Math Question

[Fianchetto]

If you have some various numbers that you want to combine to form an overall score, but each number is based on a different scale, what is the best way to go about this?

For example:

You want to compare two guys that play some sports. Let's say bowling and golf.

During the competition:

Bill bowled a 215 game, and shot a golf score of 94.

Don bowled a 160 and had a round of 79.

Is it possible to give them each an overall score based on some uniform scale, and declare a winner?


My first take on this is to convert them both to 0-100 scales and go from there. Bowling scores can range from 0 - 300, and golf scores from about 60 - 150.

Bowling:
Bill: 215/300 = 71.6
Don: 160/300 = 53.3

Golf:
Bill: (94-60)/(150-60) = 37
Don: (79-60)/(150-60) = 21

Here's where I'm kind of stuck. The tricky thing is that lower is better in golf, and higher scores are better in bowling, so it doesn't make sense to add each players numbers together, does it?

i.e.
Bill = 71.6 + 37 = 108.6
Don = 53.3 + 21 = 74.3

Would show bill as the winner, but he shot a worse golf score, and when we add his scores together we are no longer on a 0-100 scale.

There has to be a way to do this, logrithmic scale or something?

Any suggestions would be appreciated, thanks.