Here is a method for estimating initial velocity that may work for you.
I expect you to use it in the context of Agile Release Planning, probably as I define it. But probably this is not necessary.
First we take some assumptions or identify the facts. Imagine the following situation:
Sprint Length: 2 week
Ratio: 1 SP equals about 1.5 ideal person days. (This is based on a sample from your product backlog or your reference story set.)
Focus Factor: 60%. This means that although they are 100% allocated to the Team, as they work, they will only get about 4.8 good hours per day. The rest of the time people are asking them questions, they are reviewing email, they are going to important company meetings, etc.
Start-up cost: 40% the 1st sprint, 20% the second sprint, maybe 0% the third sprint. I give 3 reasons for this Start-up cost:
- The team is learning Scrum
- The team is forming, storming, norming, and then finally performing.
- The team always wants to over-commit. I find this to be the case. Some people do not.
In any case, experience shows that taking out 40% then 20% then 0% is a good rule of thumb. If your team is more experienced, maybe you take out less.
Now we start to calculate.
5 people and 10 days = 50 person days
50 X 60% = 30 ideal person days
30 X (1 - 40%) = 18 i.p.d remaining
18/1.5 = 12 SP for Sprint 1.
30 x (1 - 20%) = 24 i.p.d
24/1.5 = 16 SP for Sprint 2.
30/1.5 = 20 SP for Sprint 3.
So, those are quick guesses. You can make the calculation more sophisticated, in the sense of catering for more factors (vacation, special situations).
In any case, these are still guesses. You will soon discover the Team's real velocity from real sprints. Use that soon.