I hate to seem to be picking on Kansas City for the moment, but that's where a good amount of stadium activity is taking place.

The good folks of Kansas City are being asked to tax themselves $1 billion to provide roofs for Arrowhead and Kaufman stadiums, and to provide "upgrades" for the stadiums over the next 25 years. The main impetus for a roof over Arrowhead is so that KC can host a Super Bowl (once).

The mayor of Kansas City provides even worse justification:

Kansas City Mayor Kay Barnes highlighted the potential of hosting Super Bowl games, All-Star baseball games, college championship tournaments and extreme sport competitions at a roofed and renovated Truman Sports Complex.

"What if the Jayhawks - or maybe the Tigers - could make it to the Final Four, and that Final Four was held right here in Kansas City?" Barnes said.

KC is already paying more than $220 million for an arena, but alas that is likely to be too small to host a final four. Ok.

Yet, just how valid is the Final Four argument?

There are various ways to skin a cat, but I grabbed the information on the Final Four from 1939-2005. Since 1939, Kansas, Missouri, and (I threw in) Kansas State, have been represented in the final four 15 times. Since 1970, the three schools have made it to the Final Four 8 times.

During the entire sample period, the city of Kansas City hosted the Final Four 10 times, by far the most of any city over the history of the Final Four [mainly because the NCAA was based in Kansas for so long]. However, since 1970, Kansas City has only hosted one Final Four. Both New Orleans and Indianapolis have hosted four Final Fours since 1970, the most in the country.

Assume the allocation of Final Fours amongst cities and the quality of basketball teams is independent (this might not be true, but so be it). Assume further that Kansas City replaced Indianapolis or New Orleans and hosted four randomly allocated Final Fours over the next thirty five years. Finally, assume the quality of MissKansas basketball was the same over the next 35 years as it has been in the previous 35 years, i.e., one or more of the three teams will be represented in eight (randomly selected) Final Fours.

With these assumptions in place, it is possible to calculate the odds that Kansas City will host a Final Four when one of the three MissKansas teams makes it to the Final Four as 0.228x0.114 = 0.026 or a 2.6% chance. How did I come up with that number? Take 8/35 and multiply by 4/35 to obtain 32/1225 which is approximately 2.6% (with rounding).

What proportion of the $1 billion in taxes would the folks of Kansas City consider worthy of "gambling" on the chance of seeing one of the three teams in a KC Final Four? This is impossible to objectively measure, of course. However, the mayor puts forth the Final Four as one of five general "mega events." So, perhaps we could use 20% of $1 billion. However, this number is just too high for a reasonable argument (as we will see).

I am going to take an extremely small percentage of the $1 billion to prove my point. Let's use 1%, or $10 million, for giggles. For the $10 million to be an "even gamble," the benefits to the entire population of Kansas City of seeing one or more of the MissKansas teams in the Final Four in Kansas City would have to be $285 million ($10 million/0.026)!!! Any claim that the folks of KC would value seeing any particular team in a Final Four at this level is simply not credible.

Granted, I have assumed that all of the value of hosting the Final Four in KC rests on the probability that one or more of three MissKansas teams play in the Final Four. This is a strong assumption, but in the end it likely doesn't make much of a difference. For example, let's assume hosting a Final Four (regardless of what teams are involved) yields a $3 value for each of 1 million people in the KC tax jurisdiction. Then, hosting the Final Four would have a value of $3 million, which would reduce the break-even value of the three-team possibility to $270 million. This number is still not credible.

Therefore, while the mayor's rhetoric seems reasonable on the surface, and who wouldn't want the chance to see their favorite college team play in the Final Four in their home town, a little bit of reflection makes it seem completely ridiculous. The Mayor of KC is not unique in this instance. Just about every politician appeals to the local constituency's hopes, dreams, and aspirations. Unfortunately, if the local citizenry were asked for their objective value of the politician's appeal, it is likely to be considerably lower than what the price of the stadium/arena/venue entails.

In fact, this might be one of the worst reasons I have seen proffered for spending considerable tax money to build/renovate a stadium.

[STATA Data File]