The blurb for this blog suggests that we might talk a little baseball. As the chances of the Red Sox winning the AL East and my team winning the Kellogg Operations Fantasy Baseball (yes, it exists) are spiraling down the toilet, it seems a good time to talk about baseball stadiums and, well, toilets. Both the Mets and Yankees opened new stadiums this year and just as surely as the Mets will not win anything besides a high position in the draft, this means that some reputable news source will publish a pun-filled story on how many women’s restrooms the new stadium has. In this case, the New York Times did not disappoint (New Ballpark Statistic: Stadium’s Toilet Ratio, April 12, 2009). You may snicker at the headline, but they — unlike the Dallas Morning News — at least kept the loo humor out of the title (Cowboys’ billion-dollar home is flush with restrooms, June 5, 2009.)
What is it about a new sports arena that turns headline writers into eighth grade boys? It’s the law. Not a law of nature but regulations now in many cities that require new and renovated public facilities to have a fixed ratio of women’s to men’s toilets. These are generally referred to as potty parity laws. The impetus to pass such laws usually follows from the casual observation that at public venues ranging from sports arenas to airports to concert halls women generally have much longer waits to use the restroom than men. Next backers run out data establishing that women just take longer to use the toilet. (I refuse to go into specifics here but will note that the usual ratio quoted is that it takes women twice as long as men.) The end result is a required ratio of women’s to men’s rooms. In New York City and the state of Texas, the mandated ratio is two to one.
As my colleague Gérard Cachon has noted, this is a queuing problem. There are possibilities to mitigate delays in queuing besides adding capacity but many seem unlikely to work here. It’s hard to imagine that New Yorkers in general (and Yankee fans in particular) would tolerate having to get an appointment to relieve themselves. Thus adding capacity seems the only option.
The problem is that the mandated ratio is almost certainly wrong. The goal, presumably, is to equalize the waits. A two minute wait in the women’s room would likely be seen as fair if the wait in the men’s room were also two minute. The problem with the status quo is that the wait in the women’s is often much longer than what men are experiencing. There is no guarantee that a boilerplate two-to-one ratio of capacity will always deliver equal waits. The New York City Council cannot regulate the ratio of men to women at a Mets’ game or at a Broadway show. When there are far more men than women at a ballgame, the women might have a much shorter wait while a female dominated audience at a play might still result in long waits at the women’s room even if there is the same ration of women’s to men’s restrooms. Indeed, the Chicago Bears asked for permission to convert some women’s rooms at the renovated Soldier Field to men’s rooms to reduce delays at the latter (Bears ask for potty break, Chicago Sun-Times, April 23, 2004).
The question then is whether an imperfect but mandated solution is better than a free-for-all that results in poor and unequal performance. It seems that here the answer is yes if for no other reasons that in many cases — Soldier Field not withstanding — potty parity results in more capacity for both sexes (as is the case at both New York ballparks and the Cowboys’ new stadium).
But it is not clear that every government imposed to manage queuing systems is good. For example, California mandates a nurse to patient ratio for nurses in surgery wards. The state of Victoria in Australia has similar rules and legislation has been proposed in Massachusetts (Nursing ratios save money and lives, Boston Globe, July 9, 2008). The California rules require no more than five patients per nurse. This effectively fixes a nurse’s utilization and ignores the inherent economies of scale in queuing system. If this results in adequate staffing in a small ward, it means that a large ward has an inefficiently large and costly staff. Alternatively, if this gets staff right in a large ward, patients in small wards likely face delays in getting a nurse. One suspects that mandated potty parity ratio work because they are not that sensitive to scale. Nursing ratios will depend on scale and have different implications for small versus large wards.