A fisherman named Binay hops into his little rowboat hoping to reel in a big catch of his favorite kind of fish, goodfish. He has been reading all about goodfish, and through his research he learned that the average weight of a goodfish is 20 kg and most goodfish weigh anywhere from 18 to 22 kg, and that 5% of all fish are goodfish. Binay’s strategy is to make sure he catches every goodfish that swims by, so he is using a net that catches any fish that weighs at least 15 kg. After 100 fishing trips, Binay has amassed quite the fish stockpile (nearly 100 metric tons of fish, since the net he used can hold 1000 kg of fish at once). He looks through all these fish, and finds that 522 of the 5,394 he caught are in fact goodfish. Initially, he is pleased with his fishing strategy, since 9.6% of the fish he caught were goodfish, which is better than the fraction of all fish that are goodfish (5%).
Nevertheless, Binay thinks he can improve on his methods, so he does some more research. He learned that most of the other fish weigh anywhere from 7 to 23 kg, and that the weight distributions of the fish look like this:
Binay’s goal all along has been to catch as many goodfish as possible. Originally, his strategy was to make sure he caught every goodfish that swam by his boat, but with this new data, he isn’t so sure that this is the optimal method. He now realizes that there is a cost to using the net that catches all fish that weigh at least 15 kg, that is to say, he is catching a lot of fish that aren’t goodfish. He is willing to sacrifice recall (the fraction of goodfish swimming by that he catches) to increase precision (the fraction of fish he catches that are goodfish). In order to make an informed decision on what size net to use, Binay uses data from his fish stockpile to plot the theoretical precision and recall values for various net sizes:
After looking at this plot, he decides to go with a net that catches fish that are at least 19 kg for his next fishing trip, since that will help him catch a higher fraction of goodfish, even though it means a few of the smaller ones will escape. Binay’s next haul has 47 fish altogether, 11 of which are goodfish. He is happy that 23.4% of the fish he caught are goodfish, which is more than double the fraction he was catching with his earlier methods. Way to go, Binay!