Algorithm of 400 Clan Ranking Algorithm

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Re: Algorithm of 400 Clan Ranking for CL3

Postby jpcloet on Fri Mar 25, 2011 9:23 am

danryan wrote:A lot of very odd looking results in that output...


Yes but at some point you say clan x is overrated and clan y is under rated and they should battle, but that is not happening. In theory it should sort itself out. The same principle applies to the leap. Speaking of that, I have put an updated model in the CLA for them to review/discuss.
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Re: Algorithm of 400 Clan Ranking for CL3

Postby Leehar on Fri Mar 25, 2011 9:24 am

danryan wrote:A lot of very odd looking results in that output...

Not really, it's mostly understandable how it came out.
Maybe if you add some restrictions like minimum wars played or only privies/medals using ones it could weed out some of the more wonky ones. (Or it could just be that I'm looking forward to seeing Nem at #5 :lol: )

I'm actually trying to just discount the 'z's completely since they're no longer existing clans I presume
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Re: Algorithm of 400 Clan Ranking for CL3

Postby jpcloet on Fri Mar 25, 2011 9:26 am

Leehar wrote:I'm actually trying to just discount the 'z's completely since they're no longer existing clans I presume


yes, the z-clans are dead clans. The z was put in front so that we could display better in the clan results thread.
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Re: Algorithm of 400 Clan Ranking for CL3

Postby Dako on Fri Mar 25, 2011 9:32 am

Also, if you add criteria with 3 wars completed - then the results should be much better.
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Re: Algorithm of 400 Clan Ranking for CL3

Postby jpcloet on Fri Mar 25, 2011 9:38 am

Dako wrote:Also, if you add criteria with 3 wars completed - then the results should be much better.


In one of the ELO versions I had, I used a display factor of (.5 for wars of 1 or 2, .75 if 3 wars and 1.00 if 4 or more wars) You could do something like that. I called it a Reliability Rating.
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Re: Algorithm of 400 Clan Ranking for CL3

Postby FarangDemon on Fri Mar 25, 2011 10:53 am

danryan wrote:
FarangDemon wrote:I should add some sort of filter to only include clans that have played a minimum number of wars in the ranking.
It is only meaningful after a certain amount of data.


I'd say 3 wars or a total of 100 games played as a minimum amount of data, then it would make sense. The trouble is, some decay needs to be in there as well as clans' strength change over time. This is a hard nut to crack.


Yes, I think we'd want a 100, or maybe 150 or 200 game minimum for a clan to appear in the ranking.

As for decay, I agree with you. That's why I created a Data Window parameter. Using the default parameter (1 year), I intended for only the past 1 year of games to be included to determine the performance rating. Either jpcloet increased this value or there is a bug I need to fix.

jpcloet, which value did you use for Data Window?
Also, please provide me the data files you used so I can investigate.
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Re: Algorithm of 400 Clan Ranking for CL3

Postby jpcloet on Fri Mar 25, 2011 10:58 am

FarangDemon wrote:jpcloet, which value did you use for Data Window?


I used all of time, so I set it to 5 years.
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Re: Algorithm of 400 Clan Ranking for CL3

Postby FarangDemon on Fri Mar 25, 2011 6:19 pm

jpcloet wrote:
Dako wrote:Also, if you add criteria with 3 wars completed - then the results should be much better.


In one of the ELO versions I had, I used a display factor of (.5 for wars of 1 or 2, .75 if 3 wars and 1.00 if 4 or more wars) You could do something like that. I called it a Reliability Rating.


This is definitely a good idea. I appreciate you testing out this metric and your feedback, as I know you have a lot of experience doing this.

I came across the algorithm of 400 by playing chess online on Gameknot. The way they implemented it, if you played under 10 games, your score was computed the same as everybody else, but it was noted as being "provisional". Perhaps I could add option to include/exclude provisional clans from the ranking list.

jpcloet wrote:I used all of time, so I set it to 5 years.


It's not necessary to set it to 5 years if you want to take 5 year-old data into consideration. It's a bit confusing. It will help if I explain a little of what exactly the program does.

The way the program works, it starts at the first challenge, no matter what the Data Window value, and adds challenge by challenge, recomputing each clan's rating as it goes.

In order for this to work, every time I calculate the rating for a clan, I must pass a time parameter. The time parameter specifies what point in time I am calculating the rating. This is the date used to establish the data window that determines which challenges are counted.

