About Landing (Revisited)
For 2215 landings (up until my 10/9/15 Grand Rapids, MI post), I have had my computer (using Excel) calculate my random latitude and longitude for each landing. I programmed Excel so that it simply takes the difference in latitude from Canada to Key West, and multiplies it by a random number that is between zero and one. That gives me a random latitude between the two extremes. Similarly, it then takes the difference in longitude from Maine to Washington and multiplies that by another random number to generate a random longitude. In this way, I get a specific random location in the lower 48.
But you know, I’ve always been troubled by the peculiar distribution of oversubscribed (OS) states (i.e., those states where I land more than I should, based on area) and undersubscribed (US) states (those states where I land less than I should, based on area). And really! Why is Texas soooo US? And why is there a block of OSers across the northern states? Why is there a block of USers stretching from NM across to VA?
My answer has always been: The Landing God makes it so. Well, my son Jordan (an avid follower of my landings) has also been troubled by the skewed distribution of OSers and USers, and he didn’t buy my Landing God hypothesis (especially after 2200+ landings). So he actually thought deeply about it, and sent me this email:
Your lat longs are random, which is of course a fair way to do it, but there might be a flaw with it. Latitude is fine, as the distance between parallel lines is always the same. However the distance between lines of longitude varies based on latitude and the lines are not parallel. Take this map for example:
Look at your most OS state, Montana and compare it with your most US state, Texas. The distance between W 100 and W 110 is significantly less near Montana than it is near Texas, meaning that your landings are bound to be more dense up north and less dense down south.
Ouch. He had more to say, but when I read this, I knew he was on to something big. The most important statement is the one I highlighted – and it is absolutely true. I emailed Jordan back:
This is really sinking in. In a way, I’m devastated! What do I do now? Do I attempt to do a mathematical adjustment on the whole OSer / USer calculation? Do I try to amend the whole random lat/long generation process? But now, after 2200 landings? And what about my Score? There’s no way it’s inevitably heading towards zero . . .
The typical first paragraph of every post is crumbling before my eyes . . .
So I took the map that Jordan sent me, and added OS (for over-subscribed), US (for under-subscribed) and PS (for perfectly subscribed):
As you can see (as I was discussing earlier), Jordan’s general point holds true: there are more OS states up north and more US states down south. In particular, look at the block of OSers stretching from Oregon & Washington east to Michigan (and over to NY if you’d like). The one exception (thanks to the Landing God) is Idaho.
Down south, it’s a little more of a mixed bag, but look at CA through VA (following the border and coast). With the exception of AZ, LA and MS, it’s a block of solid USers.
So, I took a deep breath and went online. Amazingly, I found a site – GeoMidPoint.com – where you can enter a “rectangle” based on latitude and longitude, and it picks out a random location from inside the rectangle! And, as the website says:
All flat maps distort the size and/or shape of the continents and other features to a certain degree. On a Mercator projection map, for example, Greenland appears to be the same size as South America although it is actually eight times smaller.
The Random Point Generator solves this distortion problem because the calculation it uses is based on the spherical earth, and therefore when the calculator throws a virtual dart, all points on the earth’s surface have an equal probability of being chosen.
So, beginning with landing 2217, I have been using the Geo Midpoint program to get my random locations.
I can’t help myself – I’m still interested in tracking the states that are oversubscribed / undersubscribed
I had several versions of my landing spreadsheet. But at a minimum, I was keeping track of what state and what river watershed I was landing in. I began to notice that I seemed to be landing in some states more than I should, and in other states less than I should. What I mean is that, intuitively, I should be landing more often in Texas than, say, in Ohio. But after 100 or so landings, I’d find that I had more landings in some smaller states than in bigger states. This is just a statistical quirk, due to the random nature of the whole process.
I came up with a spreadsheet function that allowed me to quantify the statistical quirk just mentioned. Here’s what I did:
I figured out how to determine exactly how many landings each state “should” have, based on its area. For example, Texas contains about 9% of the area of the lower 48, so it “should” have about 9% of the landings. I had Excel do a similar calculation for every state. I could then keep track of whether a state had more landings than it should (in my head, I called that being “Over-Subscribed”), or if a state had fewer landings than it should (I called that being “Under-Subscribed.”)
I’m no statistician, but I kind of knew that if I did a million landings, I’d end up with pretty close to every state having very close to their “correct” share of landings. I came up with a way to measure how out of whack I was relative to the “correct” number of landings for the various states. For any given state, I determined the difference between the following two values:
[The percentage of total landings that a given state should have based on its area]
[The percentage of total landings that the given state actually has]
I then add up the differences for all 50 states. (For math-oriented readers, I add up the absolute differences.) Anyway, generally speaking, this sum inevitably starts out larger and gets progressively smaller as I land in additional states (headed toward a theoretically-nearly zero value after many, many landings, say a million just for the heck of it). For no good reason, I multiply this number times 100. I call this number my Score. (More about this later).
It turns out that the Score gets lower when I land in an Under-Subscribed (“US”) state, and the Score gets higher when I landed in an Over-Subscribed (“OS”) state. Every day that I land, I find myself rooting for USers and rooting against OSers. I want the Score to get lower, and am excited when I hit an all-time low.
Here’s a table showing my Score on a state-by-state basis, 29 landings after changing my random lat/long methodology:
The negative numbers reflect states that are undersubscribed (i.e., states where I haven’t yet landed) and the positive numbers reflect states where I’ve landed at least once. Note that states where I’ve landed multiple times are the most OS (check out Texas!). Also note how the area of the state enters in to the calculation – note that California is at -53 while Vermont is at -3; even though I haven’t landed in either state. Also: see that Colorado’s Score is 0? This, coincidently, means that after 29 landings, I should have landed in Colorado once, which is exactly what happened.
So, going forward, I’ll be keeping track of my Score; bemoaning oversubscribed landings and being happy about undersubscribed landings . . .