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So this is from my post in the feedback thread
http://www.teamliquid.net/forum/viewmessage.php?topic_id=57090¤tpage=40
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I am not sure if this is the right thread to ask this question, but why are Player's ELO not the average of their 3 vsX ELO? From what i understand, at the beginning since everyone starts at 2000, a very good player progress slower, because when he beats someone good it is the same thing as when he beats a bad player. On the contrary, a bad player will deteriorate slower, because when he looses against someone bad, it's as if he had lost against an avarage player.
But normally, (if everyone stays on the same level), it should converge to the same value. But if i take Bisu, who played 300 games, his ELO is 111 points above his average ELO, which is huge! If i take a player with a lots of games like nada (620!), his ELO is only 16 points above his average, so it seems indeed that it is converging, but it takes longer than what i would have thought. If i take a "bad" player like MuMyug, his ELO is 30 points below his average ELO, so this seem to confirm the above theory. (but you have some bad players like tester whose ELO is still greater than their average). In fact the divergence seems to be highest with player with high ELO.
So that means that over time there is a dilatation of the ELO (which is obvious since everyone starts at 2000... but the point is that there can be a dilatation still after a long period of play). So even if the avarage stays the same, over time a good player will be ranked higher and a bad player lower.
What about elo peaks? Bisu with 2353 is probably better than oov with 2329. But ELO is not about who is the best in an absolute time frame (otherwise it would require a lot of inflation: a 2100 player of today is probably better than oov at his prime), ELO is about who is better "at the moment". And because of the dilatation (not the inflation), a 2353 bisu is not necesseraly more dominant than a 2329 oov was.
If i take the average of the 3 matchups peak, i get these rankings for some selected people:
jaedong: 2243
oov: 2239
flash: 2226
savior: 2225
nada: 2224
bisu: 2219
boxer: 2151
I am surprised that jaedong is so high while his elo's peak is rather low, but he peaked in his vsT ans vsP at completly different periods.
My point is, i think, that ELO is a great tool for what it does (comparing different players right now), but we must pay attention not to try to use it for other things (like knowing the most dominant player of all time). The ranking with the average peak elo means nothing either, but it shows that you have a ranking a bit different with a less dilated ranking (you can still see the dilatation in effect with boxer's avrg elo rather low).
(maybe i should have posted that in a new thread.)
When you consider all time ELO peaks, you have to take into account inflation (retiring player generally retires with <2000 ELO points) and dilatation (everyone starts at 2000, so it's harder to obtain a great ELO at the beginning).
Since the three vsX matchups have less matches, there is less dilatation (it is even more obvious when you consider map specific ELO). So it can be interesting to look at the average of these ELO and average of the peaks ELO.
(Normally these stats should converge, but it takes a lot of games, and in reality players are not consistent, when they have a streak (100% win), their ELO increase 3 times more than their average ELO, so the deviation from their usual level is 3 times higher).
Here are the ranks i obtain:
1) first the current ELO rank
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ID ELO
(P)Bisu 2314
(Z)Jaedong 2278
(T)Flash 2276
(P)JangBi 2237
(P)free 2210
(T)Light 2196
(T)Leta 2190
(P)Kal 2187
(Z)Luxury 2180
(P)BeSt 2169
(T)Iris 2160
(T)fOrGG 2158
(P)Stork 2158
(Z)YellOw[ArnC]2158
(T)HiyA 2143
(Z)hyvaa 2143
(T)Hwasin 2141
(Z)EffOrt 2134
(T)sKyHigh 2124
(Z)Calm 2123
2) Now the average ELO
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(Z)Jaedong 2221.33
(P)Bisu 2200.33
(T)Flash 2197.67
(P)JangBi 2144
(P)Stork 2137.67
(P)free 2130
(T)fOrGG 2123.67
(T)Leta 2123.33
(Z)Luxury 2120
(T)Sea 2118.67
(P)BeSt 2118.33
(T)Light 2110.33
(Z)sAviOr 2109
(Z)YellOw[ArnC]2100.67
(T)Iris 2099
(P)Kal 2096
(T)Midas 2091
(T)Mind 2075.33
(T)HiyA 2073
(Z)hyvaa 2072.33
You can see the dilatation in effect, the elo of top player is much better than their average ELO. As a consequence the players move much slower in the rank. There is still a big gap between the top 3 (bisu/jaedong/flash), but i am surprised that jaedong is so high.
