Dharmesh Shah (the co-founder and CTO of HubSpot) once attended a small dinner event where someone asked Elon Musk the following question:
“What’s your advice on growing and scaling a business?”
Musk replied: “Every person in your company is a vector. Your progress is determined by the sum of all vectors.”
This vector theory is a powerful mental model for leading a company or even a team.
Let’s break it down.
Think of a vector as an arrow with a magnitude and direction.
For example, vector A has a magnitude of 5 and points east, and vector B has a magnitude of 3 and also points east.
The sum of those two vectors is a new vector with a magnitude of 8 that points east as well (5+3=8).
In other words, employee A is worth 5 units (the value they provide) and is focused on tasks in a particular direction. Employee B is worth 3 units (a lower value than what A provides) and points in the same direction as employee A.
That means your team of two employees is in great shape. Both are aligned in the same direction, and their efforts are cumulative.
Now let’s say that employee B is pointing west (i.e., in the opposite direction of employee A). Then the net effect of the two vectors is a new vector with a magnitude of 2 units that points east (5-3=2)
In other words, your two employees are canceling each other’s efforts because they’re pointing in different directions.
Although you’re still making progress in the direction you want to go, your team is not efficient.
You can also think about this in terms of performance.
For example, suppose employee C points north and has a magnitude of 7, and employee D also points north but has a magnitude of negative 3. In that case, the net effect is a vector with a magnitude of 4 pointing north (7-3=4).
Although employee D seems like they’re pointing in the right direction, their negative magnitude due to their low performance is pulling the other team member down.
A quick note to explain the illustration: a vector pointed in a specific direction with a negative magnitude just means it points in the opposite direction with that absolute value. So a vector with a magnitude of -3 pointing north is the same thing as a vector with a magnitude of +3 pointing south.
So in this case, you’re better off having one employee instead of two because the value of one of them is greater than the net effect of both.
Now imagine you have many employees in your team or organization, and everyone is pointing in a different direction with varying magnitudes.
The net effect is highly inefficient.
How to use this mental model
Think of all your employees as vectors. First, assess if they’re all aligned in the same direction. And second, evaluate their value (i.e., their performance). As a leader, make sure they’re all pointed the right way and that you’re addressing any low-performance issues.
This post is an excerpt from “Mental Models for Effective Managers.”
