Funny Things, Numbers
Tom: Good morning, Jim and Dan. We all know why we’re here. You’re relative newcomers to rifle shooting and you’ve asked me to set up a little contest for the two of you. I’m happy to do that. I want you to fire for two fifteen-minute periods, with a break of half an hour between them. You can each fire as many rounds as you wish on both occasions. The only thing that matters is your total number of shots, divided by the bulls you score, giving you an average of shots per bull. The decisive factor will be your scores over the two rounds, taken in total.
You have one target each for the first round and I’ll put up fresh ones for the second. Bear in mind your inexperience and don’t be surprised if you get very few bulls. They’re quite a long way off and those circles in the middle are pretty small. To put things in perspective, I had a short session yesterday, using an identical target to the ones you have, at the same distance. I’m considered a pretty fair shot but I got only ten bulls with thirty-five rounds.
Your magazines hold five bullets, so you’ll most likely need to reload a few times. For that purpose you each have a box of replacements. You’ll also see that I’m providing you with a spare rifle apiece, in case of jamming or overheating.
I’d like you to take up your positions, Jim facing the right-hand target for the first round, then you’ll swap places for the second. When both of you have called out that you’re ready, you’ll hear a buzzer to give you the start and finish signals. I’ll keep score. Let me remind you that the prize is a bottle of brandy.
One hour later.
Tom: Well, here we are. It’s all over and I have your scores. Jim, in the first round, you fired sixty-four shots and got four bulls. Dan, you went rather slower. You fired thirty-six shots and got two bulls. So the first round went to Jim, with an average of one bull per sixteen shots against Dan’s one per eighteen.
Now to the second round. Jim, you slowed down quite a bit, presumably trying for greater accuracy. Well, you got it, with thirty-two shots, including four more bulls. Dan, you went a good deal faster than you did in the first round, with sixty-three shots, seven of which were bulls. So that round went to Jim too, with an average of one bull per eight shots against Dan’s one per nine shots.
Jim: Good. Hand over the bottle, Tom.
Dan: Wait a minute. That’s not right.
Jim: Hey, don’t be a sore loser, Dan. You heard what the man said. I won both rounds, so where’s the argument?
Dan: I’ll tell you where it is. Tom, you said that the prize was to go to the man who did best in total.
Tom: That’s right.
Dan: Well, there’s no dispute about Jim having won the two rounds taken separately, but overall he fired ninety-six shots and scored eight bulls. That’s one bull per twelve shots. I fired ninety-nine times and got nine bulls. That’s one bull per eleven shots. I win.
Tom: He’s right, Jim. It seems crazy, but you won both rounds and lost the contest. Funny things, numbers. Here’s your bottle, Dan.
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