What formula to choose for rating calculation?

Question

Software design

There are 3 fields: wins, draws, losses . What formula should be chosen for calculating the rating, given that there can be 0 wins (in this case, for example, the player 0:2:1 is more successful than the player 0:0:1), 0 losses (in this case, for example, the player 0:2 :0 is more successful than player 0:1:0). Those. victory is paramount, then draws.
UPD:
Since the statistics are given to the user immediately for 3 levels of difficulty of the game, I want to know his rating at any time, and not calculate all the ratings of all players upon request. Also the ratio of wins/losses is predominant, then comes the number of draw games.
If in a possible formula the rating of two players is the same for different results, then the player who has played fewer games is more successful. Those. achieved results in fewer attempts.

Answer 1

What is needed here is not an algebraic formula, but sorting by two fields: the value in the first field is equal to the wins of the minutes of defeat, in the second field, draws. Sorting works in such a way that only rows in which the values ​​in the first field match will be sorted by the second field. If you still want to get a function, then the index in the sorted list will be the value of this function. The function is calculated for a specific player, but the entire list of players goes as an argument to it, and for an individual player in a vacuum, the value of the function is not defined.
An alternative sorting option can be proposed: three fields, the first - wins, the second - losses with a negative sign (players with fewer losses will be higher), the third - draws.
But the first option personally seems to me more balanced.

Answer 2

Wins + draws * 0.5 - losses = rating

Answer 3

Win - Loss * 0.5 + draw / 2
May work

Answer 4

make a matrix of players. Bars from top to bottom - the ratio of wins / losses. Add rows with the same ratio of wins/losses, then make a selection of who has the "draw" ratio. As a result, the first element in the column (player) will be the best in terms of win/draw/loss ratio, then we deduce from its row the rest, whose win/loss ratio is the same, but "draw" is worse. When the line is over, we move on to the next element of the column, and so on.

Answer 5

What is wrong with the football formula?
3 points for a win, 1 point for a draw, 0 points for a loss?!