Diving in the Shallow End

on February 14, 2024 Three Six Mafia Most guys my age have "the chat". The one with your college buddies that only exists to share memes, argue, bully, and occasionally announce that you got a promotion or had a kid. I am like most guys. Recently the discussion switched to the Three Six Rule. The idea that, to be date-able, a guy must be a 6 in 3 categories: 6 figure income 6 feet tall 6 inch pecker I'm pretty far from 6 feet. You can make any other assumptions you wish. However, I'm happily married. What's the deal? Was my wife ignorant of the rule; did she take pity on me? Or perhaps it's possible to compensate for poor performance in one area with exceptionalism in another. If so, what is the conversion rate and is there an opportunity for arbitrage? These are the important questions of our day. The Approach Back in your very first stats class you probably talked about the heights of third-graders, and someone drew a pretty bell curve. Distribution of heights is like bell curve 101, and bell curves are incredibly useful. With just two numbers, a mean (μ) and standard deviation (σ), you can describe an entire population and run all types of analysis. Where I live in the USA being 6' or great is actually pretty rare. 91% of all adult men are below this height. However, older people tend to shrink with age and are far less likely to be in the dating pool. Especially for a connoisseur of the Three 6 Rule. Let's only look at American males between the ages of 20 and 30. Height Distribution of Males aged 20-30 $$\mu = 70"$$ $$\sigma = 3"$$ A height of 6' is roughly at the 75th percentile. Hold up, percentile? We're not talking about SAT scores you nerd. We're drastically eliminating men from the dating pool based on three arbitrary numbers. Let's subtract it from 1 and call it an "Exclusivity Score". Much better. By eliminating guys under 6' we have removed 75% of the population from the dating pool and are left with the top quartile of most exclusive men. In a room of 100 fellas, 75 aren't even worth talking to. Now what about pecker size? Fortunately, this also follows a pretty standard bell curve and there's public data so I don't have to do my own research. A 6" wiener is even rarer than being 6' tall. The average erect penis length is 5.166" with a std dev of 0.654". Erect Penis Length Distribution $$\mu = 5.166"$$ $$\sigma = 0.654"$$ Do the math, carry the 1, and a 6" pecker puts you right at the 90th percentile for an Exclusivity Score of 10%. In that same room, we've eliminated 90 of them for having the pedestrian member of a mere mortal. The 10 guys left are the cream of the crop. Getting Too Big for Our Britches Here is where we starting getting a little dumb. I've got a room of 100 potential dating partners. 25 of them meet my height criteria while 10 of them have exclusive enough peckers. What are the odds that somebody is in both groups? To combine the odds of two independent actions, you just multiply them. The odds of rolling a die and getting a 5 are 1/6. The odds are doing it a second time are also 1/6. So the odds of rolling 5 two times in a row are: $$\frac{1}{6} * \frac{1}{6} = \frac{1}{36} = 2.778\%$$ What if the actions aren't independent? If I take a deck of cards and draw one randomly, there is a 1 in 2 chance it is red. If I keep that card, what are the odds the next card I draw is also red? It's not 1 in 2. The deck now has 51 cards, 26 black cards and 25 red cards. On my second turn, the odds of drawing a red card are 25 in 51. Just slightly worse than 50/50. The odds of the second action are dependent upon the first action. The odds of drawing two red cards in a row are: $$\frac{1}{2} * \frac{25}{51} = \frac{25}{102} = 24.51\% $$ Height and pecker length seem to be correlated, but there isn't a lot of great data out there. But generally speaking, a taller person is more likely to have a longer pecker. Since we can't model this relationship with a high degree of confidence, and because this exercise is incredibly low stakes, we're going to ignore it. While there appears to be some dependent relationship between height and pecker, I'm going to treat them as two independent events. So back to these two groups of 25 and 10 guys. Since we're treating them as independent characteristics we can just multiply the odds to arrive at our Blended Exclusivity Score. $$\frac{1}{4} * \frac{1}{10} = \frac{1}{40} = 2.5\%$$ Now we're talking! The Three 6 rule is really starting to shine in it's ability to enforce exclusivity. In a room full of 100 random guys, you may find two or three that can meet our criteria so far. Let's Talk About Money Humans have gotten bigger over time. However, I've yet to see height or pecker size in any CPI basket-of-goods when measuring inflation. Neither party's economy policy is to blame for the rising cost of peckers in the grocery store that is destroying the middle class. The heights of American