The price of fun

When I was just beginning as a safety analyst, I remember being very surprised at the cost of play equipment. It seemed so high! A medium-sized piece of modular equipment will cost several thousand dollars - and, with installation, a couple thousand more - and playgrounds can be much, much more expensive than that. A new playground in Sydney is slated to cost more than 8 million dollars!

Yet, is this a high price to pay? Let's do a few numbers. Suppose you, the superintendent of a playground, are in charge of what piece of equipment to buy. You have two options: High and Low. High costs $15,000 fully installed, and Low costs $5,000 fully installed. Assume that High and Low are both equal in terms of the amount of joy they bring to the children. They are NOT equal, however, in either their durability or their safety: High will last for 10 years before it needs to be replaced, and implies a 10% yearly injury risk (so, there is a ten percent chance in any given year that a child will incur a hospital-worthy accident on it). Assume that Low will last for 6 years, and implies a 15% injury risk. Assume, finally, that any hospital-worthy injury incurred on the play equipment will necessitate a $20,000 financial settlement.

So! We must balance these probabilities. First, the aging: correcting for the difference in durability, we have that High costs the owner $1,500 per year (which is just $15,000/10), and Low costs $833 per year (which is just $5,000/6). Now, each year they are operational, High has an expected loss of .10*$20,000 (the probability of an injury happening times what it would cost the playground owner if the injury DID happen), or, $2,000. Low has an expected loss of .15*$20,000, or $3,000 by the same reasoning. Add them all up and you get that High actually costs you, Mr. or Mrs. Playground, $3,500 per year, and Low costs you $3,833 per year!

So, there we have it: it can make financial sense to invest in high-quality equipment for your playground. My Uncle Nick used to tell me never to skimp on what I put on my feet, or what I put in my car; now, I can add to that list, what I put on my playground!