To find a success list in group

Question

I try to find a success list among players for my project. I thought If I find the winning probability of players , it would give me the success list in group.

I would like to give an example to explain in a score table.

• Player A won Player B 2 times in 3 matches .
• Player C won Player B 1 time in a match.
• Player C won Player A 1 time in 4 matches.

My idea to find the winning probabilities:

p(Player X)=Total Winning number of Player X / Total Match Number

Thus we can calculate individual probabilities as above.

p(A)=5/8

p(B)=1/8

p(C)=2/8

The success list shows that p(A)>p(C)>p(B)

If we get new player (Player D) and the new player gets a match with Player C. if Player D wins the match, we will get a new success list according to my formula above.

p(A)=5/9

p(B)=1/9

p(C)=2/9

p(D)=1/9

In last status: p(A)>p(C)>p(B)=p(D)

I do not feel that method is good enough because Player D won Player C but Player D is behind Player C. As a sense, I feel Player D must be more that Player C in the list.

And other disadvantages are

1. if a player do not make match so often ,it can go down in the list. For example , if Player A do not make match for a while and Other players make matches, Player A will go down in the list even if he has good winning rate among users. I feel my method does not give exact player power

2. If a player in middle of the success list makes so much match with a weak player, The middle player will get top in the list even the player is not good enough.

   Please let me know your ideas and solutions . Which methods can be used to define for better success list? How did you solve that issues in your game project while preparing a success list for death matches.

Thanks

Answer 1

• "Success list" is a term you made up, don't use it. What you want to compute is some kind of score or rating of each player as an estimate of "player power".
• The difference between a score and a rating is that a score is typically expected to increase with more games played (e.g. the number of knockouts in a boxer's career), while a rating is expected to remain constant unless the player becomes stronger or weaker, and unaffected by the number of games played (e.g. batting averages of baseball players).
• Clearly you want a rating, not a score. The closest formula to what you are doing now is taking the ratio between a player's won games and a player's total games. At the beginning A is rated 5/7, B is rated 1/4, C is rated 2/5; after D beats C, D jumps on top at 1/1 and C slips to 2/6.
• The problems with this simplistic rating formula are trusting statistically small samples too much (with only 1 game played, D should be still close to a medium "newbie" rating, not at the top or at the bottom of the ladder) and neglecting the opponent's skill: winning against a stronger player should improve the rating more. Both issues are addressed, for example, in ELO scores for chess and similar systems.