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kkeerroo
Experienced Roboteer
Joined: 17 Jun 2004
Posts: 1459
Location: Brisbane
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This is a post from the RFL forum I am insterested in and I wanted to look into it more when I got home, but instead of e-mailing it to myself I'll put it up here for you lot to read too.
quote:
A couple of iteams that I did not explain well:
1) The delta caculation should be done differently for the winner and loser -- for almost every case, this will always result in complementary values (+x and -x).
2) More properly, the delta calcuation is
DR1 = K * (S1 - E1) and
DR2 = K * (S2 - E2)
Where S1 is 1 if R1 wins and 0 if R1 looses and S2 is 1 if R2 wins and 0 if R2 looses
3) E (whitch is the expected score of each robot) is calculated as follows:
E1 = (1 / (1 + (10 ^ ((R2 - R1) / ER)))) and
E2 = (1 / (1 + (10 ^ ((R1 - R2) / ER))))
4) So, at the end of a match, the new scores for R1 and R2 are:
R1 = R1 + DR1
R2 = R2 + DR2
So, lets try that example again: Going into a match, Robot R1 has a rating of 1600 and Robot R2 has a rating of 1500. Lets say that Robot R2 pulls off the upset and beats R1. The points R2 gets for beating R1 would be:
DR2 = K * (S - (1 / (1 + (10 ^ ((R1-R2) / ER)))))
DR2 = 10 * (1.0 - (1 / (1 + (10 ^ ((1600-1500) / 300)))))
DR2 = 10 * (1.0 - (1 / (1 + (10 ^ (100 / 300)))))
DR2 = 10 * (1.0 - (1 / (1 + 2.1544)))
DR2 = 10 * (1.0 - (1 / 3.1544))
DR2 = 10 * (1.0 - (0.317))
DR2 = 10 * 0.683
DR2 = 6.83 or 7 rounded up
R2 = R2 + DR2
R2 = 1500 + 7 = 1507
So R2's rating would increase to 1507 for this upset.
For R1, the score would be calcualted as:
DR1 = K * (S - (1 / (1 + (10 ^ ((R2-R1) / ER)))))
DR1 = 10 * (0 - (1 / (1 + (10 ^ ((1500-1600) / 300)))))
DR1 = 10 * (0 - (1 / (1 + (10 ^ (-100 / 300)))))
DR1 = 10 * (0 - (1 / (1 + 0.4642)))
DR1 = 10 * (0 - (1 / 1.4642))
DR1 = 10 * (0 - (0.683))
DR1 = 10 * -0.683
DR1 = -6.83 or -7 rounded up
R1 = R1 + DR1
R1 = 1600 - 7 = 1593
Meanwhile, R1's rating would decrease by 7 points and he would fall back to 1593.
The E values, E1 and E2 are as illustrated, the expected outcome of a match relative to the "strength" of an opponent. So for R1, his actual score S was 0 (a loss) but the probably of him wining was 68.3% and so his ranking is adjusted for that error factor. Similarly, for R2, his actual score S was 1 (a win) but the probably of him wining was only 31.7% and so his ranking was likewise adjusted for this error factor.
There's about 150 posts simalar to this, so its an interesting subject. Sort of. _________________ Get Some!!!
Secretary of the Queensland Robotics Sports Club inc.
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Wed Feb 09, 2005 3:59 pm |
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kkeerroo
Experienced Roboteer
Joined: 17 Jun 2004
Posts: 1459
Location: Brisbane
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quote:
Originally posted by Spockie-Tech:
It is an interesting area, but the question is, is anyone interested enough to collect results from all of the events nationally, do all of the calculations and updating of a rankings table on a website on a regular ongoing basis out of their own time ?
So, any volunteers ?
Well as soon as Glen gives me the results from the Marayong fights from last year I'll have more a look at it. I don't like Mite-e-er sitting there with a boring score, but if I had Marayong 2's result (which I think I have here some where) and Robowars 1 (which I do have) Mite-e-er would have an interesting score, which would throw a spanner into the rest of the Metal Mayhem points, as well as The Aggressor and Mite-e-er at Marayong 4 (I have the results for Marayong 4, but I think I havn't got Marayong 3, which I'll need). I can't do much with the Annihilator so I'll forget that and the only other time Queenslanders went interstate was Robowars 2 (which I have results for) but those damn NSW bots were there and I can't figure out their scores as you lot don't post up the full trees any more.
Oh and those equations in the previous post of mine need a bit of fixing. If the K value is too low you arn't getting enough deveation from the average and therefore not getting an acurate result. But if the K value is too high you end up going too far and throwing out the results. I heard about a value of K that depended on the size of the field, something like sample size x sqrt(2).
Either way out of the 6 test pages I've seen the yanks try on the RFL results 5 ended up giving the same results for the top 10 robots in the 30lbers (the only group I've looked at) and the other test put Totally Manipultive at number 4 rather then last, so I'll ignore that one ( Totally Manipultive has an impressive losing streak) _________________ Get Some!!!
Secretary of the Queensland Robotics Sports Club inc.
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Wed Feb 09, 2005 10:15 pm |
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