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Back to school! - Determine Optimum Number Of Sprints In Agile Engagements using Mathematics

There has been a rise in adoption of Agile methodology for software development due to benefits such as absorbing late requirement changes, early availability of first version etc. However, decision of adopting Agile needs to be arrived at by balancing project priorities/characteristics (such as lack of requirement clarity upfront) and effort/cost overruns. In certain scenarios, the effort required for developing a product/application is more in Agile compared to that of Waterfall model. It can be easily observed that incorrect number of sprints planned can lead to effort overruns. Several program metrics can influence the decision to adopt Agile as well as to arrive at right number of sprints to keep the efforts in check.


We tried to bring a mathematical approach to decide on adopting Agile and planning for right number of sprints with an objective of optimizing the efforts. Based on certain assumptions, we have arrived at the equation (inequality) to help decide whether to go for Agile or Waterfall model. The value of 'n2' calculated using below equation will determine the number of sprints to be planned. Agile is preferred whenever  'n2' > 2.


((n2+1))/2 * {E+(P(n2)*R(n2)*(2n2+1))/3}  < n1*{E+P(n1)*R(n1)}


X - Total number of test cases

n1 - Number of test cycles in Single Development Cycle Model

n2 - Number of cycles estimated in Iterative Development Model 

E - Effort for one test case execution

R(n) - Rework effort during the nth cycle

P(n) - Probability of a test case failure during the nth cycle

N(n) - Percentage of test cases considered in nth cycle


We have presented this approach in detail through a paper. You can read the same here.

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