I’ve talked about this before, but I don’t think I’ve ever written it down. As more of my day-to-day involves leadership, I think about this stuff. To run an effective team, you need to think in vector sums.

As the great poet A. Yankovic once said, “Do vector calculus just for fun.” But this isn’t even calculus, just trig. :) Let’s see if we can avoid flashbacks to high school math. You can think of a vector as a value that has both a magnitude and a direction, like the wind blowing 10 mph to the NW.

Every team member is a vector. The magnitude is how much stuff that person can get done, and the direction is what they see as the end-point of their work. The goal. Unlike a wind report, the direction might consist of many different dimensions, but the basic principles still hold.

What happens when your team grows to two people?

Vectors can add. Geometrically, you can think a vector as an arrow with a particular length and orientation. Adding is stacking two (or more) arrows tail-to-head. So two vectors opposed by 180 degrees will tend to cancel each other out. Two vectors pointing exactly the same direction reinforce.

But here’s the great thing: two vectors that mostly point in the same direction give almost as much benefit as if they were exactly aligned.

Example: Team member A is pulling NW at 10 mph. Team member B is pulling NE at 10 mph. If you treat this as a right triangle, you get approximately:

Team member A contributions: 7 mph N, 7 mph W

Team member B contributions: 7 mph N, 7 mph E

The E and W components fight against each other, and you end up with 14 mph due north. Even though the team members are pointing in very different directions, they are still around 70% effective in combination. Of course, the job of a manager is to establish and communicate goals effectively to better align team members and prevent rework. Herein lies efficiency.

For example, if my math is right, in the case where team member A is pulling NNW and B is pulling NNE, the efficiency jumps from 70% to 92%.

Many managers fall into the trap of micro-managing, which is missing the point. Hire smart people, make sure they’re pointed in the right direction and let them run ahead as fast as they can. Stay just enough ahead of them to remove obstacles before they encounter them. That’s a great leader.

## Bonus epiphany

I recently realized that this principle also applies to the thoughts in your head. No, I’m not talking about an after-school-specialÂ multiple-personality situation. But thousand of thoughts rattle through your mind every day, and each one has a magnitude and a direction. You need to get them all pointing in the same direction, more-or-less, to be effective as a human being.

This is a restatement of a common concept that goes under many names such as “Personal brand.” Is everything you think about (and subsequently do) helping make you into who you want to be?