You can do a pooled variance

What is a formula for compounding net variance for repeated occurrence of some event?

Thanks.

What you have is a series of variances v1, v2, ... vn for random variables X1, X2, ... Xn, Xi representing the amount of work done in sprint i.  The key question is whether the random variables Xi are independent.  If they are, we know that the variance of the sum is equal to the sum of the variances.  You can probably assume this if you are confident that your estimation procedure for each sprint is unbiased (a gutsy assumption, I would claim).  However, if they are not independent, the computation becomes significantly more complex, requiring you in general to know the covariance of each pair of Xis.  As a practical matter, you can get a reasonable estimate of the total variance by assuming that every pair of Xis has an identical correlation coefficient, and deriving the covariances from that.  Gujarati, Basic Econometrics, second edition, pp. 634-638 gives a useful concise discussion of the relevant concepts. 

Thanks, an interesting question and a useful answer. Study of the impact of sprints is important and we have to begin with our estimation methods. I hope this research is eventually published. 

Eric, This is what I was looking for. Thanks.

There are good arguments (e.g., from Jørgensen) on how to minimise the bias.

The items being estimated are independent and in that sense the estimates are independent. It's difficult to separate out the properties of the system structure that contribute to the mean from any considerations that would link the estimates of one Sprint to another. There can also be subtle shadow effects because the estimation is relative (it's in fact relative independent of the units used) and the estimate of any current item is always relative to other items that serve as baselines. Those considerations aside, there's a good change they're independent.

Empirical studies of velocity are very, very difficult because it's hard to avoid self-fulfilling prophecies. We've done some short-term demonstrations that demonstrate this. In an exercise where a team makes paper airplanes in one-minute Sprints they can gradually increase their output up to an asymptote (say: 6). Then in one sudden, emotional Sprint we challenge them to make 12 and, voila, we suddenly get 10.

You're with Harris? I did a lot of development on the Harris (then Datacraft) 6024/3 and then the SLASH 6 back in the 1970s. I still know most of the machine code by heart.

1) if your amount of work is Cauchy-distributed, its distribution doesn't have a variance (see https://en.wikipedia.org/wiki/Cauchy_distribution). And you are in big deep trouble : many theorems on sampling properties suppose the existence of a finite variance...

2) If the distribution has indeed a variance, then the "basic properties" paragraph of https://en.wikipedia.org/wiki/Variance apply. Compute by recurrence... You'll gfet an answer similar to Eric's. Beware, however that you should try to assess if f(X_i+2|X_i,X,i+1)=f(X(i+2|X_i+1) or not, which is necessary to allow for a simple recurrence. In other words : does one unit depend only of the last previous unit, or the whole history ?

3) However, I somehow doubt that the relation between one work unit ant the following one can be simply described by a simple correlation... Try to model this realistically.

4) "When all else fails, simulate..."