From household income to capital gains, there are boundless possibilities for spinning numbers to score political points.
There are millions more people in the top 20 percent of households than in the bottom 20 percent of households. The number of households is the same but the number of people in those households is very different. In 2002, there were 40 million people in the bottom 20 percent of households and 69 million people in the top 20 percent.
.. Capital gains received in a given year can be paid for value accrued over a number of years. If you paid $100,000 for a home or a business in the past, and then sold it 20 years later for $300,000, have you made $200,000 per year when you sold it or $10,000 a year for 20 years?
At the Applied Mathematics Group−Columbia, dozens of young women bent over Marchant desktop calculators were calculating formulas for the optimal curve a fighter should trace out through the air in order to keep an enemy plane in its gunsights
.. This was a group where Milton Friedman, the future Nobelist in economics, was often the fourth-smartest person in the room.
.. So here’s the question. You don’t want your planes to get shot down by enemy fighters, so you armor them. But armor makes the plane heavier, and heavier planes are less maneuverable and use more fuel. Armoring the planes too much is a problem; armoring the planes too little is a problem. Somewhere in between there’s an optimum. The reason you have a team of mathematicians socked away in an apartment in New York City is to figure out where that optimum is.
.. But the damage wasn’t uniformly distributed across the aircraft. There were more bullet holes in the fuselage, not so many in the engines.
.. The armor, said Wald, doesn’t go where the bullet holes are. It goes where the bullet holes aren’t: on the engines.
.. The reason planes were coming back with fewer hits to the engine is that planes that got hit in the engine weren’t coming back. Whereas the large number of planes returning to base with a thoroughly Swiss-cheesed fuselage is pretty strong evidence that hits to the fuselage can (and therefore should) be tolerated.
If you go to the recovery room at the hospital, you’ll see a lot more people with bullet holes in their legs than people with bullet holes in their chests. But that’s not because people don’t get shot in the chest; it’s because the people who get shot in the chest don’t recover.
.. countries don’t win wars just by being braver than the other side, or freer, or slightly preferred by God. The winners are usually the guys who get 5% fewer of their planes shot down, or use 5% less fuel, or get 5% more nutrition into their infantry at 95% of the cost. That’s not the stuff war movies are made of, but it’s the stuff wars are made of. And there’s math every step of the way.
.. To a mathematician, the structure underlying the bullet hole problem is a phenomenon called survivorship bias.
.. a comprehensive 2011 study in the Review of Finance covering nearly 5,000 funds found that the excess return rate of the 2,641 survivors is about 20% higher than the same figure recomputed to include the funds that didn’t make it.
Hopefully you’re already doing this, if you’re not already tracking month over month growth then go implement it today. If you don’t know your lifetime value or attrition rate then get on those too. But if you do have that and still are unclear how to move the needle on some goal, maybe that goal is increasing lifetime value then we’re at the right place.
.. His example generates a variety of groupings, looking at the surrouding meta data its then possible to discover that:
The age cohort with the grimmest history, of course, is the 15-24 bracket. In real terms, this cohort has the same income as in 1967. However, the 2014 data point is off the 21st century low in 2010, no doubt because it is the cheapest and a relatively abundant source of labor.
