6 replies to this topic

[GaryLShelton]

Hi,

Since the rank boundaries have been changed, my original analysis is not applicable anymore.

I've observed the new boundaries, and they are much more straightforward: 20 points for every new rank. So the full list becomes:

100-120: Bronze Spy
120-140: Bronze Scout
140-160: Bronze Miner
160-180: Bronze Sergeant
180-200: Bronze Lieutenant
200-220: Bronze Captain
220-240: Bronze Major
240-260: Bronze Colonel
260-280: Bronze General
280-300: Bronze Marshall
300-320: Silver Spy
320-340: Silver Scout
340-360: Silver Miner
360-380: Silver Sergeant
380-400: Silver Lieutenant
400-420: Silver Captain
420-440: Silver Major
440-460: Silver Colonel
460-480: Silver General
480-500: Silver Marshall
500-520: Gold Spy
520-540: Gold Scout
540-560: Gold Miner
560-580: Gold Sergeant
580-600: Gold Lieutenant
600-620: Gold Captain
620-640: Gold Major
640-660: Gold Colonel
660-680: Gold General
680-700: Gold Marshall
700-720: Platinum Spy
720-740: Platinum Scout
740-760: Platinum Miner
760-780: Platinum Sergeant
780-800: Platinum Lieutenant
800-820: Platinum Captain
820-840: Platinum Major
840-860: Platinum Colonel
860-880: Platinum General
880-99999: Platinum Marshall

The post above provides what our current system is.

Below are three images of the Ranking Badges but with the old numbers (so ignore numbers):

http://volleybal-vcn...tego_bronze.png

http://volleybal-vcn...tego_silver.png

http://volleybal-vcn...ld_platinum.png

[GaryLShelton]

This table shows how the change in rating points after the outcome of a game depends on the difference in two player's ratings. The first column is how many points are gained by the winner AND lost by the loser if the lower rated player wins the matchup. The second column shows the same in the case where the higher rated player wins the matchup.
Rating Lower Higher Difference Wins Wins
1 to 27 ........... 13 12
28 to 56 ......... 14 11
57 to 85 ......... 15 10
86 to 115 ....... 16 9
116 to 147 ..... 17 8
148 to 181 ..... 18 7
182 to 219 ..... 19 6
220 to 263 ..... 20 5
264 to 315 ..... 21 4
316 to 381 ..... 22 3
382 to 477 ..... 23 2
478 to 676 ..... 24 1
677 and over 25 0
The next table shows how many points are gained or lost following a draw, depending on the difference of the two player's ratings.
Rating Points Difference for Draw
0 to 13 .......... 0
14 to 41 ........ 1
42 to 70 ........ 2
71 to 99 ........ 3
100 to 130 .... 4
131 to 164 .... 5
165 to 200 .... 6
201 to 240 .... 7
241 to 288 .... 8
289 to 346 .... 9
347 to 424 .... 10
425 to 552 .... 11
553 and over 12

[GaryLShelton]

For those who are interested, here’s an explanation about how the ELO rating system works at this site:  
 
Let D = Your opponent’s rating minus your rating.  (If you have a higher rating than your opponent, D will be negative)
 
Your approximate probability of winning a matchup is given by P = 1 / [ 1 + 10^(D/400)] 
 
If you win the matchup, you will win 25*(1 – P) points.  If you lose the matchup, you will lose 25*P points
 
If it’s a draw you win 25*(0.5 – P) points if you were the underdog, and you lose 25*(P – 0.5) points if you were the favorite.
 
For example, if you have a 330 rating and your opponent has a 250 rating, you should win P = 1 / [ 1 + 10^(-80/400)] = 61.3 % of the time.
 
If you beat this opponent, the your rating increases by 25*(1 - .613) = 9.67, or 10 points, rounded to the nearest whole number.  If you lose, your rating decreases by 25*(.613) = 15.33, or 15 points.  A draw works out to a loss of 2.83, or 3 points for you. 
 
Instead of probabilities, we can also think in terms of odds.  Let R = the odds against you winning.  For example, if you have 25% chance of beating a particular opponent, then the odds against you are 3 to 1, so R = 3 in the case. R is related to P by the formula R = (1 – P) / P  or  P = 1 / (R + 1)
 
Now, there is a very nice formula that relates R and D:   R = 10^(D/400).  This means a player with 400 more rating points with his opponent is 10 times as likely to win the game.  It does not matter if it is 200 vs. 600 or 500 vs. 900.  With ELO, all that matters is the difference of the ratings.
 
One more thing:  A precise definition of P is that it's your probability of winning plus one-half the probability of a draw.  So in reality your probability of winning a game is slightly less than P.

[GaryLShelton]

A player’s rating is influenced by three factors:

(1) Win ratio*, which determines how often you gain points versus lose points.

(2) The strength of your opponents relative to you, which determines how many points your gain for a win or lose for a loss.

(3) The number of games played, more of which will tend to increase your rating up to the point where it matches your true skill level. After that, your rating will stabilize unless you improve as a player.

*Technically the relevant statistic is win ratio in ranked games since you last had a 100 rating. Since no rating can drop below 100, new players are not penalized for losses. For example, a player who wins only 5 out of his first 20 games and then wins his next 8 out of 10 will have about the same rating as a player who started out winning 8 out of 10.

[GaryLShelton]

This post in my series explaining the ELO ranking system examines the degree to which results of past games affect one's current rating.  In a recent thread, Nortrom correctly stated that “ELO is too much of a today's ranking, not a long time ranking”  So, by how much does ELO favor new games over older ones?  After running a number of simulations, I concluded that any given game counts about 3% less than your next game.  Over time this accumulates, to the point where a win or loss 23 games ago counts only about half as much as does a game today.  The math on this is .97^23=.496
 
You might be wondering how this happens, since you earn the same number of points for a victory against an opponent with a given rating difference with you whether the game was played today or three months ago.  Well, suppose you just lost a couple games that you think you should have won.  This means your rating is 50 points lower than what it could have been (Note here that all games, no matter the ratings of the players, result in a 25 point net difference between winning and losing).  So then, say 40 games later, is it still true that your rating would be 50 points higher had you won those two games?  No, it’s not.  This is because during those 40 games you were getting slightly more points for each win and slightly fewer points deducted for each loss than would have otherwise occurred had you started that sequence of 40 games with a rating 50 points higher.  In fact, after 40 games, the difference those two games has on your rating is now only about 15 points ( 50*.97^40=14.79).
 
So take this as a bit of comfort after a tough loss.  Its impact gradually gets wiped away as future games are played.  After about 100 games, that one game makes only 1 point difference to your rating, and after about 130 games it’s likely the effects will have vanished entirely.

[Midnightguy]

I would prefer more simple scales where we only used the title of each unit but, it takes more games to get to the next level and as you get to the higher titles such as Colonel, General and Marshal it would take many more key wins. 

I've said it before it just seems odd to me that we would have a guy who was once a Marshal then suddenly has to be a Spy again to proceed in the ratings. Also in the real military it's usually difficult to make quick advancements especially when you get to the higher rankings.   This is just an example of what I propose.

 

 

Spy 100-199 

Scout 200-299

Miner 300-399

Sergeant 400-499

Lieutenant 500-649

Captain 650-799

Major 800-999

Colonel 1000-1199

General 1200-1499

Marshal 1500+

[GaryLShelton]

Here are the four league leaderboards:

Bronze League
http://game.stratego...html?leagueid=1

Silver League
http://game.stratego...html?leagueid=2

Gold League
http://game.stratego...html?leagueid=3

Platinum League
http://game.stratego...html?leagueid=4