A formula to calculate percent improvement on a custom Logarithmic scale.

[ROSJ61]

I wish to run a competition among my stores based on percent improvement over time. Since all stores start with a different initial performance scores, I wish to know how to calculate percent improvement among stores fairly. To do this fairly, I must account for the fact that as scores approaches a perfect score more effort is required for smaller gains. For example, it can require more effort to improve a score of 95 to a 98 than it requires to move a score of 50 to a 75. I am looking for a formula that I could use that account for this asymmetry of effort required as you approach a perfect score. Any help is much appreciated.

 

[JeffM]

I wish to run a competition among my stores based on percent improvement over time. Since all stores start with a different initial performance scores, I wish to know how to calculate percent improvement among stores fairly. To do this fairly, I must account for the fact that as scores approaches a perfect score more effort is required for smaller gains. For example, it can require more effort to improve a score of 95 to a 98 than it requires to move a score of 50 to a 75. I am looking for a formula that I could use that account for this asymmetry of effort required as you approach a perfect score. Any help is much appreciated.

Being completely fair would require a ton of experimental work. For one thing, location, demographics, etc would all need to be taken into account. This would involve not just a lot of research, but perhaps would involve some math that would not be easily explained and so might not be perceived as fair.

However, if you are willing to be simple and far less scientific, there are many different formulas that you could use. A very simple one would be this

Take the difference between a perfect score and the starting score. Let's call that the potential. Now measure the performance, that is the difference between the starting score and the ending score. Divide the performance by the potential. Call that quotient the percentage of potential achieved. Base your awards on the percentage of potential achieved. NOTE This method will not work if any store already has a perfect score.

Let's see how this would work out in your example

Store A: starting score = 50, and ending score = 75. Potential = 100 - 50 = 50. Performance = 75 - 50 = 25.
Percentage of potential = 25 / 50 = 50%,

Store B: starting score = 95, and ending score = 98. Potential = 100 - 95 = 5. Performance = 98 - 95 = 3.
Percentage of potential = 3 / 5 = 60%.

This may be TOO simple, but it addresses the question you asked.

 

[ROSJ61]

Good Suggestion.

Jeff -

Thanks, simple is what I'm after. Like you point out, if nobody can understand how their being measured there won't be much buy-in. Is there a way to modify the formula to take into account the time period required to make the improvement. For example Store B made the improvement over 2 months, while Store A did it in 1?

Regards,
Robert

 

[JeffM]

Jeff -

Thanks, simple is what I'm after. Like you point out, if nobody can understand how their being measured there won't be much buy-in. Is there a way to modify the formula to take into account the time period required to make the improvement. For example Store B made the improvement over 2 months, while Store A did it in 1?

Regards,
Robert

Robert

If I were doing a consulting engagement, I'd have a number of suggestions to discuss with you, but this is a free site primarily devoted to helping students, and my time is limited.

To answer your question, again being very simple, you could simply divide by the number of months involved to get average percentage of potential achieved per month. But, usually, this kind of competition has a definite time frame so everyone is being judged over the same duration of time. If that is the case, you can ignore time as a variable.

My point is this. To make the competition seem fair, it has to have a time period that is the same for all. While you would obviously be pleased as punch if store A had a 50% improvement to reach a score of 75 in one month with no further improvement in month 2, it's kind of demotivating for the manager of store B to be told that getting a score of 98 is less impressive. Furthermore, if A can get to 75% in one month, there is probably something more that can be improved in month 2.

Jeff