You have surely seen the “motivational formula” that if you are just 1% better each day, then within one year, your performance multiplies by more than 371. Alas, this message is way too simplified. It gets it right that small improvements go a long way, but it sets unreasonably high expectations (which are bad for your happiness); improvement/productivity is not constant.
Can we make a still simple but more realistic scenario that compares multiple paths productivity, while acknowledging the randomness of the problem?
I wrote a Python program to do exactly that—as any experiment, it comes with assumptions. Note that the numbers are arbitrary, so do not compare the numbers to the real world. At the start, our accomplishments are set to 1, and I am simulating what happens after 2500 work days.
I compare three strategies:
a sustainable (slow but steady progress)
a volatile (big gains and almost zero progress)
a matched volatile (the parameters are tweaked to get the same result as the sustainable strategy, but with a larger variance than in the case of the sustainable strategy)
Strategy details
The sustainable strategy means that daily productivity lies between 1% and 6% (each value is equally probable; i.e., uniformly distributed).
The volatile strategy includes everything between 0% and 100%, but these values are not equally probable2. These numbers were chosen to express that you cannot maintain excellent performance over the long term.
The matched volatile strategy admits gains between 0% and 75%, which are also not equally probable.
Simulation results
The simulation samples 2500 numbers randomly and then calculates the compounded productivity. Starting with a productivity of 1 and improving with X% and Y% in two days, the result will be
I repeat this 2500 times.
Daily productivity
The daily productivity values for all strategies visualize the difference between hustle-then-burn-out (volatile) and the show-up-every-day (sustainable) strategies. I told you that the matched volatile strategy was created to get the same end result as the sustainable one. Before looking at the cumulative plot, let us highlight how different the daily values are.
If we pool the values together into a histogram, the difference stands out even more:
In 78% of the days, the volatile strategy performs worse than the minimum (1% ) of the sustainable strategy; even the matched volatile strategy does so in 55% of the days.
Compounded productivity
After carrying out the multiplication from above, I get the following plot:
The result is quite remarkable:
the volatile strategy is very far away from the other two, even if the Y-axis is on the log-scale.
Fix productivity budget
A fair objection to the above results is that the difference might be because the productivity budget (the sum of X and Y over all days) is different in each case. To eliminate this factor, I also simulated what happens when we fix our productivity budget (I use a budget of 5, which is equivalent to the productivity of just 0.2% each day; I will call this uniform) and compared the results. Intuitively, we can expect that the uniform strategy will be the best :
Volatile < volatile (matched) < sustainable < uniform.3
Think about
There are multiple means to the same end; it is up to you which one you choose. However, forming habits—i.e., leaning towards a sustainable strategy—is shown to be beneficial. But for that, you need to show up consistently.
Lower values are more probable (the mean is approximately 2%, the mode is 0%). It follows a beta distribution with
The numbers are approximately 141.9 < 145.4 < 147.5 < 147.7.