rating is below you.

I don't you will see teams with ratings much higher than 2500. Unless a team wanted to play dozens and dozens of games a week AND got paired against other teams doing the same thing, no one is going to get up that high. So the fact that the returns diminish at that point is just academic.

Right - the unknown variable here is what do people start off with? How quickly are they able to gain or lose rank? In theory, 30% or more can attain "high levels" of advancement. In practice this depends on how they seed the scale. In Magic: The Gathering and in Chess (both ELP), attaining much more than an average rank is well - non average and thus quite hard.

We will have to see how ELP like this system remains I suppose.

speculations like this are only moderately useful unless you know something about the amount of time/successfull matches needed to achieve a rating of X=2500.

Thinking a fixed number of teams with fixed skill, you will arrive at an equally fixed ranking of those teams after some time, depending on skill (well, and gear). In such a state, all teams would get something close to 50% wins. You will know that you are playing above your skill/gear level when you lose more matches than you win, and be downranked appropriately if the system works, and the other way round.

Assuming Blizzard gets a way of linking that skill/gear (meaning the combination of both your team is playing at) level to the right amount X of Team Rating, there's not really something you can do to increase that rating, instead of getting better skill or better gear, thus winning more matches against other groups that remained at that level, effectively moving up the ladder. If you don't increase your skill or gear, playing more or playing less doesn't really mean anything, random win/loss streaks aside.

Unless we know more about how X is arrived at, and if it behaves nicely dependant on skill, or can be bullshitted with by doing stuff like losing for a while to sink in rank to get worse opponents to win more afterwards, resulting in a net gain of X, we cannot really find any optimizing strategies. If some of this is in fact known to the world and I overlooked it, I apologize and will be happy for a hint ;)

I would assume that Blizzard wants the distribution of points to be as close to a bell shape as possible (so having most of the population with a similar amount of points in the middle somewhere). This would mean most people would be at a roughly equal level of power (gear acquisition from PvP).

Having drop offs in reward to effort ratio at the lower end and upper end would help reinforce this bell curve distribution.

P.S. Hi Xzin! How's your attempts to 40-box a raid going?

I wrote this up on our guild forums. It's pretty helpful to see what you want to average per week to gear out.

The cost to buy arena items: (2handers and bows cost 2 items)
Items Cost
1 1125
2 2625
3 4500
4 6375
5 8250
6 10125
7 12000
8 13875
9 15750
10 17625
11 19500
12 21375
13 23250
14 25125
15 27000
16 28875
17 30750
18 32625

Total Arena Points earned over a Season(12 weeks)
Rating 5vs5 3vs3 2vs2
0 1188 713 475
100 1435 861 574
200 1682 1009 673
300 1930 1158 772
400 2177 1306 871
500 2424 1454 970
600 2671 1603 1068
700 2918 1751 1167
800 3166 1899 1266
900 3413 2048 1365
1000 3660 2196 1464
1100 3907 2344 1563
1200 4154 2493 1662
1300 4402 2641 1761
1400 4649 2789 1860
1500 4896 2938 1958
1600 6046 3628 2418
1700 7398 4439 2959
1800 8957 5374 3583
1900 10716 6430 4286
2000 12651 7590 5060
2100 14721 8832 5888
2200 16871 10122 6748
2300 19036 11422 7614
2400 21150 12690 8460
2500 23152 13891 9261
2600 24995 14997 9998
2700 26647 15988 10659
2800 28093 16856 11237
2900 29333 17600 11733
3000 30377 18226 12151

The number of games you play will only help you get to you true strength faster. After that, every game should have an expected value of 0. Beyond maybe the first week, there is no reason to play more than 10 games.

Throwing games cannot help in a real ELO system, assuming you get paired by your actual rating, which there is no reason not to do. The best that could happen is that you get an easier pairing, win, and get back up to your old rating, where you are in the same situation.

You can't start at 0, since it's zero sum, and half the people would then have negative ratings. Most systems are centered at 1600, that I know of.

The problem with blizzards implementation of the ELO system is that the pairings aren't random. You are intentionally paired with those with similar rating as you. Now the first week will be the same as a normal ELO system, second week less so and maybe up to the third week it will still be close to random pairings. But after that, you will start going up against teams of similar skill as yours and your win lose ratio will be about 50/50 making it very hard to get your rating up to your true strength.

Blizzard seems to have condensed all the highest skilled teams to a rating much closer together than they should be in a normal ELO system. But in doing this they can kind of cap the amount of points the top teams can get. Figuring out that cap should be fun for the next few months.

I am not seeing any problem, all ELO systems involve playing people with similar ratings. When you are winning 50% of matches, that is your correct rating. That's the whole point of the system.

