Talk:Darkcanuck/RRServer/Ratings

Battles per Pairing

I just wanted to comment on the statement, "It's uncertain how well it works with less battles or incomplete pairings." My experiment with the MC2K7 shows that separate runs of 75 battles can still show more than 1% variation for a given pairing. This affects any scoring system, and is a fact that we have to live with. The reliability of output can only be as good as input, no matter how fancy the interpolation is for incomplete pairings. The hope is that the variance will become a wash when seen over 600+ pairings. --Simonton 15:25, 26 September 2008 (UTC)

I think David Alves commented that targeting challenge scores also varied by almost 1% at 15 seasons, so I agree there's lots of evidence that more battles per pairing are needed, which would take a very, very long time in a 600+ competitor environment. You're right that as the number of competitors increases, variabilities cancel each other out. But at the same time, the bigger the competition, the more risk of a "black swan" competitor whose scores are all skewed in one direction. -- Darkcanuck 15:31, 26 September 2008 (UTC)

After scratching some things down on paper which are mostly intuition rather than statistics, I believe the odds of having such a "black swan" are either exactly the same or reduced by increasing the number of bots. --Simonton 16:05, 26 September 2008 (UTC)

Well, if there are 3 bots, the chance of one getting lucky against both others is 1/4th, multiply by 3 bots, and the chance of a "black swan" in 3 bots is 75% I believe. With 4 bots, the chance of one getting lucky against against all others is 1/8th, multiply by 4 bots, and the chance of a black swan is 50%. For 5 bots... it is 31.25% chance of a black swan. For 650 bots with one pairing each, the chance of a bot having above average score in every pairing is about 1 to 2.78*10^193. So if we presume getting lucky is anything above the mean score and there's a 50% chance of that in any pairing, and that a "black swan" is only when all pairings are lucky, then the chance of a black swan sharply decreases as the number of bots becomes larger. Of course perhaps what would be more useful than simply chance of there being a bot with all pairings lucky, would be the chance of luck making the score 1% different. I could calculate this, but only if I had a number of what the "standard deviation" of the percent score of an average robocode battle is. --Rednaxela 16:28, 26 September 2008 (UTC)

My intuitive hypothesis remains unshaken, but I don't have any numbers to prove it. But I can't argue with something to the power of 193. :) I'll look into adding standard deviation to some of the tables. What would be most useful, within a pairing, across all pairings, or across all final scores? -- Darkcanuck 16:43, 26 September 2008 (UTC)

Ah, now that you put the statistics that way I can see how to do it. With 3 bots each has 2 pairings, so the chance of both coin flips being "lucky" is indeed 25%. However, the chance of at least 1 of those bots hitting its 25% is (1 - 75%^3) ~= 57.8%. Generalized, this formula is 1 - (1 - .5^(bots - 1))^bots. If you graph that you can see it reduces to pretty much zero pretty quickly. --Simonton 17:18, 26 September 2008 (UTC)

Oh right, I got slightly mixed up and was multiplying by 3 when I should have been working with powers. --Rednaxela 17:35, 26 September 2008 (UTC)

You've got an extra leading paren, but that makes sense to me. Nothing to worry about! -- Darkcanuck 18:05, 26 September 2008 (UTC)

Glicko-2 Rating System

Looking at things as my recently added versions have gained battles, it's seeming like Glicko-2 seems FAR faster to converge to a realistic expected score far quicker than ELO or Glicko-1, and seems quite stable. Glicko-2's performance seems to really impress me. I wonder if maybe we should remove ELO and Glicko-1 at time point maybe, and just keep APS and Glicko-2? (Would that make uploading a little faster?) Also, maybe it would be good to make a modified APS that uses the Glicko-2 ratings to estimate the scores of missing pairings, in order to make the APS ranking less distorted by cases when there are incomplete pairings still? --Rednaxela 21:25, 25 November 2008 (UTC)

Bad uploads are becoming a recurrent issue.

But there is a way to shield the ranking from these uploads using median instead of mean when calculating pairing APS, as long as bad uploads don´t outnumber the others. The drawback would be a performance hit in CPU/database during uploads.

I think an outlier resistant APS system may be good, but I do have a concern that using the median may 1) distort scores when valid data would cause a distribution that has a skew, and 2) In the cases where there are no outliers for it to fix anyway, it would generate more noisy values (The median generally has larger fluctuations than the mean as samples are added).

I'd think it may be worth considering statistical methods to calculate the probability of a data point being an outlier, and ignoring it if it's beyond a threshold. It may be possible for such methods to not alter the means of skew caused by valid data, and will have smaller score fluctuations.

Another thought is, regardless of if we change the APS system or not, it may make sense for the rumble to have a page that lists recent outlier results, to make it easier to spot them.

One way to see skewed distributions is median taking it into account while mean assuming all distributions are symmetric. So it is not "distortion", but it may affect APS as we are used to.

But yes, mean needs less battles than median when the true average is near 50% (symmetric distributions) and there are no outliers.

There are other more sofisticated statistical methods for dealing with outliers, like percentile, which is somewhere between mean and median. But for me, median is good enough and is fully automated.

(I would never even imagine these things exist if it were not for Robocode and the quest for the ultimate statistical gun)

About the skewed distributions, fair enough. I still am concerned about the greater noise of medians though.

The more sophisticated method that was coming to my mind, was calculating the z-score of each sample per pairing, tossing out results that have too extreme of a z-score value, and using the mean of the remaining samples. The reason this appeals to me, is because it changes the existing scoring system as little as possible.

