Playing with Odds (Part II)

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I could go on all day about different fields and instances where an extra thought to the probabilities behind varying occurrences could help shed some light on what feels like chance happenings. So I will!

Thanks for coming back! … or go check out Part I if you are not, in fact, coming back! Now let’s get started with this.

Calculated risks exist everywhere in life; from the decision between the main road and the back-alley shortcut to financial asset allocation, we can find a little bit of probability playing its hand. It is good to always balance pros and cons and the likelihood of events.

The Creepy Back-Alley

Say that a back alley has a .01% chance of a mugging with extreme consequences, but cuts 10 minutes off the daily commute versus perhaps a .0001% chance of something similar happening on the main street. Now, I know we don’t necessarily have these numbers (in fact, I would be impressed if you did have those numbers about the sketchy shortcut) but we often have a reasonable perception on what these numbers may be or at least a gut feeling based on prior knowledge.

At this point, consider how much those 10 minutes mean to you and the ramifications of being mugged. Who knows, perhaps the 10 minutes mean a whole heck of a lot (getting back on time for a date or something of the sort) and you expect little harm to come from a mugging because you don’t keep much in your wallet. But then factor in the possibility of physical harm and that could be a game changer. It’s these kinds of thoughts that are constantly running through my mind.

The Crazy World of Finance

Similarly, these risk/reward tradeoffs permeate the realm of finance. There are choices within choices within choices that allow someone with the right time and money to have a good sense of what they are getting into. Just to scratch the surface we have speculative buying, ETFs, asset allocation, domestic versus global markets, government versus corporate, growth versus value. All these choices make it possible to get into investments with a full sense of what the likelihood of loss is and what we can expect as a return.

As a perfect basic examples we have the efficient frontier, which describes how we can consider how to invest in different assets to balance standard deviation (our risk factor) and our expected return (our 😀 factor). You can read up on it if you find that kind of thing interesting.

Blindly jumping into a stock pick isn’t that far off from haphazardly playing Mario Party. I may have some “skill”; perhaps I am close to the company (in a non-insider trading kind of way). I read blogs on the gaming industry and have a generally better idea of the industry than the guy to my right and to my left. But investors aren’t necessarily the guys to my right and to my left; at the end of the day it (quite frustratingly) matters less if the next generation system is the greatest thing of all time and more about what Samuel Pierpont Escher’s DCF says about the company.

Blindly jumping into a stock pick isn’t that far off from haphazardly playing Mario Party.

Anyways, you get the point. It’s everywhere in finance, but to an uninformed investor, the whole thing could seem a lot like pure luck. Do you like a company? Think they are going to do well? Buy in! Right? If that is your thought process then it pretty much IS luck. It can be fun and addictive because it is a lot like gambling, and without that insight of the risk versus reward, it’s easy to jump in blindly.

Let’s Get Sporty

Another place where probability (and statistics) is omnipresent, is in sports. I remember my Games Gambling and Statistics professor freshman year showing that the “slumps” we see in baseball and other sports, can be explained with a quick distribution calculation. This draws from the cumulative probabilities I touched on in the Fire Emblem example. When people are hitting with a .250 batting average, and are up to bat 500+ times, a streak of 20 or so misses starts to become likely.

Beyond the stats that are visible to an average watcher, there are often thousands of behind the scenes statistics that help understand likelihood of events and the reasons for events in general. This video from Numberphile neatly scratches that surface.

I haven’t looked into this deeply, but I’m curious about how teams use models like the ones he mentions to strategize tactics. I’m sure the models shed some light on what risks are valuable and what opportunities have high risk of counterstrike. I personally would love to analyze similar models in badminton. Seeing how grid positioning for certain types of shots most often leads to results X, Y or Z would be really neat.

You’re Making Up Numbers WRONG

One last thing I wanted to mention, since it neatly relates to forensic accounting (my current occupation), is Benford’s Law. This talks about the probability of leading numbers in a dataset that spans multiple orders of magnitude.

The law is often used by the FBI and other forensic accounting departments as a litmus test of if fraud is afoot, since people siphoning money are prone to do so in a systematic way, which would lead to a “skeptical Benford is skeptical” moment. Not much to say particularly about risk and reward, except that it’s risky to break the law, so don’t do it! Check it out if you don’t know about this mathematical concept.

Wrapping it Up

I could go on all day about different fields and instances where an extra thought to the probabilities behind varying occurrences could help shed some light on what feels like chance happenings. So I will! Nah I’m just kidding.

Let me know what you guys think about some of these ideas. Do you numericize events a lot in your life like I do? Or perhaps really analyzing the numbers takes some of the fun out of it for you?

I think there is a lot to be said for pure intuition in some cases; tons of repetition for sports players, for example, may be a good counterpoint when it comes to split second decisions. If Lin Dan knows that in position X a cross court smash has been generally successful after years of playing, perhaps he doesn’t need a stat telling him to cross court smash in the heat of the moment. So when the going gets tough do you lean towards intuition, numbers, or try to reconcile the two?

Thanks for stopping by! Until next time, game on and learn on!

~Dylan

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