RS Ladder/Ratings examples

13 total games.

Overall ratings

• Not fair to directly compare an XvT-only player with a JA-only player. They have no way of directly competing. Make individual game ladders be the focus for these types of people.
• For the unusually versatile, suggest an "overall" ladder that adds up every rating the person has earned. This goes hand-in-hand with the "Renaissance" category of awards. Participation in all 13 games is almost mandatory to have a chance at 1st place, due to the automatic +50 pts boost from a new game. A score for someone with only 1 match in all 13 games would be around 650.
• The "overall" ladder will not be emphasized - not placed as the #1 ladder. Suggest placing the most active ladder as the most prominent. Also have a permanent order, by genre.

Game ratings

• Suggest the range is 0-100, with decimal points. Display 2 points on ladder, store up to ~6.
• 0 and 100 should never be achievable - to do so would let someone stop playing entirely and never be beaten.
  • OR, these ratings are achievable, but reset after a given interval (when months change?); that way people can claim to have reached "perfection". This would be a rare case, as we would make it very difficult to achieve rock bottom or top.
• All newbs start off with the rating of 50.
• Wins move rating towards 100. Ties move rating towards 50. Losses move rating towards 0.
• Newbs' ratings should be considered "unstable". A stability point is needed: at least 20 matches against at least 4 opponents to be considered "stable".
• The maximum rating movement should be 5 in either direction per match. This will occur when: 1) the opponent is "stable"; 2) the opponent's rating is at least 25 away in the target direction.
• A total newb, with 0 matches to date, should merit a maximum of 2 in either direction. An opponent who has done 1-19 matches will have a maximum from 2-4, accordingly, evenly divided.
• The midway rating points should be 75 for wins and 25 for losses. Any ratings which attempt to go beyond these will be reduced to a portion of the maximum, according to how close the rating is to 100 or 0.
• 25-75 category wins against another 25-75 will be worth 1-5 rating pts.
• The difference between two previously equal parties will be 2.
• In any given period, likely one month, two opponents' ratings changes will be reduced, starting at 5 matches and becoming constant at 20 matches.

Other concerns

• We are slightly concerned about the devious, talented player who will become "stable" with zero wins, then prey upon the high-rated players to quickly bring down their 98+ ratings. However, the establishment of a "revert match" option should be included with the system, and such unusual activity rebuked and the player's account removed.

Mathematics

Formula

1. Calculate "stability" quotient of opponent to get max points (range: 2-5)
2. Calculate difference between opponents' current ratings to determine max points (range: 1-5)
3. Calculate, if applicable, frequency penalty of playing opponent often already this month (range: 10%-100% of full score)
4. Calculate own handicap: only if currently 0-25 with new loss, or 75-100 with new win
5. (Optional) if applicable, calculate presence of special requirements for achieving temporary 0 or 100
6. Apply all calculations. Rating is complete.

Tables

Matches vs. maximum points (for opponents who are newbs)

Mat Pts
 0  2.0
 1  2.1
 2  2.2
 3  2.3
.......
10  3.0
11  3.1
.......
19  3.9
20+ 5.0

25-75 range results, stable players (P1 beats P2) - projected results

P1   P2  P1:  P2:
25   75  30   70
40   75  45   70
50   75  55   70
55   75  59   71
60   75  63.5 71.5
65   75  67.8 72.2
70   75  72.2 72.8
75   75  76.8 73
....
25   50  30   45
30   50  34   46
35   50  38.5 46.5
40   50  52.8 47.2
45   50  52.2 47.8
50   50  52   48
55   50  56.8 48.2
60   50  61.6 48.4
65   50  66.4 48.6
70   50  71.2 48.8
75   50  75.9 49
....
25   25  27   23.3
30   25  31.8 23.5
35   25  36.6 23.6
40   25  41.4 23.8
45   25  46.2 23.9
50   25  51   24.1
55   25  56   24.1

75-100 range results, stable players (P1 beats P2) - projected results

P1   P2   P1:  P2:
75   75   76.8 73
75   80   77.3 77.8
75   85   77.7
75   90   78.1
75   95   78.5
75  100   79   95
85   75   86.1
85   80   86.3
85   85   86.6
85   90   87.1
85   95   87.5
85  100   88
95   70   95.4
95   75   95.6
95   80   95.8
95   85   96
95   90   96.3
95   95   96.5
95   98   96.8
95  100   97
98   70   98.2
98   80   98.3
98   85   98.4
98   90   98.4
98   95   98.5
98  100   98.6
99.5 70   99.52
99.5 90   99.58
99.5 99.5 99.71

Frequency, P1 vs P2 in a given month (e.g. June 2009), matches vs. reduction:

Alternate: Linear reduction from 6 to 20.

Mat Red
 5  1.0  (none)
 6  0.9
 7  0.85
 8  0.8
 9  0.75
10  0.7
11  0.6
12  0.5
13  0.45
14  0.4
15  0.35
16  0.3
17  0.25
18  0.2
19  0.15
20  0.1
21  0.1
22  0.1
....