ELO computation changes

pier4r
Skynet
Skynet
Posts: 3353

Re: ELO computation changes

Post#101 » 15 Feb 2017, 00:51

So I have an idea since high school that improvements (in skills or whatever) follows more or less a logarithmic curve. It means, at the start the improvement is significant for relatively little effort, then the effort needed for every significant improvement is a lot. Of course, every individual has his curve.

Translated in gladiabots this should mean the following: the more one plays, the stronger one gets over the others. There are a lot of obstacles to this though.

First if there are two players with very similar development, they will end up (thanks to the glorious elo formula) with similar scores and a winning ratio against each (direct fights) other of 50% more or less.

What if there are more players like the first player? What if a player does not play continously so the player's tactics gets obsolete and has to catch up again? What if one is testing losing points in the process? And many other obstacles.

In those cases, before building a complicated analysis, one could do one with assumptions.
The following analysis compares the median score of a player between a range of games (say, between the game no 200 and the game no 300) against the median score of the opponent. This should also help to minimize the effects of elo inflation (see FAQ thread) and caps due to league max score limits and therefore limited population. One has always a reference against the actual, active, playerbase that define the opponent median score.

If the score formula is well done (and it is) and the matchmaking is well done as well (and it is, but was less good in the past), a player that is improving his score will increasingly match against players with higher score too. If this does not happen, it is because the player is able to retain points most of the time, so having a median score higher than the opponents. That is, aside from few matches against players with similar high score, the bulk of the matches are done against players with lower score. Of course this can be also due a poor matchmaking (and it was the case in the early stages of alpha 7.8, but only for few days).

results so far for some players: http://pastebin.com/a7FVEfQ6

Let's see some examples

Code: Select all

playerid:290, jbdb
1_100,1030,1038,-8
101_200,1186,1168,18
201_300,1170,1179,-9
301_400,1211,1162,49
401_500,1206,1236,-30
501_600,1307,1307,0
601_700,1342,1374,-32
701_800,1286,1388,-102
801_900,1325,1420,-95
901_1000,1357,1428,-71
1001_1100,1316,1374,-58
1101_1200,1326,1364,-38
1201_1300,1372,1368,4
1301_1400,1363,1365,-2
1401_1500,1263,1396,-133
1501_1600,1481,1394,87
1601_1700,1438,1436,2
1701_1800,1391,1427,-36
1801_1900,1385,1430,-45
1901_2000,1347,1475,-128
2001_2100,1383,1464,-81
2101_2200,1370,1433,-63
2201_2300,1365,1475,-110
2301_2400,1427,1471,-44
2401_2500,1453,1474,-21
2501_2600,1446,1469,-23
2601_2700,1464,1468,-4
2701_2800,1426,1455,-29
2801_2900,1378,1450,-72
2901_3000,1391,1521,-130
3001_3100,1425,1486,-61
3101_3200,1478,1397,81
3201_3300,1394,1404,-10
3301_3400,1417,1419,-2
3401_3500,1395,1381,14
3501_3600,1387,1472,-85
3601_3700,1456,1444,12
3701_3800,1468,1430,38
3801_3900,1432,1443,-11
3901_4000,1420,1429,-9
4001_4100,1457,1425,32
4101_4200,1488,1482,6
4201_4300,1547,1502,45
4301_4400,1507,1516,-9
4401_4500,1592,1508,84
4501_4600,1613,1534,79
4601_4700,1649,1596,53
4701_4800,1569,1659,-90
4801_4900,1607,1713,-106
4901_5000,1606,1522,84
5001_5100,1598,1451,147


In the case of jbdb once can see that aside from few periods were the player is able to hold a (median) score higher than the opponent playerbase, in general his score matches with the opponent playerbase (remark: for the analysis done in the past, being within 100 points is like being very similar). In this case the player evolution reached a limit so far (whatever the reason), that is: the actual playerbase is mostly a though challenge to the player.
It can be noted that, nevertheless, the median player score is slowly raising, so the system accounts for inflation nevertheless.

An example of a player that is dominating the opponents

Code: Select all

playerid:13298, TcT
1_100,1201,1155,46
101_200,1541,1403,138
201_300,1735,1352,383
301_400,1825,1396,429
401_500,1985,1526,459
501_600,1975,1592,383
601_700,2016,1557,459
701_800,2063,1571,492
801_900,2100,1679,421
901_1000,2097,1630,467
1001_1100,2136,1645,491
1101_1200,2168,1622,546
1201_1300,2190,1549,641
1301_1400,2196,1525,671
1401_1500,2195,1712,483

Notice how the median score of the player is always very high and quite constant. This, given the score formula and the matchmaking rules, it is quite impressive and indeed the difference with the median opponents score is remarkable.

Another example:

Code: Select all

playerid:84920, Aw0093
1_100,1171,1158,13
101_200,1275,1361,-86
201_300,1223,1259,-36
301_400,1279,1266,13
401_500,1503,1508,-5
501_600,1498,1475,23
601_700,1569,1525,44
701_800,1646,1721,-75
801_900,1698,1720,-22
901_1000,1709,1522,187
1001_1100,1679,2057,-378

One can see that although the last entry of the list shows that the player is in difficulty, one can notice that the opponent pool is way stronger than before (likely a couple of games against 2000+ players), so in this case is not yet sure if the player reached a temporary plateau, because one can see from the progression that the player median score slowly raises catching up with the median of the opponent playerbase.
http://www.reddit.com/r/Gladiabots/wiki/players/pier4r_nvidia_shield_k1 -> Gladiabots CHAT, stats, insights and more ;

pier4r
Skynet
Skynet
Posts: 3353

Re: ELO computation changes

Post#102 » 16 Feb 2017, 11:54

I was checking the score of Marion (a good player that unfortunately is xp level 4 in grand master) and I realized another point about elo inflation.

We have those players that are within the interleague score (so 200 points of difference compared to those players in the lower league) that mostly win against players of the lower league. Since 200 points of difference is not so big, this means that they are able to harvest good points for every victory. Like +5 or more.

Then, at the same time, those players are not yet good for the current league, so they are harvested by better players. This means that they release back those points harvested from players of the lower league.

So it is like a chain, the players that can do "interleague" fights harvest points that then are passed to stronger players and the ultimate accumulation end up with top players.

Only if stronger players (not necessarily top players) go inactive this process is a bit balanced out, but so far the net accumulation is still faster than points frozen due to inactivity. Of course it is slowed down a lot compared to the first days of alpha 7.8 . Before reaching 1900+ was not that hard, now it is, so the amount of harvesting for top players is decreased or at least distributed among more players.
http://www.reddit.com/r/Gladiabots/wiki/players/pier4r_nvidia_shield_k1 -> Gladiabots CHAT, stats, insights and more ;

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