Solved

Need a formula to compare percentages based on different amounts (weighted?)

Posted on 2008-10-27
1,140 Views
Okay, I probably knew how to do this at one point, but I haven't cracked a math book open in quite some time. How can I fairly compare averages based on different amounts?

Say a runner runs 100 races and wins 25 of them. He has a winning percent of 25%. But if another runner runs just 10 races and wins 5, he has a winning percent of 50%. Now, the second racer has a higher winning percentage, but the first runner has won more races and could be construed as a "better runner".

I know I could extrapolate and assume that if the second racer runs 100 races, he will win 50 of them, but I'm looking for a more accurate comparison of what they've actually done and not what they may do.

Is there some formula or theory I can use?

0
Question by:StarbuckLives
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

• Help others & share knowledge
• Earn cash & points
• Learn & ask questions
• 2
• 2
• 2
• +1

LVL 18

Expert Comment

ID: 22817066
0

Author Comment

ID: 22817987
This looks like it's about figuring out the reliability of an estimated number, not the comparison of two accurate percentages.
0

LVL 27

Expert Comment

ID: 22819166
"looking for a more accurate comparison of what they've actually done and not what they may do."
-
There is no better way. It depends on what you are looking for. If you want a runner who was won the most races, take the first one.
If you want the runner who wins the highest proportion of his (or her) races , take the second one.
You are asking for two different things.
Consider baseball players and their batting averages. some players have a large number of hits but still have a (slightly) smaller batting average. Which one do you trade for?
If a player has only a few at bats, people tend to discount a large batting average. After a certain number of at bats, the precise number of at bats tends to be disregarded.
In the case of your runners, what or the quality of the races. The 10 race guy might have enter only races in Podunk. The 100 race guy may have run only in the olympics and world championships.
I know a golfer who has won several tournements. He could not get into the PGA if he tried.
You are asking for two different things (albeit related). There is no more accurate comparison
0

LVL 27

Expert Comment

ID: 22819178
The confidence limit will help you out a bit. If you  put a statistically significant + or - on the percentage you can see if they overlap. If they do there is little difference between them.
0

LVL 18

Expert Comment

ID: 22820413
there isn't really any reasonable extrapolation, A may improve and win 75 more races, but there's no evidence to support this any more than him losing all future races, so you can only really calculate the probability that B's .5 rate was a blip, and his underlying win rate is lower.  whether or not this is true binomial isn't clear though, because strength of field is critical.

I would recommend looking at personal best times, strength of field etc, but not forgeting that fast and slow races occur for diferenet reasons.

0

LVL 3

Accepted Solution

jtm111 earned 500 total points
ID: 22835657
But if you're talking about aggregating the result of multiple runners, then you certainly would use the weighting scheme you mentioned.

For example, if you had 5 runners:

Runner    Wins    Number of Races
1               10               50
2                5                10
3                5                20
4                2                 3
5                1                 1

If I wanted to express the aggregate performance of the team, I'd weight the percentages by the number of races:

10/50 * 50 +
5/10 * 10 +
5/20 * 20 +
2/3 * 3 +
1/1 * 1

Then divide the whole thing by the sum of the weights (50 + 10 + 20 + 3 + 1)

That way you get the answer: 23/84 = .274 or 27.4%

This reflects the proper weighting of each member of the group.

If not the answer you're looking for, maybe enough to get you thinking in the right direction.

0

Author Closing Comment

ID: 31510523
This is more what I was looking for, thanks.
0

Featured Post

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Suggested Solutions

Title # Comments Views Activity
Proportion 4 52
My 2003 Land Rover discovery 2 key for code for car alarm 7 157
x2 – x2 = x2 – x2 conundrum 12 79
Two Dice Roll Probabilities 3 85
This article provides a brief introduction to tissue engineering, the process by which organs can be grown artificially. It covers the problems with organ transplants, the tissue engineering process, and the current successes and problems of the tec…
When we purchase storage, we typically are advertised storage of 500GB, 1TB, 2TB and so on. However, when you actually install it into your computer, your 500GB HDD will actually show up as 465GB. Why? It has to do with the way people and computers…
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
Finds all prime numbers in a range requested and places them in a public primes() array. I've demostrated a template size of 30 (2 * 3 * 5) but larger templates can be built such 210  (2 * 3 * 5 * 7) or 2310  (2 * 3 * 5 * 7 * 11). The larger templa…
Suggested Courses
Course of the Month6 days, 14 hours left to enroll

732 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.