Today we bring you another post by our guest writer extraordinaire, Matti.
Another topic covered in the Complete Man Workshop was calculating Expected Value (EV). This blog post will probably be a bit drier than the Bunt vs Home Run post, because I don’t know how to drop references to f*cking busty blondes in the arse while talking about calculating ratios…
So let’s say you want to make a bet on the likelihood of a certain event happening. For this example, I’ll use hitting a 3-pointer (if you don’t know what a 3-pointer is learn sports f*ckface). Let’s say I historically hit 25% of the 3-point shots I attempt. Converting this to a fraction is pretty simple it’s 1/4, if you can’t calculate that, stop reading this right now, go jump off a building while holding an elementary school math textbook. For those of you intelligent enough to get 1/4 from 25%…read on.
SOOOO we have a 1/4 chance of me hitting a 3-pointer. Converting this to a ratio is very easy, yet 99% of the population can’t do it (including myself pre-workshop). Errbody and they mama would convert 1/4 to 1:4 ratio…WRONG! Rule of thumb, both sides of the ratio must add up to the denominator (bottom number) of the corresponding fraction. Therefore 1/4 corresponds with a 1:3 ratio. In our 3-pointer example, for every one 3-pointer I hit, I miss three, aka 1 out of 4.
So now that we can turn a fraction into a ratio, we can calculate the expected value (EV) of the average outcome. First we need to put a value on all the possible outcomes. Say someone wants to bet me on a 3-pointer. They’d be all like, “Biiiitch, you owe me $10 if you miss that 3-pointer”. Since I know I hit 25% of my 3-pointers and can calculate EV I’d be like “aaight dog, well you gotta pay me $31 if I hit that shit.” Why $31? All you gotta do is multiply the probability by its value. The value of a miss is -$10, the probability of a miss is its corresponding number in the ratio, in this case, 3. Sooo over time, 3 misses at -10$ each puts me at -$30. If I value a hit as $31, its probability is 1 which puts a hit at $31 over time. Add these together, and you get +$1 therefore, the Expected Value (EV) is $1. So on average I earn $1 every time this scenario plays out. .
Anytime there is a positive EV scenario, the smart thing to do would be to take that proposition. There is one exception, and that is the risk of ruin. That is when the negative outcome is too much of a risk for that individual. Say someone’s net worth is $100,000 and they are presented with a +EV opportunity, BUUUT, the negative outcome would lose them their entire $100,000. In this scenario, even though they would earn money on average, under no circumstances are they in a position to lose their life savings. Therefore, it is not worth the risk.
-Matti
