Ones and Twos, Twos and Threes

Organized basketball has some different scoring rules from pickup basketball. In organized basketball, a regular shot is worth two points and a long shot is worth three. In pickup, a regular shot is worth one and a long shot is worth two. Also, in pickup half-court games, most people play that the team that made a shot gets the ball again ("winners"), while in full-court games (pickup and organized), the team that made a shot does not get the ball ("losers").

This has some strategic implications. To take an extreme case, suppose you're playing with 1's and 2's, and ignore offensive rebounding and turnovers. In losers, a 51% chance at a 2-pointer is better than a 100% chance at a 1-pointer. In winners though, if you can make a 1-pointer 100% of the time and you can get the ball, you always win.

Suppose you can make a regular shot 50% of the time, and again, assume no offensive rebounds or turnovers. What percentage do you need to shoot a long shot instead?

If you're playing with 1's and 2's, losers, it's 25%
With 1's and 2's, winners, it's 33%
With 2's and 3's, losers, its 33%

If you can make a regular shot 33% of the time:

If you're playing with 1's and 2's, losers, it's 16.7%
With 1's and 2's, winners, it's 20%
With 2's and 3's, losers, its 22%

As a side note, if you're in an NBA game, you should generally feel indifferent between a 3-pointer and a 2-pointer if you're 50% more likely to make the 2. But if you deciding between a 2 and a 3 at the very end of a game, making a 3 means that you definitely win, where making a 2 means that you're going to overtime. So assuming that you think you have a 50-50 shot in overtime, you need to be twice as likely to make the 2 as the 3.

Taxi Regulation

I am a Matthew Yglesias supporter but I don't agree with this post about taxi regulation: http://thinkprogress.org/yglesias/2011/06/20/248717/market-prices-can-match-supply-and-demand-of-taxis-and-taxi-drivers/ He argues that there is no reason for government to restrict the number of taxis and that the only reason for restrictions is to protect incumbent taxi drivers. To see why this is not necessarily correct, consider a very simplified version of the market for taxis:

Suppose there is a fixed number of taxi rides every day, riders don't care if they have to wait, and there is a fixed price for the rides. Also, a potential taxi driver is choosing between being unemployed and earning 0 and driving a cab, which will earn him (1000 / N - 50) dollars per day, where N is the total number of taxi drivers. That is, there is $1000 in daily revenue to be divided up by all of the cab drivers, and each driver pays $50 per day in costs of gas, etc.

In the free market there will be 20 cab drivers: each one earns $50 of revenue every day and pays $50 in gas, for a net of 0. No one wants to enter the cab driving market because they would be the 21st driver, and earn negative profits. No one wants to leave because they earn zero either way (assume that if they choose to work and earn 0 rather than be unemployed).

But this is actually a pretty terrible result for society. The world would be much better off if there was only one cab, who collected all of the revenue, and earned a profit of $950 per day. The government could enforce a medallion system where there was only one medallion, which cost $950 per day. Then everyone would earn a net of 0, just as in the free market system, but now the government has an extra $950 to use to give unemployment benefits or anything else. Note that in this system there would be people who tried to drive people around for money, and presumably Yglesias would say they should be allowed to do so. But they should not.

Of course, the taxi market is much more complicated than this. For one thing, consumers benefit when there are more cabs (because they do dislike waiting). But in any case, this effect - the reduction in productivity of all cabs caused by the entrant of one more cab - is real. It is possible that a number of different effects will perfectly offset and that the competitive equilibrium associated with free entry will give the perfect number of cabs, but that is a difficult claim to make and it is not sufficient to announce "Free markets!" and declare victory.