I just rolled the ball again in his court, wow :). He replied as:

“Your sums are correct but the answer is much simpler. The six days are worth 6 x $50k = $300k. If it costs you more than $300k to avoid the 6 days delay (and it will not become more!), do not change and incur the $300k claim (Liquidated damage, or LD). If you can correct (e.g. avoid the 6 days overrun) at a cost of less than $300k, say $200k, then you have “increased” the profit on the project from $700k to $800k. Do realize that when you discovered that you “certainly” would have a six (6) day schedule overrun, your project had decreased in value from $1000k to $700k. 

The standard deviation comes in when the 6 days overrun are uncertain, or when the corrective action of $200k is uncertain or whether the corrective action has a 100% chance of avoiding the schedule overrun. This will make it all very complex without giving extra “message” to your management. That message, in fact is: Either accept the loss of $300k because correction costs more, or apply the corrective action and improve the position that has already happened, e.g. the drop in value from $1000k to $700k. 

Of course it all assumes that the Client does not become so angry with the 6 days overrun that he will not buy from you again. But then the cost of the 6 day overrun must also include the lost profit on the next project. And then a corrective action of say $400k may still be good economics for your company and for the project. “

Another Risk savvy presented the solution differently as:

“As a general comment, if your project duration forecast distribution looks like a Normal distribution, it is very likely that you didn’t include (enough) relationships between tasks. Also, you should review if you took into account the true risks that would cause the project to take a lot more time than expected. A more typical forecast distribution would look right-skewed, i.e. have a long ‘right tail’.

Aside from this, you raised an interesting question. The use of the standard deviation as a measure of risk is really mostly useful when your distribution is (approximately) Normally distributed. When this is not the case, the interpretation (and calculations with) a standard deviation become a lot harder. So, in your case, assuming that the total duration of the project indeed follows a Normal distribution, there would be about a 77% probability that you will meet the deadline and therefore a 23% probability of not meeting it. Given that you don’t make the deadline, your expected value is 72.32 days (you can easily see then we specifying a Normal distribution with mean = 67, StDev = 4 and Lower Truncation = 70). Your expected value therefore is 23% * 2.32 * $50,000 = $27K (i.e. this is the expected claim the client will have). Your expected value given that you do have an overrun is 2.32 * $50,000 = $116K (i.e. this is the expected value, conditional that you do have an overrun). I would recommend against using a standard deviation in this case, since this really doesn’t give a lot of insight. What you could do instead is show the actual distribution of claims (preferred option), or alternatively calculate a P10 and P90, since percentiles are easier to interpret and have the same interpretation, independent what distribution you are considering.”