# Math Help - Ratios and what do they mean relative to each other.

1. ## Ratios and what do they mean relative to each other.

If you have 5 players, each with a win/loss ratio that varies according each individual player and you add up all those ratios and divide by the 5 players, what does the resulting ratio mean in relation to each other.
Suppose player 1 is 1.5, player 2 is 3, player 3 is .8, player 4 is .7 and player 5 is .9.

If you add up all these ratios and divide by 5 to get the average, you get an average ratio of 1.38. What does this ratio mean? Does it mean that the players have a 1.38 ratio of win to loss? If so how does that make sense when in the win to loss spread the addition of the numbers should equal 0, i.e. There should be an equal amount of losses as there is to wins.
I'm sorry if the question is a bit confused, or muddled but any help would be appreciated.

2. In general, averaging win/loss ratios does not have any mathematical meaning.

Assuming that each player played the same number of games, you can average the win *percentage* (wins/total games played) and get the average win percentage. You can then find the win/loss ratio with this, but averaging win/loss ratios itself does not give any meaning.

3. Why would it matter if they played an equal number of games, if they have a win to loss ratio of 1.5 it means that they win more matches than they lose i.e for every 5 matches, they win 3? If you got every player's win loss ratio and added them together, divided by the number of players, you would get an average ratio, would that be the average win to loss ratio of the group of players, and if that's the case, should it not be 1 as opposed to 1.3 or w/e seeing as there will be as much wins as there will be losses? What im struggling with is not how to calculate things, but rather what does it mean, if you are allowed to do what I am doing.

Edit: I understand what you are saying with the percentages, but can the same thing not be done with the ratios?

4. Hello, Beggarsbelief!

Why would it matter if they played an equal number of games?

Suppose on the first week of the season, the team won 1 game out of 2.
. . Their average is: . $\frac{1}{2} \,=\,50\%$

Suppose during the rest of the season, they won 98 games out of 98.
. . Their average is: . $\frac{98}{98} \,=\,100\%$

Would you say their average is: . $\dfrac{50\% + 100\%}{2} \;=\;\dfrac{150\%}{2} \:=\:75\%\,?$

Is that true? .They won only three-fourths of their games?
. . Certainly not!

During the entire season, they won 99 games out of 100.
. . Obviously, their average is $99\%.$

. . $\begin{array}{c}MORAL \\
\text{Do not average averages.} \\
\text{Do not average percents.} \\
\text{Do not average ratios.} \end{array}$

5. First playing equal number of games each matters.

If your top player plays almost all the games, clearly your stats would be close to that of the top player.

Averaging ratios does not give meaningful numbers. If you don't believe me, just do the calculations directly using the following example.

Player 1: plays 100 games and wins 20 times.
Player 2: plays 100 games and wins 50 times.
Total: plays 200 games and wins 70 times.

Total win/loss: 70/130 = 7/13

Average win/loss: (20/80 + 50/50)/2 = 50/80 (this does not mean anything)

6. Ok you have answered my question, I understand now what was wrong and why it wasn't making sense to me. Thanks a plenty people.