Nerding out on chrono checks

I have always wondered if the chrono check can be gamed as it is clearly statistically biased, but I never had the time to work thru it until last week. It is actually pretty easy to simulate via Monte-Carlo methods. All you have to know is the standard deviation of your bullet mass and velocity. Both are likely to be normally distributed, and all the calculations can be done in a spreadsheet. Post 2010-ish the random number generator in Excel is more than sufficiently random.

If you are shooting a true 125.0 PF load there is about a 95% percent chance you will pass chrono. If you drop down to 122.5 PF there is only a 50% chance you will pass. 120 PF and you are looking at a 1% chance. Conversely, only a 126.0 PF gets you about a 99% of passing. While biased, it is pretty fair in that if you actually have a 125 PF load you will pass, and that there is a high likelihood you will fail the check if you drop to a power factor that gives a real advantage (IMHO).

Chance of passing each step of the chrono procedure as a function of power factor (%). The final column is the difference between the chance of passing by checking the weight of the 8th bullet and the chance of passing when you choose to shoot it.

Another interesting question is when you get the the eighth round, do you pull the bullet or take another shot? For MY current loads (25 FPS and 0.7 gr standard deviations) there is really no advantage one way or another. However, if you have really inconsistent bullets or handloads you can gain a roughly single digit advantage in the probability you will pass by making the correct choice. For practical purposes, it is probably better to know if the first first bullet was an outlier one way or another. Then you could make an informed choice.

Difference in chance of passing between the two options for the eight round. If the number is positive you should check the bullet weight. If it is negative, send it!

Finally, please don't confuse this for load advice. I am not saying that if you "develop" a 126 PF load by measuring five shots on a 100 °F day and shoot a match on a 30 °F day using ammo assembled from different lots you will pass chrono. That is a different question. Atmospherics, component constancy, and your reloading skill are going to dictate how much of a safety factor you need to build into you loads to insure you pass on a given day. All this shows is that you could fail chrono with a load that is really right at the power factor, but the chances of that are only 1 in 20.

Link to the spreadsheet.