Also early on teams with equal ratings won't necessarily even be close in skill. It will take a while for the great teams to filter out those who have been lucky, or faced mostly relatively weak teams thus far.

marketa - is that table of arena points earned per person or team? It would seem per person, otherwise you are earning the same points in every bracket.

Forgive a guy who hasn't been in a calc course for nearly 7 years... can someone simplify all the gibberish and tell me what the optimal point of effort reward is? :(

This is my first post on this forums but I've lurked in the shadows for a long time so don't rip into me too hard. I really don't know why I'd pick this topic to make my first post but here it goes.

I used to play in competitive ladder systems (online) a few years ago for a few different games. The game I stated with was chess (of course since it was the game that created this kind of rating system - as far as I know) but after a while I just couldn't put up with the 2-3 minute wait some people felt were needed for every move. I maintained a rating of 2500-2600 for about 3 months before giving up on it. I then moved onto Canasta and Dominoes and while those games were not as competitive at the high end, a high rating was much harder to achieve (without cheating the system) because a lot more people with low rating were playing.

Now in those games you could choose who you played. If you had a few challangers, you had to play the one closest to your rank. I'm not sure how Blizzard will do this, but if it will be up to the team to choose who they play, then a lot of drama will be created. People will try to cheat the system and make sure they secure top spots for themselves or their friends.

If however, Blizzard just sets ranges (of ratings) that teams in the queue must face, then people will play only the required amount in order to maintain rank and avoid losses.

Either way, I see a lot of drama serverwide, faction wide as well as battlegroup wide. Hopefully it won't be that bad but it's human nature to figure out the weaknesses of a system and find ways to get yourself to the top.

I find it amazing that people maintain that they PvP for fun when over the past week I've had many "pre-made" teams AFK out of the guild team we had going in AB. I know I want the honor for those items but I love those close 2000-1990 games (we actually had one of those).

Ok. After spending all night learning the math behind the ratings and how its updated after each match, I have figured out the minimum true strength you need to get all the arena gear which includes a 2-hander, 5pc set, and ranged. First of all your true strength is the absolute skill level of your team. Since thats an unknown, the ELO system tries to infer it from your wins/loses. A few assumtions I made.

1: Every match you play is against someone whos true strength is their current rating. Unlikely, I know, but on average it should be correct.

2: Your win/lose ratio vs a team of different true strength is a fraction and used to determine your rating. This means I came up with several fractions of ratings and used those fractions to determine the points awarded. This again is based on averages and your results may vary.

3: A season is 13 weeks and you played 130 games during that time.


Heres my results of my calculations:

You need a true strength of 2226 to get everything as a hunter. (the xbow costs 2x as much as all other ranged weapons).
You need a true strength of 2109 to get everything as any other class.
You need a true strength of 2600 to get everything as a hunter and end up with 5k points at the end of the season.(5k is the cap I think)

With 1500 rating the entire season you can buy a 2 hander and the cheapest armor piece.




Things to note:

With 2109 true strength, you reached 2000 rating at week 5. The took the rest of the season to gain 100 more. With 2226 true strength it took 6 weeks to get to 2125 rating and the rest of the season to get 100 more. The last 2 weeks you were only gaining 0.1 - 0.2 rating per game.

Ok I'm sorry, what do you mean by "strength", do you mean ratings/points?

If they weren't possible, why choose a curve of this shape? Up to around 3000 the second part of the function can be approximated by a line, so if you couldn't ever get to the curved part of the curve, why not just use that line?

Also the only ranged weapon I see on thott beta is the crossbow, are there others, perhaps a wand?

No. True strength is your skill that the ELO system tries to figure out by assigning you a rating and changing it depending on your wins and losses. You will notice taht at the beggining of a season your rating will change alot and by the end it will stop changing as much as it gets closer to figuring out your true strength.

Theres a wand, relic, libram, totem, and thrown thats available for purchase for 1875 arena points. Thats half as much as the hunters xbow which means hunters need on average 100 higher rating to get the equivilent equipment. :(




Anyways, after posting my last post I started to figure out the diferentials, integrals, and probobility densities of the curve that Blizzard has predicted and implemented.

First we need a logarthmic function with a min of 0 and a max of 1 with a point of inflection at 1500. I'll save you the rouble of figuring that out and give you this:

P(x) = 1/( 1 + e^(-(1500-x)/400))

P(x) tells you the probability of getting x rating. With x = 2109, you get .82 which means that 18% of the teams should get 2109 rating which has the benifit of allowing them to get all the items. In other words, using the above formula, you can determine how many people are better or worse than you.