How much is a second pool worth?
It's an absurd question to get your real estate thinking cap on. At the heart of this question, and all real estate valuation, is the law of diminishing returns - or - the more of something you have, the less each unit is worth. This is the reason why tiny bungalows and enormous homes can have the same price per square foot.
The most obvious place to see this law at work is in the value of land. Henrico County was chosen as it has a wide variety of land usages, and a sample of the county will show how the principle applies in all applications.
At first, this seems like a senseless graph. This is the Price/Acre per acre in this time frame. What we see is that the less land you purchase, the more you will pay in price/acre basis. Conversely, as we move to the right, as you purchase more land, the price/acre goes down. But lets look closer...
As we move closer we see a wide variety of data points, but the same trend. Each variant from the median line can be explained by the desirability of that particular parcel being higher/lower than the median (water front, high end plans, busy high ways, etc). If we were to be selective about our sample, we would have the basis of valuing an individual piece of land by performing the power regression represented by the black line and equation above. This equation essentially says, that a perfectly median piece of land in Henrico county is worth...
$44,884 x (number of acres)^-.604
So, land adjustments aren't linear, but rather power-based. Obviously, the "perfectly median" piece of land is rarely what you're trying to value, which is why picking good comparables is ALWAYS the most important step in an analysis.
But what does this have to do with pools?
Nothing in real estate is linear in its contributory value. Imagine for a moment:
What is the value of one bedroom and one bathroom in a 1000sf home ? Throw a number against the wall.
What if that 1000 sf home had 0 bedrooms and 0 baths?
What is the value difference between that and having one of each
What about the 2-4th?
What about the 100th bed and bathroom in a 1000 sf home?
At some point the value becomes negative. The graph would look similar to the above, but the bottom line would cross below zero representing the market's reaction saying, "I need to fix that!" The thought experiment set upon by thinking of "too many" of something in real estate helps us discover the shape of contributory value, and keeps us from being slaves to linear thinking. Just because "$20 per square foot" worked in one appraisal back in 1983 doesn't mean that it worked on all properties, much less today.