Who Deserves a commission? HELP with a statistical formula please

#1
If I had introduced punchcards in my restaurant and wanted to positively encourage the usage for my cashiers, how might I decide who has been the most efficient? The stats that I have:
-how many new customers are signed up per cashier
-the percentage of customers signed up, for ex, Bill had 100 transactions and signed up 50= 50% of users were signed up. This automatically factors out any returning customers who have already been signed up since Bill didn't have a chance to sign them.

My first instinct is the amount signed up because I just want as many people as possible. Although, I feel like it wouldn't be fare in a scenario such as the following:
Bill- 100 opportunities to sign customers, 50 enrolled total= 50% signed
Kate- 300 opportunities to sign customers, 100 enrolled total= 33.33% signed

Kate clearly enrolled more customers, although she is not quite as good as Bill. Maybe Bill didn't have as many opportunities because his shifts were slower, or the majority of customers he dealt with were already signed. How do you make a fare decision on who should get a commission for stimulating the program? I also have the stat, percentage of transactions done with the punchcard. Not sure if that's too useful, but we want to encourage it's usage after initial signups of course too.

Any help, comments, suggestions are GREATLY appreciated!!

Thanks,
 

Mean Joe

TS Contributor
#2
My first instinct is the amount signed up because I just want as many people as possible.
You could split the commission. Give Kate commission for signing up the most (she worked hard, it is tough to fault her for not having the best rate since in a lot of things it is difficult to keep up a high rate over time), and reward Bill for his efficiency.

You could also consider: what is the overall (add up all cashiers) signup rate. Is Kate above the average?
 
#3
Thanks Joe. So let's consider the following:
Bill- 100 opportunities to sign customers, 50 enrolled total= 50% signed
Kate- 300 opportunities to sign customers, 100 enrolled total= 33.33% signed
Rick- 20 opportunities to sign, 18 enrolled, 90% signed
Sam- 25 opportunities to sign, 20 enrolled, 80% signed
Jan- 45 opportunities to sign, 0 enrolled, 0% signed
Dan- 40 opportunities to sign, 10 enrolled, 25% signed
Melissa- 50 opportunities to sign, 10 enrolled, 20% signed

You are saying to take the average from the percentage signed, amount enrolled, or total opportunities?

Thanks again in advance!!
 

Mean Joe

TS Contributor
#4
Adding up all cashiers: 580 opportunities, 218 enrolled = 37.6% signup rate.

We can make a few statements now, that should influence your decision:
1) Although Kate signed up the most people, her 33% rate was "below average" of 37.6%. What if Rick was working in place of Kate?
2) If everyone had 300 opportunities, who do you think would have signed up the most people? If you know nothing/have no insight, then I guess you have to go with the guy who had a 90% conversion rate. It is a rather small sample size, but it's likely he would have converted more if he had 300 opportunities.
 
#5
Thanks again Joe!

What are your thoughts on picking the cashier with the most enrollments, that is above the average sing up rate? I feel like that might be a decent compromise. Ultimately in the beginning we want as many as possible. This seems like a more efficient way to me because Bill still did a great job at getting a lot of people, but he also was above the average. Kate did as well, but her performance was below average and hence shouldn't be rewarded.
 

Mean Joe

TS Contributor
#6
What are your thoughts on picking the cashier with the most enrollments, that is above the average sing up rate? I feel like that might be a decent compromise. Ultimately in the beginning we want as many as possible. This seems like a more efficient way to me because Bill still did a great job at getting a lot of people, but he also was above the average. Kate did as well, but her performance was below average and hence shouldn't be rewarded.
I think that's good problem solving. One question: Did you tell the workers about the commission reward program beforehand? If so, what rules did you lay out? You do not want to anger them by "changing the rules in the middle of competition". If you told them beforehand that you would reward whoever did the most signups, and if they are aware of how many each of them signed up (ie they can discuss with each other their own numbers), then you might not want to go back on your word. Maybe Kate decided to work more hours to get more opportunities, to get that commission.