Saturday, November 01, 2008

Guest Column #8: A Brief Look at the Econometrics of Sweeney Todd (by fPendl)

[Excerpted with fPendl's permission from his groundbreaking Fermi-problem novel "Freakonomics"]

...Notice, of course, Mrs. Lovitt's comment "With the price of meat being what it is", an obvious reference to the incredible hyperinflation that existed in 18th-century post-Revolution London. However, it is at this point that the unrealistic setting of Sondheim and Wheeler really comes to the forefront.

Here, for the sake of convenience, we'll assume a few postulates in order to simplify our scenario:
1) Mrs. Lovitt's meat pies are about four inches in diameter and more importantly, weigh in with about 4 oz of "meat" apiece- this is about the size of your typical McDonald's hamburger, which we are using for a mass and quality comparison.
2) Despite local variances in pricing due to haggling, variable competition from the fish-monger, and other such problems, we're going to fix the price of meat at about twelve shillings per pound.
3) Not to throw any doubts upon Scotland Yard, but we're assuming a minimal level of competency from the police in investigating Todd's murders.
4) Mrs. Lovitt's is presumably open for lunch and dinner (at least one scene- "The Worst Pies in London" and "God That's Good" is set in each mealtime) and we'll assume she serves breakfast as well.

Now, let's take a look at Sweeney's victims. Assuming male-only victims on what would be in today's standards a slightly deficient diet (1200 cal/day at most, the majority from starch and protein), we can see Sweeney barbering gentlemen not larger than about 5'9" and say, 160 pounds soaking wet. We can divide these body masses into two different segments: inedible bones, organs, gristle etc. and meat (that is, fat and muscle, and given Mrs. Lovitt's well-known pragmatism, liver). From human physiology and our good friend Pierre Alfredo we know that the inedible composes a large proportion of the human body mass *up until a certain point* at which adding more bone structure, larger heart etc. is simply a diminishing-returns game and muscle (which is heavier by volume) becomes the majority of weight gain. However, this point is far beyond the parameters of our scenario so it is safe to say Sweeney's victims will have about 20% of their body mass be meat or about 32 pounds (384 shillings worth).

Some quick arithmetic tells us that this works out to 128 4 oz servings of meat pies per victim. Now it gets interesting.

Mrs. Lovitt's, at the peak of its operation, is shown to contain at least 20 guests at dinnertime, which, extrapolated over a 4-hour dinner time, is 80 guests a night. Add in about 20 guests over a 3-hour combined lunch/breakfast period and you have a total of 100 hungry chorus members demanding more hot pies.

Assuming each member eats only a single pie, that's 100 pies needed per day...which translates to 600 pies per week (Sundays off)...which translates to 2400 oz, or 150 lbs. Think about that for a second. That would mean Sweeney and Mrs. Lovitt would need to kill 4.6875 people *per week* to be able to sustain their business model.

Let's go a little further into Sondheim and Wheeler's delusions. When Anthony goes to retrieve his lovely Johanna from the mortgage, she specifically says, "We were to be married on Sunday- that was six months ago!" That day goes with the same day that Sweeney and Mrs. Lovitt begin their business plan. Some more arithmetic goes and shows that Sweeney would have had to kill about 112 people in order to keep the pies a comin'.

That is, of course, assuming all of the meat could be used at once.

If we allow for more inefficiency in the process, the amount of bodies required jumps again: without a refrigerator to store meat, they would have to cook 128 pies at once to avoid wasting any, and although the furnace is large enough for Mrs. Lovitt to be burnt in at the end of the musical, it is highly unlikely that a single woman would be able to cook 128 pies at a stretch four times a week while also renovating her establishment to a more-reputable place.

But let's give them some dramatic license and say that Sweeney murdered only about 112 people over the course of six months. The average murder rate in many modern cities is less than 10 per 100,000 people per year (http://wheelgun.blogspot.com/2007/01/crime-in-uk-versus-crime-in-us.html), except in Washington DC, because that's like, where the President lives and everything; take away guns, gang feuds, and modern transportation and you could easily cut that number in half. Given that London's population was about 1.5 million in the 1800s, we reach an average murder rate of, at most, 150 per year. Sweeney nearly doubles the rate in SIX MONTHS. As incompetent as the police are, you think they would have noticed a trend in the disappearances?

Now, the investigative methods...

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