Show your Tikka ten round groups

[Tommyhaak]

Except you never get to 100% certainty, since you aren't shooting 100rds at one target. You always have something less than full confidence, especially when you're testing with only ~10rds per load. So then the question becomes, how quickly can I increase confidence in this metric I'm using to evaluate loads? And the answer is to use data from every single shot, instead of just the extreme 2 shots. The formal term here is statistical power. Using shot radius data gets you more power for the same number of shots.

I’m looking for a circular group/pattern that fills in comparable to a Gaussian distribution. The more rounds I fire, the larger the pattern/cone, and the greater confidence I have in the mechanical capability of my weapon/ammo combo. Why not fire 20, 30, or 100 rounds into the same group to gain confidence in actual performance? Then, I care about my worst two rounds to determine actual capability. MR doesn’t give me this information, and delivered by itself, is useless for judging hit rate at distance or capability of that weapon/ammo combo.

 

[Formidilosus]

The load on the left will put more shots closer to POA. We happened to get a big outlier in this example. They both have the same ES (according to my sketching abilities). MR tells you this story where ES doesn't. Agree that if you want to characterize the effective accuracy of the system, you need to look at mean + 2-3sd radius OR ES of a meaningful shot count. As I've discussed many times before, tracking individual shot radius data and using mean + sd method will get you to the "correct" or "true" answer in fewer shots than ES method. However you can get the "correct" answer with both methods.

ETA: For comparing loads with smaller shot count groups, say 10, using this more "information rich" metric will give you a more accurate comparison. So for example (not perfect numbers but illustrates the point), 10rds of radius data is equivalent to a 15rd group ES in terms of telling you the real performance of the load.

That is not correct. You and every one else will zero off the cluster of shots, ignore the “flyer”, and then that flyer- is way off POA and falls outside the expected cone.

ES people zero off the center of all rounds, and all shots fall within the expected cone.


You are math dorking for the sake of math dorking. I have long history with this well before the last couple of years where certain groups are pushing it. There is “the math says…” And then there is- “reality on target in the field, shows…”.

I don’t have to math dork, I don’t have to convert, I don’t have to guess, or anything else. Shoot 20-30 shots, zero to center of all shots. Done. And at the same that 30 rounds tells me the 95% probability in MOA. 30 shot 2 MOA ES, at a base if I am missing 2 MOA targets- it is me, not the gun.

 

[Kimber7man]

Which one tells you what size target you can actually hit on demand?

As stated, hunting is “worst shot”- not “average of best”.

Best and worst if it only takes one shot to kill it.....

 

[Yooper25]

How many grains of 4831?

BT: 43.5
Eldx: 42
Eldm: 41
I did pressure test the BT and got up to 47.5 with just the slightest ejector mark. Going to load some at 47 and see how it shoots

 

[stan_wa]

That is not correct. You and every one else will zero off the cluster of shots, ignore the “flyer”, and then that flyer- is way off POA and falls outside the expected cone.

ES people zero off the center of all rounds, and all shots fall within the expected cone.


You are math dorking for the sake of math dorking. I have long history with this well before the last couple of years where certain groups are pushing it. There is “the math says…” And then there is- “reality on target in the field, shows…”.

I don’t have to math dork, I don’t have to convert, I don’t have to guess, or anything else. Shoot 20-30 shots, zero to center of all shots. Done. And at the same that 30 rounds tells me the 95% probability in MOA. 30 shot 2 MOA ES, at a base if I am missing 2 MOA targets- it is me, not the gun.

I don’t have to math dork, I don’t have to convert, I don’t have to guess, or anything else. Shoot 20-30 shots, zero to center of all shots. Done. And at the same that 30 rounds tells me the 95% probability in MOA. 30 shot 2 MOA ES, at a base if I am missing 2 MOA targets- it is me, not the gun.