men aren't driven by interest rate policy. Incomes are. So when we talk about a 6 figure income, we need to nail down a date. For now we'll look at 2014 since that is the most recent data I found. The other trouble with distributions of income is they aren't normal. Look at that long tail off to the right. But if we take the natural log of our incomes, it suddenly becomes normalized with a mean of 10.8 and standard deviation of 0.758. We can always convert our values back to dollars by raising e to that number as the exponent. Income Distribution Normalized with Natural Log $$\mu = 10.8$$ $$\sigma = 0.758$$ Taking the natural log of $100k gives you 11.513 or an Exclusivity Score of 17%. To illustrate that 11.513 corresponds to $100k we can quickly check: $$e^{11.513} = $100,007$$ Setting a Baseline We already talked about the odds of finding someone in a group of 100 guys that is both 6' tall and 6" endowed. If we add in their salary we arrive at our Improved Blended Exclusivity Score. $$BES = \frac{1}{4} * \frac{1}{10} * \frac{17}{100} = \frac{17}{4,000} = 0.425\%$$ In a gaggle of 100 suitors, it's actually unlikely that a single one will meet all three criteria. Perfection. We now have a truly unreasonable set of standards by which to choose our dating partner. Even better, we now have a standard by which we can measure other permutations of height, pecker length, and income. As long as we remain more exclusive than 0.425% of the population we can explore the data and start to answer the big questions: Can you still date someone that is 5'3" if their income is $200k+? How tall does someone need to be to compensate for a micro-penis? Is there a pecker length at which height and income become irrelevant? Sure, we're not following the letter of the law, but Jesus told me to follow the spirit of the law. I'm pretty sure this is what he was talking about. Diving In Let's hold income steady at $100k for a bit and focus on just height and pecker so we can start building a model for conversion. Remember that our mean height is 70" with a std dev of 3". This means that for every inch we grow, we move 0.333 std dev from the mean. At 6' we are 0.666 std dev from the mean. Meanwhile, every inch that our pecker grows moves us 1.53 std dev from the mean. An inch of pecker is worth a lot more than an inch of height when measuring our Blended Exclusivity Score. How much more? We already determined that our target Blended Exclusivity Score (BES) is 0.425%. If we hold salary constant at $100k, which has an exclusivity score of 17%, we can choose any length of pecker and determine the minimum height required to reach 0.425%. $$ES_{Height} * ES_{Pecker} * ES_{Salary} = BES$$ $$ES_{Height} = \frac{BES}{ES_{Pecker} * ES_{Salary}}$$ $$ES_{Height} = \frac{0.425\%}{ES_{Pecker} * 17\%}$$ Since we need to use Exclusivity Scores (ES), not inches, we will use some excel functions to make this easier. To find the ES of a certain pecker we type in: $$ES_{Pecker} = 1 - NORM.DIST(Length, \mu_{Pecker}, \sigma_{Pecker}, true)$$ To take an Exclusivity Score and convert it back to a height we just do the inverse function: $$Height = NORM.INV(1 - ES_{Height}, \mu_{Height}, \sigma_{Height}) $$ If we build a table for various pecker lengths roughly between -3σ and +3σ and throw it on a chart, we get something like this. Notice that for 6" peckers we need the predicted ESHeight of 25% which corresponds to 72": Now this is an interesting chart. On the shorter end of the penile spectrum our height is essentially flat at almost 6'6". At the extreme short end of pecker length there is very little exclusivity difference between 3.25" and 4.25". They're so small that you have to be on the extreme end of the height curve to get back to a BES of 0.425%. In the middle of the chart, we see the steady curve that we likely expected where height is being driven by pecker length. Then we reach the right side of the chart and things get crazy again. Once our pecker length reaches 6.5" (2σ from the mean), our ESPecker score becomes so high that height becomes a non-factor. In fact, ESPecker * ESSalary is already more exclusive than our target of 0.425%. Exclusivity score have to be between 0 and 1. There is no number in that range you can multiply by to get a bigger number. This creates the concept of a valley that we'll come back to. Let's do this one more time but hold pecker size constant at 6". This time we will measure the salary required for various heights to maintain our BES. To measure our required salary, we do the same thing as before except we also have to convert our normal distribution back to dollars. $$ES_{Salary} * ES_{Pecker} * ES_{Height} = BES$$ $$ES_{Salary} = \frac{BES}{ES_{Pecker} * ES_{Height}}$$ $$ES_{Salary} = \frac{0.425\%}{17\% * ES_{Height}}$$ Again we need to convert our heights into Exclusivity Scores using Excel: $$ES_{Height} = 1 - NORM.DIST( height, \mu_{Height}, \sigma_{Height}, true)$$