the last one has $ 60,000. As an actuary, my job is to determine what to charge each of you for an envelope. In this case, pulling all three envelopes from the hat would get you $ 150,000, so the actuarially fair price for an envelope is $ 50,000. An insurance company adds its profit to that actuarially fair price, so we might charge $ 51,000 per envelope and make a $ 3,000 profit.”
Jim nodded his understanding, so Henry continued.“ What I do is use statistics to evaluate complicated combinations of hats and envelopes. For life insurance, let’ s take a group of 100 people. If the characteristics of this group tell me that I can expect one of them to die this year, and the policies I’ m selling pay $ 100,000 to the surviving spouse, I would have to charge $ 1,000 per policy to break even. Give me a group of 100 people, and I can give you a fairly good estimate of how many are going to die this year.”
There was something about Henry’ s description that made Jim flash back to Harold’ s comments about statistics. Normally, Jim would have found a way to change the topic, but there was a common thread nagging at him, so he let Henry continue.
“ In a group of 1,000 we can predict mortality rates much more accurately than we could in the group of 100, and in a sample of a million people we have outstanding accuracy. Of course, I can’ t tell you which people in a group of a million will die, but we get so close to the actual number, it can seem a little creepy.”
A tiny voice told Jim that something about Henry’ s comments was important, but he’ d heard enough about statistics for one lunch hour and was grateful when David Buchanan’ s voice came over the paging system to summon his brother to lunch. Jim remembered that Harold had mentioned Las Vegas as evidence of the power of statistics.“ Well,” thought Jim,“ maybe it’ s just another example how businesses that understand statistics make big money,” but he felt as though some larger truth was lurking there, just beyond his reach. Returning his attention to his lunch, he decided that he didn’ t mind when statistics lessons appeared unexpectedly, as long as they arrived in small bites.
One Week Later
A week to consider Harold’ s position hadn’ t brought Jim any closer to accepting it. In fact, the carefully organized arguments Harold made last Wednesday had gotten jumbled in Jim’ s head, and Jim wasn’ t really sure why he had considered letting Harold’ s logic overrule his instincts. On his way to see Harold he resolved to stand behind his instincts more firmly. As he walked into Harold’ s office, Jim saw Harold had a big smile on his face and a curious collection of items on his desk— three miniature wooden oars that looked like oversized ping pong paddles and a dishpansized open-top container of white and red marbles.
Jim walked over to the desk and hefted one of the paddles.“ So, Harold, am I in for a spanking?”
Harold chuckled.“ Well, Jim, I don’ t think there is any reason to give you a spanking, but I may just spank some of your old assumptions about sales quotas with that real-world example you asked for last week.”