3) The Peak ELO rank:
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(P)Bisu 2353
(T)Flash 2336
(T)iloveoov 2329
(Z)Jaedong 2309
(Z)sAviOr 2301
(P)JangBi 2290
(P)Stork 2289
(T)NaDa 2285
(Z)GoRush 2269
(P)BeSt 2267
(T)Hwasin 2259
(T)Leta 2259
(T)XellOs 2258
(T)Midas 2258
(Z)July 2251
(T)fOrGG 2246
(Z)Luxury 2244
(T)Sea 2239
(Z)YellOw 2236
(P)Anytime 2235
(T)Iris 2226
(P)Reach 2224
(T)BoxeR 2224
4) And the peak average:
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(Z)Jaedong 2239.67
(T)iloveoov 2239.33
(T)Flash 2226.33
(Z)sAviOr 2225
(T)NaDa 2224
(P)Bisu 2219.33
(T)Sea 2210
(T)Midas 2205
(P)Stork 2201.33
(Z)July 2197.33
(Z)YellOw 2187
(P)BeSt 2185
(Z)GoRush 2174.33
(T)XellOs 2173.33
(P)JangBi 2167.33
(P)Reach 2167.33
(T)Hwasin 2165
(T)fOrGG 2164.33
(T)Iris 2160.67
(Z)Luxury 2157.33
Oov is a monster! He is still number 1 (almost...)! This really show the kind of domination he had. Jaedong is very high, but you have to remember he peaked at very different times in his matchups (2008/02, 2009/02, 2008/10) while ooV peaked almost exactly at the same time (around 2004/06). If JaeDong had done the peakings at the same time, he would have had oov's domination level! It's quite interesting that Savior,Nada and Flash are at the same level.
Flash peaked at his 3vsX roughly aroung 2009/02 (what is strange is that he peaked at his elo on 2008/06), savior around 2007 (except is vZ in 2009) and nada around 2005 (except his vT on 2007). So by taking into account dilatation you have that nada>savior>flash in term of domination. You can see the dilatation effect in that nada did not peak in his bonjwa's days, but in his second (or third?) resurgence.
Bisu's average is rather low compared to his peak elo, but it's because he peaked at almost exactly the same time (2009/03), so each of his matchups combined to give him a crazy elo. And his current elo is way better than is average elo, because of the dilatation effect, he his near maxed in each of his 3 matchups, but his current elo increase a lot more than his vsX elos (this illustrate what i said about streaks from players)
Still oov peaking at 2004 having the same rank as jaedong picking around 2008, this is monstrous!
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Nice! These stats rock, interesting to see Jaedong owning the average elo so hard. I mean the top three were pretty much set in stone but to see him beat out Bisu and Flash by such a margin is really something. I guess he's the most consistent out of the three, and his vZ probably helped alot.
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Really interesting stuff, thanks a lot.
(I did read your post in feedback btw, just too lazy to reply before weekend :/)
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This is cool to see, but the averages are obviously going to be a little skewed towards players who are in their prime at the moment, because they havent had their avg lowered by their inevitable downturns.
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United States1865 Posts
On March 06 2009 04:38 sixghost wrote:
This is cool to see, but the averages are obviously going to be a little skewed towards players who are in their prime at the moment, because they havent had their avg lowered by their inevitable downturns.
Well if I think I understand it correctly, the 1st list is the best players at the moment (Avg. ELO), so that wouldnt matter, because a player who was good in the past truly isnt one of the best players at the moment, and the second list Avg. ELO Peak, only takes their absolute peak for each matchup for measurement, so it would not include the downturn at all, which is why the top is dominant players from different eras: jaedong, oov, savior, nada, flash , bisu, etc.
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On March 06 2009 01:08 Makhno wrote:
Nice! These stats rock, interesting to see Jaedong owning the average elo so hard. I mean the top three were pretty much set in stone but to see him beat out Bisu and Flash by such a margin is really something. I guess he's the most consistent out of the three, and his vZ probably helped alot.
it's cuz JD doesn't slump
when he wins only 6/10 of his last games people are like "OMG JD IS PLAYING SO BAD HE MUST BE IN A SLUMP"
bisu and flash have had their ups and downs
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Uh, people who started playing as newbies (like Bisu) and then grew into the monsters they are now will obviously have issues with average ELO and peak ELO. Bisu also hurt his hand at some point. It's not all about slumps.
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On March 06 2009 04:14 PoP wrote:
(I did read your post in feedback btw, just too lazy to reply before weekend :/)
No problem, I wasn't expecting an answer, i just thought this was interesting so i posted it somewhere where it could be seen 
I think i can explain a bit more the difference between ELO and average ELO (and peak ELO vs average peak ELO):
1) ELO increase and decrease 3 times more than average ELO. To illustrate this fact, imagine a super bonjwa that wins 100% of his games. He plays against average players that are all rated 2000. Each game he plays, he gains more ELO points. But his average ELO will be 1/3 of what he gained, so his average ELO increase 1/3 times slower.
