Jim noticed a matrix of five rows and 10 columns of marble-sized dimples on the paddles.“ Harold, what do you have in mind, exactly?”
“ I am borrowing this right from W. Edwards Deming,” said Harold.“ He was famous for using paddles and marbles to illustrate his ideas, and I am going to adapt Deming’ s example somewhat to illustrate my point. You were having trouble accepting that salespeople who worked equally hard and were equally smart could have significantly different results. This will show that when you eliminate the effects of skill and hard work from the situation you still can get results that are just as far apart as the results we discussed last week.”
1
“ What is this supposed to prove, Harold?”
“ If I can show you that we can get very different results even when the effort and skill are exactly and precisely the same, then you should be able to genuinely embrace statistical thinking instead of just feeling that I bullied you into agreeing because you didn’ t know enough math to fight back.”
“ OK, what do we have here and what do you have in mind?” Jim asked.
“ What we have here are 5,000 very well-mixed marbles— 2,500 white and 2,500 red. Let’ s say when you draw a white marble, it means none of the things that prevent a sale from happening occurred, and in that case the salesperson always gets the sale. Drawing a red marble means something got in the salesperson’ s way and the sale wasn’ t possible— the customer service person was rude, or we were out of stock or we couldn’ t match the competitors’ price.
“ Each salesperson dips a paddle into the pile and draws out 50 marbles. We already have stipulated that all the salespeople are equally hard-working and smart, and the 50 dimples represent the 50 calls that are the most a salesperson can make in a given week. So let’ s do an experiment and we’ ll see how well they perform. To give everyone an exactly equal chance, we return the marbles to the bin and remix them after each pull, so each salesperson has exactly the same chance to pull out white marbles. And as long as it’ s my experiment, I’ m going to name the salespeople Hamilton, Jackson and Franklin, and the sales manager Grant. You get to dip the paddles to choose the marbles, and I’ ll keep score— one for white and zero for red. So let’ s see how our sales force did on their first week, shall we?”
Jim dipped the marbles from the bin, and Harold recorded the results on a chart.( Figure 1.)
“ Grant interprets these numbers without understanding statistics,” says Harold.“ In Grant’ s words:‘ Looks like Hamilton didn’ t quite hit his target and Jackson is in a bit of trouble, but it’ s bonus time for Franklin!’”
Jim stirred the marbles from his first pick back into the bin, and then dipped each paddle into the marbles again. Harold charted the results again.( Figure 2.)