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Aren't there all kinds of paired comparison models that would allow Blizzard to handle this?
I mean, you can find plenty of extensions of the Bradley-Terry model that incorporate, for example, home field advantage in football.
Seems like it could be the same thing here.
Even a simple additive model like:
Pr ( player 1 Wins | skill1, skill2, race1, race2, map) is proportional to:
skill1 - skill2 + race1_race2_offset + race1_race2_map_offset
As long as all of those variables are inferred together, it should tease out skill from the race offsets, even if, say, player1 only ever plays Protoss. This is because Player1 will play against all the other races, each with their own offset, in addition to playing against other players with a wide enough range of skills. It'll easily separate skill1 from each race offset.
It would require them to have an entirely separate system than their match making system. This system would have to start over from day 1 to avoid being biased by the match-making. Hopefully they've kept all that match data.
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That would be possible, but if they did that, why did they share with us completely meaningless match up win %ages, without any information whatsoever about how they corrected it? I mean why bother giving numbers at all?
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On October 09 2010 14:12 Mearis wrote:
That would be possible, but if they did that, why did they share with us completely meaningless match up win %ages, without any information whatsoever about how they corrected it? I mean why bother giving numbers at all?
probably too make a mass appeal where only a select few actually know that its bullcrap. Tnx for the read guys im not that good at math myself and this made for a very interesting read.
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On October 09 2010 14:12 Mearis wrote:
That would be possible, but if they did that, why did they share with us completely meaningless match up win %ages, without any information whatsoever about how they corrected it? I mean why bother giving numbers at all?
I dunno. How many people on battle.net's forums are comfortable discussing paired-comparison models?
If they modeled skill and balance separately, it wouldn't be a huge jump to then simulate what happens when equally skilled players compete as, e.g. PvZ, and get their win percentages that way.
Sounds pretty complicated if you haven't had a few stats classes, but it's not really that bad.
Maybe fine for a teamliquid audience, but I don't know the battle.net forum audience as well.
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United States12274 Posts
On October 09 2010 14:12 Mearis wrote:
That would be possible, but if they did that, why did they share with us completely meaningless match up win %ages, without any information whatsoever about how they corrected it? I mean why bother giving numbers at all?
If you read my post on Page 3 it explains a lot more. It sounds pretty solid to me.
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On October 09 2010 07:13 Grond wrote:
There are enough things that are so obviously wrong right now that I don't think it's time to focus on statistics. I don't care if Terran win rate is 1%, stimmed Marauders killing a CC/Hatch/Nexus in just a few seconds is bad game play. I'd rather they fix the game play first.
As much as I agree with Mearis, darmoussah etc. on the impossibility of Blizzard's so called player skill rating, I agree it is more important for us to try to get Blizzard to focus on the good gameplay aspect first. Good dynamic gameplay that punishes and rewards appropriately makes a game simpler to balance than this kludgefest we have going on at the moment.
If the Beta period was longer and the only race that was selectable was "random", the data they collected would be much more useful than it is now. It would be better still if this portion of Beta remained closed to skilled players and they maintained constant feedback.
And before someone comes in to this thread with the obligatory it took BW to balance SC1 therefore wait for the expansions before drawing conclusions... try to think of SC2 as being an expansion of SC:BW instead... same company, same franchise, different engine, similar units, similar mechanics etc.
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On October 09 2010 14:58 Excalibur_Z wrote:Show nested quote +On October 09 2010 14:12 Mearis wrote:
That would be possible, but if they did that, why did they share with us completely meaningless match up win %ages, without any information whatsoever about how they corrected it? I mean why bother giving numbers at all? If you read my post on Page 3 it explains a lot more. It sounds pretty solid to me.
Well no, the post on page 3 says they have a way of measuring match up imbalance that's independent of results, without even ever going into details about how they do this beyond 'millions of matches'.
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On October 09 2010 20:16 Mearis wrote:Show nested quote +On October 09 2010 14:58 Excalibur_Z wrote:On October 09 2010 14:12 Mearis wrote:
That would be possible, but if they did that, why did they share with us completely meaningless match up win %ages, without any information whatsoever about how they corrected it? I mean why bother giving numbers at all? If you read my post on Page 3 it explains a lot more. It sounds pretty solid to me. Well no, the post on page 3 says they have a way of measuring match up imbalance that's independent of results, without even ever going into details about how they do this beyond 'millions of matches'.
No, I think you misunderstood them. They basically use the same mechanism of determining the match making rank to determine race imbalances. So the result of every single match has a tiny influence on the perceived race imbalance.
It should work like this:
Based on the player ranks, you get an initial win probability for each player, this is the classic matchmaking system. This probability is then modified by a global race-vs-race matchup modifier, say +3% for Protoss in a PvZ. Lets say the Zerg player had a 45% chance to win based on MMR, and consequently an estimated 42% overall chance of wining. After the match, if P won, then nothing happens(well, as it is the predicted result the variance decreases, but lets focus just on those percentages). However, if Z won, then his MMR increases and the P's MMR decreases, so that perhaps in a next match the system would assume a 46% chance for the Z to win based on MMR. Additionally, the PvZ modifier gets reduced, as perhaps the racial imbalance was overestimated. So instead of 3% it assumes 2.999%. Here there is only a tiny adjustment, as there are so many matches played. Then over a lot of games a somewhat stable modifier arises, and that are the numbers blzzard gave us.
However, I had thought of a different way to get a rough estimate on global race balance, so no race vs race estimates. A while back somebody made a chart of the number of diamond players for different ratings. One could clearly see how the number of players decreases as the rating increases, and this decay looked suspiciously like an exponential decay. Now I do not know if this distribution is enforced by the match-making algorithm, but if that is the case, we could estimate the decay parameter per race, giving us numbers lambda_t, lambda_z and lambda_p. In a perfectly balanced world those numbers should be equal. However if one race is overall favoured, then the parameter for that race is smaller because that race is able to reach higher ranks. If I remember the thread with the picture I will give a link to it, at the moment I can only give this idea as food for thought.
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assuming that zerg was underpowered against terran prior to 1.1, the average zerg versus terran match up would still have a 50% relative win rate, simply because the average zerg at a rating of X would be more skilled than the average terran at the same rating.
I just want to point out that this isn't quite correct.
The average zerg matchup would have a 50% win rate, and the average zvz would be 50%, but the zvt and zvp would not. This is because, a zerg at rating X may fair better against a terran at rating X than against a protoss at rating X. His overall win rate is 50%.
However, the second part of your sentence: "the average zerg at a rating of X would be more skilled than the average terran at the same rating" may still be correct.
The statistics blizzard gave us on matchups tells us a bit about the relative strengths of each race, but you cannot infer the skill or ability required to play the different races at that rating X. Therefore the game can still be imbalanced.
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