Many things in life don’t have a clear estimate at a first glance – many times, 10% will seem like an underestimate, and 100% will seem like an overestimate. In these situations, I’ve learned that it’s actually pretty good to take the geometric mean of the two as a ballpark estimate: ~30%, or roughly something like 1/4 ~ 1/3.
Let’s take a few examples:
- Energy efficiency of humans. Empirically, it doesn’t seem like we convert all our energy from calories into work. (Think about how hot we get after a run!) That must mean that our energy production is less than 100%. However, it doesn’t seem that our energy efficiency is as low as 10% either – that would mean that most of our energy is by far wasted. With these two conditions met, we then ballpark human efficiency as 30%. It turns out that this is empirically true – humans are about 25% efficient at producing mechanical work!
- Energy efficiency of (gasoline) cars. By the same logic above – with all the heat, etc., we can say that roughly the same setup holds for cars for the same reasons it holds for humans. Therefore, we can once again make the claim that cars are ~30% efficient. Once again, this is empirically roughly true!
- Food at restaurants. Thinking about the amount of money that actually goes into the ingredients of food at restaurants (as opposed to other factors like labor, rent, etc.), we realize the same setup holds. Due to overhead, restaurant efficiency cannot be 100%; due to food prices, it seems extremely unlikely that restaurant efficiency is only 10%. We once again take 30% as a ballpark estimate. It turns out that this is fairly accurate (and as a side note, it seems like employee costs are about the same as well)! I’ve also seen this number noted as low as 20%.
- As a last example, we know that last week, Stanford lost to Cal in our yearly Big Game (and I know that Cal’s football isn’t great)1. Well, obviously Stanford can’t be winning all their games, and they are hopefully winning more than 10% of their games (being a private school and whatnot), so we take their winning proportion to be 30%. It turns out their actual standing in PAC-12 North is dead last at 3-8 (overall), which is pretty close to our estimate.
The last tongue-in-cheek example aside, hopefully you’re convinced of the use of this ballpark estimate. Now that we’re armed with this weapon, as we know too well2, it’s a lot more interesting to find places where wielding it gives us invalid results:
Berkeley tuition: Sourced through internal means, we’ve gathered that around ~$100 is spent on classes per student-unit on teaching staff. This translates to ~$400 for a 4-unit class, or $1600 for the standard 16 unit schedule. Accounting for $150 for instructor salary ($150k for 1k students, as per 61A standards), we get ~$2200 per semester in money spent towards teaching staff. In-state tuition is $9k / semester, as I checked on CalCentral, so we do end up getting a value of $2.2k / $9k = ~25% efficiency. Fantastic!
Now we consider out-of-state students, who pay ~25k per semester. This is $2.2k / $25k ~= 10% efficient. Where is all the money going? I unfortunately don’t have an answer. What I do have, though, is a dire situation on hand: Somehow, the EECS department doesn’t have enough money to staff their classes next semester, even running at a subpar efficiency. I’m very curious as to what’s up!
Writing code: In Clean Code, Martin asserts that the ratio of time spent reading versus writing is well over 10 to 1. We are constantly reading old code as part of the effort to write new code. Taking this at face value, it definitely doesn’t satisfy the 1/3 ~ 1/4 rule. Based on my limited experience in industry (as a senior at the time of writing), this doesn’t seem empirically true? I’ve spent perhaps a third of my time reviewing other code and getting a hold of my bearings, and the other two thirds producing. It’s perhaps the case that these ratios switch as software engineers become mentors, but I’m curious here as well to understand what’s up!
In closing, this rule of thumb is quite similar to the Pareto Principle. Perhaps it’s getting at the same underlying cause! I find, however, that the 1/3 ~ 1/4 rule of thumb has been more helpful to me thus far, and I hope you took something out of this as well.