SC2 Ladder Analysis: Part 2 - Page 4

On August 08 2010 15:32 brad drac wrote:

Do we have evidence for this? Isn't it possible that a player is displayed favoured if his MMR is greater than your own minus a factor based on sigma? Or something along those lines. I don't really see how you could directly compare displayed rating to MMR considering displayed ratings are division independent, not to mention league independent, while MMR is an absolute measure of a player's success in the system.

Therefore, a corollary here is that when determining rating increase, the hidden threshold value for your league is added to your displayed rating, then compared to your opponent’s MMR, for purposes of computing the gain/loss to your displayed rating.

Example: ExcaliburZ and I play a game. His MMR: 2600, sigma: 100, displayed rating: 300. My MMR: 2500, sigma: 50, rating: 150. Diamond’s MMR threshold: 2300. Excal wins because he rules. What happens?
- His MMR will increase
- My MMR will decrease
- Both of our sigmas will decrease
- His rating will increase. How? By comparing my MMR (2500) against his rating + diamond’s MMR threshold: 300 + 2300 = 2600, his gain is thus off 2600 vs my MMR of 2500
- My rating will decrease. In the same way: his MMR: 2600. My rating + threshold: 150 + 2300. Thus I lose points proportionally

On August 08 2010 15:47 Excalibur_Z wrote:
[snip]
For the record, though, displayed ratings are not division independent -- they're comparable across all divisions in a league because everyone in that league is playing against (mostly) the same player pool. I'm going to be careful about taking this too far because there's little evidence to support it, but it's an idea to throw out there that makes rating values translatable across leagues.

On August 08 2010 21:08 ZapRoffo wrote:


This is not really consistent with we generally observe, which is at a rating of diamond 300 and being well above the skill that gives a likelihood of being demoted, people are gaining many more points than they are losing at equal matches. The fact that you gain more points at a low number of games indicate that the point gain formula either depends on sigma, or is still using a version of comparing displayed to opponents MMR.

On August 08 2010 21:08 ZapRoffo wrote:


This is not really consistent with we generally observe, which is at a rating of diamond 300 and being well above the skill that gives a likelihood of being demoted, people are gaining many more points than they are losing at equal matches. The fact that you gain more points at a low number of games indicate that the point gain formula either depends on sigma, or is still using a version of comparing displayed to opponents MMR.

Ok, how does all of this tie into displayed rating and the whole “favored” deal? If you remember back to WoW, ratings changed based on a direct comparison of your displayed rating to the other team’s MMR. So if your current rating was 500 and you were playing people with MMRs of 2000, your rating would jump significantly after every win because of the wide disparity. Now, we’ve identified that on the loading screen quite often players are seeing the other person as favored and the opponent (who is nominally “favored”) also sees his opponent as favored! How can this be? The theory put forth here is the system is again comparing your displayed rating to your opponent’s hidden MMR.

The reason for this is so that the system brings you toward your MMR more quickly. kzn explains:

On August 08 2010 14:30 kzn wrote:

On August 08 2010 23:34 SnakeChomp wrote:


I think it is entirely reasonable to assume that your displayed rating value is allowed to swing upwards very quickly when you win in if the displayed value is much less than your actual MMR. This is how it works in WoW after all. The bonus pool is a relatively simple addition to this which just works like rest xp to help players who are not able to play as often keep up (in terms of ladder ranking) with those who can.

So in the above example, instead of the player with a higher MMR gaining rating due to the addition of diamond's MMR threshold and displayed rating (which is a highly arbitrary algorithm and doesn't make much sense given that displayed ratings cannot be compared between two players), it is instead simply: if you win you will gain rating based off the difference between the two players MMR additionally modified by the difference of your displayed rating and your MMR. If displayed rating is < MMR, the rating gain will be higher than if they were equal or if displayed > MMR (which only occurs due to the bonus pool).

Such a system implies though that display ratings will quickly converge towards your MMR and then slowly exceed your MMR due to the bonus pool. I don't think enough players have a display rating high enough to test this though, would need to be 2000+ up in diamond. Once players are there we can observe their point gain/loss compared to earlier games to determine if the displayed rating gain slows once it reaches MMR.

On August 09 2010 02:10 Caponed wrote:
I think a better system than "Blizzard checks MMR after every 30 games" would be "You get promoted when your sigma is below a certain threshold." This would improve the game's certainty factor, and, though it would take longer to get you where you need to be, would probably put you in exactly the right spot. Maybe even set certain sigma thresholds along the way, i.e. the system checks your MMR at sigma 100, 75, 50, 25 and adjusts your positioning accordingly.

Either way, interesting read.

On August 09 2010 02:15 Empyrean wrote:
Random question: did you use R to generate those graphs? Because they look suspiciously similar to R's basic graphics package ;D

On August 08 2010 23:47 barrykp wrote:

I think you have misunderstood Kzn's clarification. I think he is suggesting that the system compares your displayed rating to your current MMR and not your opponents (not that this makes much of a difference mathematically since, in theory, your MMR and your opponent's should be very similar). Having a large difference between your displayed rating and your MMR will result in the system skewing rating changes to favour reducing that difference. Eventually your displayed rating becomes very close, or the same as, your MMR. At least that's how I think it works in wow.

On August 09 2010 02:28 Excalibur_Z wrote:


We didn't make them. The top-down one is from a public .ppt from MS research Cambridge and the 3D one is from Google image search. :V