Story point and person⋅month, are they the same thing?

When a story point is assigned to a story, it tends to indicate the complexity of the story or task to be done. Whatever method is decided to arrive at the story point, it ended up being a number and usually without a unit. So, what exactly is the unit of a story point?

If we go further into the process, typically story points are then used to decide which stories can be picked up and fit into a sprint, in which the team’s velocity is used as a measure. Let c represents story points, then team velocity v is simply c/sprint. The sprint is a measure of time; thus, we can write v = c/t. Then c = vt. We yet to know what the unit of v is, but we can see that c or story point has some relationship with time.

If we now turn our attention to person⋅month, we can see that it also has a similar relationship with time. If we let e be a generic representation of person⋅month and p be the person in person⋅month, then e = pt.

Now we have 2 equations that are quite similar, showing a relationship with time t.

Let us pull in a popular equation from physics that you might be familiar with. The kilowatt⋅hour (kW⋅h), is the amount of energy delivered by 1 kilowatt for 1 hour. A kilowatt or watt is a measure of power. We can express energy as energy = power * time. Power is the rate of work with respect to time. We can simplify:

energy = work/time * time = work