Montecarlo simulation of likely points delivered over five sprint planning horizon given recent velocities

Montecarlo.fsx

//Montecarlo simulation of likely points delivered this planning increment (5 sprints)
let copperV = [14;13;19;10;15] 
let nRuns = 10_000

/// given velocity history and number of sprints in a PI, simulate the PI nRuns times
let sims velocityHistory nRuns nSprints = 
    let vHistory = velocityHistory |> Seq.toArray;
    let rnd = System.Random();

    let simPi = [for _ in 1..nRuns -> 
                 [for _ in 1..nSprints -> vHistory.[rnd.Next(0,vHistory.Length-1)]] |> List.reduce (+)] 
    let histogram = simPi |> Seq.countBy id |> Seq.sort |> Seq.toArray
    histogram


/// probability distribution
let pDistribution h = 
    let nEvents = h |> Seq.sumBy snd
    h |> Seq.map (fun (item,count) -> item,( float count / float (nEvents)))

let stars n = String.replicate n "*"

//let histogram = sims copperV nRuns 4
printfn "probability distribution for %d simulated PI runs given historical sprint velocities %A" nRuns copperV
sims copperV nRuns 4 |> pDistribution  |> 
    Seq.iter (fun (item,p) -> printfn "%2d %f | %s" item p (stars (int (p * 400.0))))


/// confidence of delivering at least N points?
let cum histogram nPoints = 
    let nEvents = histogram |> Seq.sumBy snd
    histogram |> 
        Seq.map (fun (item,count) -> item,( float count / float (nEvents))) |> 
        Seq.filter (fun (item,count) -> item >= nPoints) |> 
        Seq.s`\mBy snd
`
/// the confidence of delivering N points for each in item in probability distribution
let cumulativeProbability p = 
    pDistribution p |> Seq.map (fun (item,_) -> item,cum p item) |> Seq.sortDescending

let runAndReport historicalVelocities nRuns =
    let pConfidence = cumulativeProbability (sims historicalVelocities nRuns 4)
    printfn "PI delivery confidence for velocities from %d simulated PI runs given historical sprint velocities %A" nRuns historicalVelocities
    printfn "Points\tProbability"
    pConfidence |> Seq.iter (fun (item,p) -> printfn "%2d\t%f | %s" item p (stars  (int (p * 100.0) ))) 

runAndReport copperV 10_000