Each clan war provides one data point, which is either +/- 400 of the opponent clan's rating at the time of the challenge. For ties, the opponent's rating is used unaltered. Data points are dated to the time of conclusion of the challenge.

For example, when I calculate THOTA's rating for Mar 25, 2007, it will only be looking at challenges that happened prior to that date. If Data Window is set to 1 year, the rating will be computed by games-weighted averaging the data points (i.e. results from challenges) between Mar 25, 2006 and Mar 25, 2007. However, given that one of these THOTA challenges (against Z-Nihilists) concluded on June 6, 2006, the value of that data point would be based on Z-Nihilists rating at that time (June 6, 2006), meaning it would have been computed by averaging data points of the Z-Nihilists' challenges between June 6, 2005 and June 6, 2006. If the Z-Nihilists played against Z-Beelzebubs on July 14, 2005, it would then need to calculate rating of Z-Beelzebubs on July 14, 2005. This required looking at all of Z-Beelzebubs' challenges between July 14, 2004 and July 14, 2005. And so on and so forth until the beginning of time.

So since it starts at the beginning, you can be assured that all 5 years of data will be used as the algorithm computes and recomputes ratings over the past 5 years no matter what the Data Window setting.
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Re: Algorithm of 400 Clan Ranking for CL3

Postby FarangDemon on Sat Mar 26, 2011 1:34 am

I've updated the script.

http://www.killersapp.com/algorithmof400.htm

Decay Factor

There is now a decay factor. If the Data Window is set to 2 years (default), then a war today is weighted 100%, a war 6 months ago is 75%, 12 months ago is 50% and 18 months ago is 25%.

decay factor = Elapsed time from start of data window to clan war record / total length of data window

The weight changes continuously, day by day, so that over time, a clan's score will will not perceptibly spike up or down except immediately after conclusion of a new clan war.

Min Weight to Display in Ranking List

Restricts display of clans in the ranking list to those with minimum weight total. Total weight = Sum of products (decay * games) for each clan war record within data window. This ensures reliability of ranking.
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Re: Algorithm of 400 Clan Ranking for CL3

Postby shocked439 on Sat Mar 26, 2011 1:52 am

JP why are results from 3 years ago important? Clans are fluid and the skill of the clan 3 or four years ago don't matter. A true ranking should show who you are now. It should have a beginning and an end to the ranking period and take into account the results during that period. This system has merit if used appropriately but the results of the first ever clan war don't matter now, maybe in a historical ranking but does the 1927 Yankees winning the world series have any impact on the 2011 Yankees winning it? Nope. So define a clan year and base the rankings on challenges begun during that year.
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Re: Algorithm of 400 Clan Ranking for CL3

Postby jigger1986 on Sat Mar 26, 2011 1:58 am

This is some interesting info and I thank you for it. According to FD's initial calculations there we alot of surprises in the league.
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Re: Algorithm of 400 Clan Ranking for CL3

Postby Qwert on Sat Mar 26, 2011 6:51 am

farang can you give results start from 2011.
If i understand correct-every clan start with 1000 pt.
Can you tell me if THOTA play against T4c- how many pts will get thota if win,and how many pts will get T4C if win?
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Re: Algorithm of 400 Clan Ranking for CL3

Postby jpcloet on Sat Mar 26, 2011 7:17 am

shocked439 wrote:JP why are results from 3 years ago important? Clans are fluid and the skill of the clan 3 or four years ago don't matter. A true ranking should show who you are now. It should have a beginning and an end to the ranking period and take into account the results during that period. This system has merit if used appropriately but the results of the first ever clan war don't matter now, maybe in a historical ranking but does the 1927 Yankees winning the world series have any impact on the 2011 Yankees winning it? Nope. So define a clan year and base the rankings on challenges begun during that year.


You have to look at the history of clans, some are not as active as the others. I simply used all the data to start with. Various other ELO's I used removed older data as we went along. 2 Year RPI was the last 24 months when it was in use.
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Re: Algorithm of 400 Clan Ranking for CL3

Postby FarangDemon on Tue Mar 29, 2011 3:18 am

The rankings presented below are based on all clan wars I got from jpcloet and all Clan League (1-3) that had finished at time of posting.

http://killersapp.com/Algorithmof400.htm

Note: I'm not advocating that the particular model with these specific parameters is the best model to use to compare clan performance. There are a lot of parameters that could be tweaked to result in higher accuracy. I used rough estimates for end dates of CL1 and 2. So consider this post as an illustrative example of how to use my script to create and evaluate your own models. More details below.

