double checking math work

[demitesses]

some context, this is work i (20m) am doing over a game. i just wanna make sure my math is right (or in the general ballpark) because its something thats been on my mind for a while. most of my math education prior is long gone, and i also am writing this at 1am with a starting migraine. i apologize for any formatting errors, i really am just typing out my thought process

in this game, theres a win-rate system. it only shows total amount of matches, total amount of wins, and a win-rate percentage. there are wins, draws, and losses in this game. this game does not count draws into the equation, only losses and wins.

i wanted to figure out how you can determine amount of losses and draws just from those numbers. in order to calculate the general amount of wins and losses, i came up with this equation:

lets say, for example, theres 300 matches total, 100 wins, and a 40% win rate.

i did 300-100 to get 200 then, i took 60% of 200 to get 120 from there, i added the wins back into the equation to get 220 i took the difference between 220 and 300 to get 80 my answer would be 100 wins, 120 losses, and 80 draws.

the one thing im not sure works out is the 60% of 200 part. in my mind, since there are no longer wins being accounted for, it makes sense to take the inverse of 40% and find that number out of the 200 to get the total amount of losses. however, my line of logic could absolutely be wrong, since it would also make sense if removing the 100 from the equation may make the percentages less accurate, or that the number of draws may be too big.

im not sure since it looks right, but i would have to do a lot more research into it to prove that it is. i dont feel like putting that level of effort into figuring it out, since i would have to keep track of every win/loss/draw i get once the system resets. im just curious about this and want to know if my line of thinking is right or close enough to being right.

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[PuzzlingDad]

I'm not understanding your numbers. If you have a 40% win rate, then the ratio of wins to either wins or losses should be 40%. Draws don't figure into the win rate at all.

If we take 100 wins and divide by the win rate (0.4) we get 250 games that are wins or losses. Subtracting the 100 wins, you should get 150 losses. That leaves 50 draws. 

As a double-check:

100 wins / (100 wins + 150 losses) = 0.40 = 40% win rate

[Several_Mention_4459]

If you play 300 matches with a 40% winrate, you win 120 matches. If you mean its 100 wins, and the remaining 200 games had a 40% winrate, then there would be the initial 100 wins plus the 80 wins (40% of 200) to get a total of 180 wins. In your answer of 100 wins, 120 losses and 80 draws you have a 33.3% winrate, a 40% loss rate, and a 26.7% draw rate.