I agree that this is practically a great approach. I would like to point out what started this exchange was a discussion on ES versus MR for choosing between different loads in my original post it was about which bullet to choose from. in the context of distinguishing between loads. Asking which bullet is going to be better i.e. more precise. Can you agree that MR is more insightful than ES especially for evaluating precision of different loads . all of this is a little bit silly because if you shoot a group that’s at least 10 or bigger. The one with the biggest ES will basically always have a bigger MR. My claim is that MR is still better than ES and evaluating precision as a single number dor determining which load to choose from .

evaluating rifle capabilities and comparing loads are too slightly different subjects

And I 100% agree with the statement

people zero off the center of all rounds

specifically, I just let the 4dof tell me what the center of the group is and dial zero in according

Mathematically the best to worst evaluation metric would be
1. Mr + 2 sd
2. Mr
3. Es aka group size

Practically if you shoot 10 or more per group the load with the “ best group “ will have the smallest of each of these evaluation metrics
And if the same load doesn’t minimize all 3 , the compared group’s probably aren’t very different anyways

 

[ckt3]

Honestly trying to understand the difference here, and admittedly need to read more into ES and MR... but if I shoot 100 rounds in a 2moa group, my ES is 2moa, and I know I have a 100% chance of hitting a 2moa target (excluding outliers like weather, ammo lots, etc). If I shot 100 rounds with 95 of them inside 2moa, and 5 of them outside of, say 2.5moa... then I have a 95% chance of hitting a 2moa target.

Isn't the ES telling me what I can hit with 100% certainty the more valuable metric in the field as a hunter?

Just trying to see both sides here.

Both ES and MR are metrics that aim to quantify the dispersion of your system. As Form points out, ES is better for getting a quick measurement in the field to have a simple and practical way to gauge the limits of your system given a big enough group. MR, in terms of what it tells you about your system, is better than ES. It is using all the information from your group to represent the underlying distribution (the Rayleigh probability density function), so you can do a lot more with it than ES and have more confidence in your estimates.

For practical purposes, if you did what you state in your example on a big group, you’d be fine (even though the true percentages are different from what you state). But if you really want to evaluate your system well and be able to answer questions like, “With what probability will I hit an A inch target at B yards?”, you use MR, not ES (you can approximate with ES but it’s noisier and throws out a lot of data).

I just ran some simulations and plotted them to explain better. All we have to assume for this is that the the x and y coordinates of each impact follow a Normal distribution. We get to choose the parameters of this distribution for the simulation, so here I chose the “truth” to be that this system will put a shot in a 1.5 MOA target with 99% probability. Now we run random simulations of varying group sizes (each different group size is a new row; each column is a repeated trial with that same group size). Imagine each plot here is your paper target after shooting the same rifle at each target to get a group. And for the sake of the example, imagine the target is a 100 yards away and that’s a 1.5 inch diameter black circle you’re shooting at.

We know the true 99% probability circle (1.5 inches). We can calculate the mean radius from the shots on target and then use those to estimate a 99% probability circle (we don’t know the “truth” about our system as a shooter, we only know our shots on paper, and we do our best to estimate the truth). We can also measure the extreme spread.

You can see a few things: 1) predicting via MR gets you much closer to the truth much faster. At only 10 shots, the predictions are very close to 1.5 inches. It takes ES more shots to get close. 2) MR converges. It approaches the truth and with more shots only gets more precise in its prediction. ES is not stable, and artificially inflates (starts too small and keeps getting bigger). 3) When ES is wrong (which it often is at common group sizes <30), it is usually being overly optimistic about how accurate the system is. So the argument of “prepare for the worst” actually favors MR.

There’s some other neat stuff in the plots, but those are the main ones. Overall, yes bring a ruler to the field and get a quick practical ES measurement on a big group. But understanding what’s happening under the hood and how ES can mislead you is helpful. It’s all manifestations of probabilities and randomness. A “1 MOA” rifle statement begs the question of “at what confidence level and across how many shots”. You can take shortcuts with ES and get by just fine if you do it right, but using MR will yield higher quality probability estimates. It comes to defining your objective and understanding the pros/cons of the statistical tools you have.

Lastly, after all this math dorking and egg heading, if you want to know how you’ll shoot at distance, nothing beats shooting at distance.