Most bad results we see are near-zero scores which should be quite distinctly detected by a z-score test, so reliably tossing them out without changing the overall scoring system would be quite doable I think.

Using z-score as threshold will need tuning to work properly, because it has unpredictable robustness. Remembering sampled standard deviations are also affected by outliers.

Choosing a very low percentile and a very high percentile as boundaries and averaging everything in between may have the effect you want without relying on noisy sampled deviations. Like 25%/75% (1st/3rd quartiles).

Taking that a step further, you could take the probability of a data point being wrong and look at how many of those are coming from each user, and over a certain threshold, all their uploads (or all within X hours of this happening) are ignored. (Or an email is fired off to Darkcanuck to look into it. =)) I like the idea of public page listing outlier results, too.

The median idea also seems good though, and very simple. I'd be curious to see if/how much the Rumble scores change using median instead of mean. My guess is by no noticeable amount.

The deviations from all data points for each uploader could be combined into a statistic about how "suspicious" each uploader is and then list it in a public page. I thought about that too.

But median is simple, with robust statistics theory backing it and fully automated. No need to bother Darkcanuck unless the server is attacked with tons of bad uploads.

I was thinking in another tie-breaking for the PL ranking system (Copeland). Currently it uses full APS as tie-breaking, but it sacrifices ISDA, which is a key property from Copeland to prevent low ranked competitors from interfering with the top ones (king-making).

Tie-breaking could use only APS between tied competitors instead, to preserve ISDA.

Example 1: DrussGT, Diamond and Tomcat are all tied in first place. Tie-breaking score for DrussGT would use only Diamond and Tomcat. Score for Diamond would use DrussGT and Tomcat. Score for Tomcat would use DrussGT and Diamond. As if those 3 were the only competitors in the rumble.

Example 2: DrussGT and Tomcat are tied in first place. Tie-breaking score for DrussGT would use only Tomcat. Score for Tomcat would use DrussGT. It would be a head-to-head comparison between the 2.

Competitors not tied to anyone else can have any tie-breaking score, as it would not change the ranking.

I had forgotten to respond to this when I first read it. But I quite like this idea. It has for a long time seemed strange to me that PL used APS for tie breaking, considering the goals/philosophies of the systems are so different.

Just mad idea about rankings. What if robot's rating is: <percents from 1st place's APS in 1-vs-1> + <percents from 1st place's APS in melee> * 0.6 + <percents from 1st place's APS in temas> * 0.3?

For example for DrussGT it will be 100 + 0 * 0.6 + 0 * 0.3 = 100, for Diamond 99.23 + 99.8 * 0.6 + 0 * 0.3 = 158,88, for Shadow 94.43 + 98.68 * 0.6 + 100 * 0.3 = 183,64

It allow develop melee and teams rumbles

I think that's kind of looking at it backwards. I don't think the combined ranking would make people more interested in Melee/Teams, but I do think if more people were building cross-divisional bots, such a ranking would be more interesting. =)

I don't think it's the lack of rankings that make people uninterested in Melee/Teams, I think people just like 1v1. And in that case, people will just focus on 1v1 rankings, even if combined rankings are available. I think the best thing you can do to get people interested in Melee/Teams is to work on them yourself!

I also think about other rule sets occasionally. Sometimes I think about building a MegaBot Twin Duel team, even if it couldn't compete in the rumble.

It´s been a while, but I finally implemented a Schulze ranking using everything that Schulze paper offers. It has tie-breaking and path reconstruction, together with some statistics and coloring to make easier to track what the method did. It uses pairing APS as ballot.

Tried using % wins in Schulze but it failed miserably as everyone from rank 8 to 817 were tied together, making the system deteriorate into a random ballot ranking. Shadow tied together with Worst with tie-breaking relying on a coin-flip was not what I had in mind. As far as I understood what went wrong, normalizing wins dividing them by the number of battles sacrificed resolvability.

The results can be downloaded here (data using Darkcanuck 2011-08-09 backup): [1] [2] [3] [4]

I also added other ranking systems, like APS/Elo (batch), Premier League and APS that everyone is used to. Also added a Simpson-Kramer ranking, due to Skilgannon request to see who is performing best against each bot. Simpson-Kramer is also good as statistics for Schulze.

I took Chase "for fun" advice seriously and tried to make something more appealing.

You know, since there's a little bit of disagreement about what kind of rating system best reflects the kind of improvements valued in robots, I wonder if it would make sense to have a mixed system for overall ranking? What about using a condorcet voting method to resolve the rankings, where each ranking system is a "ballot" that fills out the rank of all robots? One "ballot" could be APS, another "ballot" could be W%, and perhaps another "ballot" could be S%. The resulting rankings would essentially be based on the consensus of the three component ranking systems. I think it's natural for robots that excel in all three metrics to rank high, and is perhaps a more universally agreed and more general notion of strength than just one metric alone.

Thoughts?

I like that approach myself. Though I think I would limit it to APS and W%.

Nevermind, forget what I said. I didn't read it close enough. I was thinking that I would like something that averages APS and W%, with the weight of each not necessarily being equal.

Averaged would be nice in that it would allow easier differentiation between small changes, but on the other hand, condorcet ranking has the property of not allowing one metric to dominate. I think there are advantages to each way of mixing.

Both condorcet and averaging can allow one kind of metric to dominate through clones. Similar methods together will overweight other unique methods. Ballots need to be independent from the candidates (methods) to avoid the clone problem.