Decision Making as a Random Walk

Monte Carlo Simulation from Numex Exchange.

Do I make every decision I make correctly? Probably not. What happens when I accept that I will make wrong decisions — how do I use this knowledge to improve my effectiveness? This post is about what it means for decision making to be a stochastic process, and how to use this knowledge to be better.

If you flipped a fair coin 10,000 times, and each time it came up heads you took a step forwards, and tails you took a step back — how far would you expect to get? As it happens, not very far.

But let’s say this coin isn’t fair — it’s weighted such that it lands heads 65% of the time. How far would you expect to get this time? Probability tells us you’d average 3,000 steps forwards. 20% come up heads? 6,000 steps backwards.

Random walk position simulation with forward p=0.65 with steps=10000; graphic from WolframAlpha.

What does this have to do with decision making? Well, in the past year I sent 10,487 emails. Each one of those emails can be seen as a coin flip with the intent of moving my organization forwards. Every email is also a decision: prioritizing features, following up on a build’s delivery, crafting RFP responses.

Not all decisions are created equal. Here I will discuss different factors affecting decision making and examine their impact. Then I will use the impact and use it to show how decision making success isn’t binary, and show the different ways in which we can improve decision making for ourselves.

To start, I will review the following factors:

• Probability of correct decision
• Speed of decision
• Size or scope of decision

Probability of correct decision

This is rather straightforward — if you make the correct decision more frequently, you end up further forwards on the random walk. If you make the correct decision less frequently, you end up less forwards or even backwards (and away from your company objectives).

Random walk position simulation with forward p=0.65 (left) and p=0.75 (right) with steps=10000; graphics from WolframAlpha.

However, the magnitude of the difference is quite important. A 10 percentage point increase in decision making success — from 65% to 75% — results in 2,000 more steps forwards. In this case, that’s a 40% increase in net results. Thus as a manager, focusing on improving decision-making amongst your reports can lead to great returns — particularly amongst the lower performers. Even professional coaching, executive education, and workshops that can improve decision-making are likely to be worth the 40% ROI netted.

Similarly, making poorer decisions is equally damaging. A 55% decision making success rate compared to the original 65% reduces the net steps forward by 2,000 steps, leading to a 67% decrease in overall result — quite damaging.

Speed of decision

Now let’s look at speed of decision making. Let’s imagine that we make decisions 10% slower so in addition to an unhappy inbox, we end up making only 9,000 decisions instead of 10,000.

Random walk position simulation with forward p=0.65 with steps=10000 (left) and steps = 9000 (right); graphics from WolframAlpha.

A 10% decrease in the speed of decision making leads to 250 fewer steps forwards, or a 8.3% decrease in steps forward. The reason that speed doesn’t have as dramatic an effect is that not only are you making fewer correct decisions and thus not getting as far, but you are also making fewer incorrect decisions thus not hindering progress as dramatically.

Accuracy (left) versus precision (right). ThoughtCo.

Another factor that changes moderately is the standard deviation — taking 9,000 steps instead of 10,000 leads has about a 5% smaller deviation in expected results. This can be neglected though as decision making tends to focus on accuracy rather than precision. After all, getting precise, mediocre results is generally less desirable than scattered, positive results.

Size of decisions

The last factor to look at size of decisions as measured by impact. To simulate this, we increase step size — a correct decision that’s twice as important leads us 2 steps forwards instead of one, but an incorrect one leads us two steps backwards.

Random walk position simulation with forward p=0.65 with steps=10000 and step size = 2; graphic edited, original from WolframAlpha.

When doubling step size, we double our expected results — from 3,000 steps up to 6,000 steps in this scenario. However, if your expected results are negative (such as if p=0.45), then you are doubling results and going further into the red.

Interestingly an increase in step size leaves standard deviation unchanged, so you are changing results without any change in precision.

Synthesis

Now that we’ve examined the factors that impact our random walk, what are the key takeaways?

• Making correct decisions matters a lot more than making decisions quickly. Thus, taking the time to think things through and make the correct decision is overall more beneficial than making more decisions.
• Large decisions have an outsized influence on your results, without sacrificing precision. If we think of precision as a proxy for risk, then making fewer, more important decisions is better for outcomes.
• Combining these, to maximize performance it is paramount to get high-impact decisions correct, but low-impact decisions may be negligible. There is therefore value in being able to identify which decisions are likely to have the highest impact, and thus be able to spend time focusing on making the correct decision.

How should we use these takeaways to improve our decision making?

1. Quickly identify which decisions are the most important to make and focus on them and assign your best decision-maker.
2. Small decisions that may be fast to make are good candidates to delegate. This provides team members opportunities to practice and decision making in an iterative process. A feedback loop and education is key to improving outcomes over time.
3. Small decisions that take a long time should be compromised upon. As an example, small decisions about your product’s color palette may take an inefficient amount of time to answer by a generic product manager — how much harm is done in flipping a coin? Alternatively, find competence within your organization to make those decisions quickly — in this example having a UI designer take care of this decision may improve speed of decision and therefore outcomes.
4. Time-box the decision-making process to avoid wasting time making negligible improvements in decision outcome. Eventually spending twice as much time making a marginal improvement in probability of success becomes wasteful.

Can we think about decision making stochastically? What other aspects of our work can and should we rethink? Let me know your thoughts in the comment below!