I've updated the script to:

  • Graph the top clans' performance over specified time window

      Click image to enlarge.
      image

      The graph above used Data Window of 2 years and Graph Window of 3 years. Data Window of 2 years means that whenever performance rating is computed, clan wars from 2 years before computation date are weighted 0% and clan wars from computation date are weighted 100% (values in between are scaled linearly between 0 and 100%).
  • List all clan wars, in order of decreasing weight, which contributed to each clan's final rating (Display Basis of Each Clan's Rating)

      If the final rating was lower or higher than expected, you can look at the reason why
      Click image to enlarge.
      image


      Note: Yes, TOFU only got a rating of 476 from beating The 4th Crusade with 80% win rate (applied with relatively high weight of 13% unfortunately for TOFU, as it was a big challenge / relatively recent in time). At the time T4C had a rating of only 76 because they lost to TIME when they were 433 and Knights of the Future when they were 524. Kind of a funny situation... But there are two ways to possibly alleviate this injustice (both described in more detail below):

      • Tweak parameters to modify point gain/loss based on win margin,
      • Use more accurate dates for end of CL1 and CL2 challenges.
  • Compute accuracy of the model, in terms of how often the higher ranked clan actually won

      Now you can know how accurate the model is in real terms, measured by how often the higher ranked clan wins for various rating difference intervals

      Min Weight to include in Accuracy = 100
      Image

      This means, that given a match between two clans, where one clan is 109 points above the other, it is 82% likely to end in a non-upset. Btw, this 109 point value was auto-calculated as 10% of the range between min and max ratings (after excluding clans below weight threshold).

      You can take a look at the ratings below to see if it makes sense to your perceived chances of success against a clan.

      Click image to enlarge.
      image

  • Change parameters to allow rating for a clan war to increase/decrease based on win margin. The model I have provided is just an example. You guys can:

    • Add/adjust Data
        I didn't look up when every clan war from CL1 and CL2 actually ended, so I just used one date for each regular season. It would be great if someone could update this to reflect the actual dates because this model is time sensitive and the clan wars took place over many months.
    • Play around with the parameters
        Try to use parameters that result in high model accuracy
Last edited by FarangDemon on Mon Apr 25, 2011 2:33 am, edited 1 time in total.
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Re: Algorithm of 400 Clan Ranking for CL3

Postby FarangDemon on Wed Mar 30, 2011 1:04 am

Dako wrote:Also, if you add criteria with 3 wars completed - then the results should be much better.


I forgot to implement this! So what I've implemented now, if a clan has under 3 wars, any query on their score will result in the average of 1000 and the otherwise regularly computed score. This is what gameknot did, though they may have used a different cutoff value.

So if a clan has only completed 1 war against a clan with 1000 points, they are considered a 1200 instead of a 1400 at that time. This prevents clans from skyrocketing positive or negative by playing just 1 or 2 games, which adversely affected TOFU in the example in my previous post.

This is what it looks like with this fix and using 600 points max delta (if one clan wins/loses 100% of games in a war), 200 points min delta (if a clan barely wins/loses).

(All screenshots from the same model)

Click image to enlarge.
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As you can see above, this model is a lot more forgiving to higher-ranked clans that take on lower-ranked clans (as all clans that participated in CL3 did). Using the standard implementation of algorithm of 400, a higher ranked clan is automatically penalized even for winning against a clan less than 400 points below them. With this model, they can make up for the point differential by having a high win margin.

Example, in this model TOFU is penalized 200 points for the 80% win against T4C. In my opinion, this is fairer than the 400 point penalty resulting from previous posts' min=400, max=400 standard model (with top-of-post-mentioned fix for clans with less than 3 wars).

Click image to enlarge.
image


For the accuracy calculation, I've made the interval length a user-defined parameter, so you can play around with different values that you think provide more meaningful results.

This table shows that according to this model, any clan that is about 22-66 points ahead of another has a 67% chance to beat or tie the lower-ranked clan. For an 67-110 point lead, the chance is 83%.
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