One of the more interesting books I’ve read in a quite while, but not exactly a curl-up-on-the-couch kind of book. Takes an engaged and active mind to really understand what the author is communicating through his many historical narratives, numbers-based mind benders, and statistical reasoning. I could take this review any number of ways, but this is a blog mostly about outdoor things, so I’ll try to keep my few observations as on topic as possible.
But heck, this is about randomness, so I’ll be random. My daughter scribbled this on her etch-a-sketch. It’s awesome…and random.
The odds of rolling two 6′s with dice is based on probability, it’s not random. But here’s a fallacy of throwing dice, if you throw 10 sets of dice and don’t get a 6, your odds are no better of achieving that 6 on your next throw. You’re never “due” as we like to say. Dice rolls are INDEPENDENT outcomes, which essentially means that the outcome of the last dice roll (or of the last 50 rolls) does not influence your next toss.
How does that apply to the outdoors? Well, I know a good many people who sit in the same deer hunting stand year after year after year, and proclaim that they are due.
For those who do this year after year unsuccessfully, maybe you should re-evaluate! But for those who are occasionally successful, the “I’m due” phenomenon is all too often mentioned. No, for your deer stand, there is a probability of annual success – let’s say it’s 16.67% (same as tossing a specified number with 1 roll of a die). This essentially means that you can expect to kill 1 deer every 6 years. Expect is the key word, 1 out of 6 doesn’t mean those are the results you will actually experience. You may get back-to-back success years, this doesn’t sentence you to 10 consecutive unsuccessful years in the future. One year’s outcome does not influence the next’s. Makes my head spin just thinking about it. If I was as good a writer as Leonard Mlodinow, perhaps this wouldn’t be so confusing.
The bell curve or normal distribution. One of the most frequent questions I got asked during my time in Alabama was this – “what is the antler score of the average mature Alabama buck?” They asked, so I’d answer, usually somewhere in the 110-120″ vicinity. Inevitably, they would bark at me that there is no way that’s the average because they just killed a monster 130″ buck just last weekend. Welcome to outliers in normally-distributed data. The shape of a bell curve is centered on the mean or average, and the spread or width or narrowness of the curve is based on the standard deviation. If you look at the %’s in the figure above, you can see that 95.44% of the bucks can be expected to score within +/- 2 standard deviations of the average. 100% – 95.44% = 4.66% leftover. By dividing that 4.66% by 2, we get 2.33% (roughly in 1 in 43). That means for every 43 bucks that are shot, you’re going to get a really low outlier (think 8 year old 4 pointer with 10″ spread) and one really high outlier (think 4 year 12 pointer with 19″ spread and grossing in the upper 160s).
Here’s a couple other examples:
The values on the horizontal axis represent the change in antler score from one year to the next for a mature whitetail buck in south Texas. “Let em’ pass this year, he’ll be way bigger next year.” Maybe, maybe not. The bell curve I’m staring at here suggests it’s a total coin toss. Some will blow up, note the 2 animals all the way at right that added 40″ of antler growth. Some will shrink drastically, look far left. A lot will experience menial/insignificant change.
I defend my answer for Alabama bucks. Here’s a chart based on deer from the Faith Ranch in south Texas, data courtesy of Texas A&M University folks. Go to south Texas to shoot a B&C buck right? Well, how’s 5 out of 251 mature bucks strike you? Dad and I saw this exact scenario play out back in 2007 when we went down to the mighty King Ranch to assist a helicopter deer capture operation for a couple days. We (our group collectively) handled 70 or 80 different bucks in that amount of time. 0 170″+ bucks. MAYBE 1 160″ buck. The King Ranch!!! Numbers don’t lie.
Back to random, my 3 years and 7 months old daughter (slightly older now) created this beautiful work of art.
Take a minute to “see” the horse and then marvel at her random work of art. Seriously, it’s random scribbling. Random, huh?!?!?! Kind of like seeing a Mother Mary apparition in a piece of French toast.
Back to the book “The Drunkard’s Walk”, I highly recommend it. It will alarm you how badly you understand probabilities, randomness, and numbers in general. It’s even more alarming to see how our lives might look very different if we did understand those things better. Very entertaining read with examples ranging from the New York Yankees to OJ’s murder trial to Vanna White to Hollywood movie producers. It’s eye opening.