Seattle v. Math

When Tim Burgess fired his most recent salvo in the War on Guns, it came as a proposal to tax guns and ammunition sold within Seattle city limits. His proposal was accompanied by a staggering statistic – a City Budget Office estimate that the tax would bring $300,000-$500,000 new revenue to the city, to be used for a violence reduction program.

I am the proud owner of one of only two Seattle’s dedicated firearms stores, and boy –do these numbers disagree with what I see at the cash register! $300k in tax revenue would require sales of 10,000 guns AND a million rounds of ammunition a year. Nothing I am observing in the local market comes anywhere near that.

Then, The Seattle Times article by Daniel Beekman came out and shed light on the methodology used by the City to arrive at this estimate.

What they did was take the total number of background checks in the state of Washington, divide it by the total number of federal firearms licensees (FFLs) in the state, and multiply it by the number of licensees in Seattle, of which they counted 22. From this they deduced the $300,000-$500,000 range. Glen Lee, the City’s finance director, was quoted by The Seattle Times saying "We feel confident that the range we’ve provided is relatively conservative".

Now, anyone who has taken Statistics 101 knows quite well that a confidence interval cannot be derived from an average alone, and this case illustrates why.

The majority of people and companies with firearms licenses do not actually sell guns. These are gunsmiths, importers-exporters, very small "kitchen table FFLs" that only do Internet transfers, tiny pawn shops (that reserve the right to take a firearm in, but never really do), and the like.

Of the companies which actually sell new guns to the public we have Precise Shooter with about 100 sales a month, Outdoor Emporium - which has the same inventory size – perhaps a bit more, but nowhere near an order of magnitude more, and 4 more very small players like three Big 5 locations and Discount Gun Sales, which have one tenth of the inventory of Precise Shooter.

Tim Burgess often talks about Cook County, IL, which generates $800,000 per year from a similar tax. But Cook County is ten times more populous than Seattle. And if you scale that number to Seattle’s population, you would get $80,000, not $300,000-$500,000. Further, this assumes that customers would not choose to simply go to one of the 10 stores just outside of Seattle city limits where the tax would not be collected and the prices would be dramatically lower. Which is not such an easy option in Cook County as it is ten times bigger.

All this merely illustrates that fact that in order to know the confidence interval, you need to know more than the average. You have to understand the distribution itself. In a room with 99 average people and one Bill Gates, the average income in this room will be humongous, but the 98% confidence interval will be far more modest. This is what we are dealing with here.

Yet the City’s finance director has just made the claim that he can derive a confidence interval from the average alone – a mathematical impossibility. Understanding of statistics must be a minimum job requirement for anyone dealing with the money professionally, much more so for someone who is in charge of finances for the United States' 20th most populous city.

This scares me. Regardless of where you stand on the gun issue, the fact that City Council is to make a decision based on a number so completely bogus should concern anyone. What other financial or business decisions are made based on data so horribly wrong, and the ability to analyze it so awfully lacking? Should we perhaps be looking for more mathematically inclined – or maybe, just more logical – city managers next election season?