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Well actually it is a bit more complicated, because each time he plays he gains less ELO points. So lets say he gains x_1, x_2, x_3, ... points. If he plays only against Terran, he will gain x_1, x_2, x_3 in his vsT, so his average Elo will gain x_1/3, x_2/3, x_3/3... But if he plays the 3 races 1/3 of the time, he will gain x_1, x_2, ... in each of his vsX mu. So after 3n games, his ELO will be 2000+x_1+...+x_3n while his average ELO will be 2000+x_1+...+x_n. Now from what i understand (but i am not sure), we have x_n ~ a/(k^n+b) for big n, so x_1+...+x_3n will be converge so x_1 +...+x_n will be closer and closer. So his elo and his average elo will converge to the same value. But this would require a huge number of games, so this is not really relevant.
What does this mean? Well roughly this mean that when you look at the current average elo (table 2 in my post), it oscillate a lot less than the current elo. So bisu's elo is better than jaedong, so currently bisu has been doing better than jaedong. However his average elo is less than jaedong's, so when you consider a longer period of time, jaedong has done a bit better on average than bisu.
(there is another factor too: if bisu beat a lot of good players that are a bit less good in their vP, his elo will increase more than his vX elo too, so his average will increase even slower).
2) Now about peak elo. Is a 2353 peak bisu more dominant than oov? Well of course he plays better, but elo does not measure this, it measure the relative strength of people at a given period. I am pretty sure than every good programmer right now could beat oov when he was peaking, yet they are not at 2300+.
So is bisu more dominant than oov was? This is difficult to answer but i would argue not. First i think there is inflation in elo (the average increase because of retiring player), so everyone has a bonus elo.
Second and more importantly, ELO need time to converge. I will give an example:
- it's 2001, starcraft is beginning everyone is at 2000 and someone named boxer wins the msl. Let say he gains 100 points for that. In his second starleague, his opponent did not play many games so they are still around 2000, he still wins the starleague but he gains a lot less points because he was starting way above them.
- 8 years later, the good players have had the time to get to their true ranking. A player named bisu wins the msl. Bisu plays against starleaguers, so they are good players, they stand around 2100. Let's say bisu starts at 2100 too, and he wins as convincingly than boxer. He will gain the same number of points, so he will be at 2200. So his peak elo will be higher, even through he was as dominant. (the point is not that he was starting at 2100 so he gained 100 more points, the point is that since he plays against 2100 players, it is much more easy to dominate them enough to be at 2200, 100 points above them, than to dominate them enough to be 200 points above them like what was required from boxer).
So the elo needs some time to converge. If you could look at the standard deviation over time, you would see it increase (but slower and slower of course). Since in the average elo the convergence is roughly 3 times slower, the dilatation over the time is less visible, so it makes a bit more sense to comparate the peak elo in different period of times (this is roughly the same effect than for the current elo vs average elo: the time windows where the comparison is pertinent is longer). So that is what the table 4) in my post was for.
3) TL; DR
In permanent regime, the average elo will oscillate roughly 1/3 less than the current elo, so the current elo shows peaks in form, while the average elo shows average form in a longer period of time.
It takes a long time to converge to a permanent regime. And it takes longer, the better (or worse) you are compared to average to reach your true elo. A true 2300 player of today starting at 2000 will reach 2300 much faster than he would have if he had started at the beginning of starcraft. Again, with the average peak elo, the dilatation is slower, so you can compare them better.
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gondolin:
I've crunched a few numbers off of TLPD and found that the inflation is approximately 27.6 ELO points per player at this current moment (pretty much Bisu's peak). Obviously with Boxer it was probably ~0 points (but TLPD doesn't have all tournaments he's played in) and then every other bonjwa from there has had somewhere between the 0 and 27.6 ELO points... of course, greater as time goes on.
But yeah, as I stated in a couple of the other ELO threads the fact that Boxer was facing pretty much all 2000 ELO opponents makes his peak ELO less than the subsequent players.
If we could go back in time with TLPD we could run a couple standard deviation analyses of the peaks of each of the bonjwa's vs. average ELO of all players as well as top 3, top 5, top 10, etc. to see who was more dominant compared to their peers and/or everyone. I think that would give a more accurate representation of dominance.
I asked POP to hopefully implement a "time period" feature to TLPD so hopefully he will come through. 
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+ Show Spoiler +Bisu's average ELO up to 2214 after tonights WL matches. Close to JD's top spot as he droped to 2217 after getting beat by Stork in OSL.
Previously:
(Z)Jaedong 2221.33
(P)Bisu 2200.33
Peak average now 2224. Up to NaDa's peak average:
Previously:
(Z)Jaedong 2239.67
(T)iloveoov 2239.33
(T)Flash 2226.33
(Z)sAviOr 2225
(T)NaDa 2224
(P)Bisu 2219.33
Also, ran up some stats today:
~iloveoov to his peak was 77-20 which is pretty much a monstrous 79% or so.
~Bisu from ClubDay group stage last Oct is 74-22 which is ~77%. Very close to oov level domination.
Still waiting for the go-back feature so I can analyze the std. deviations though.
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EPT
