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Hit Probability: An Error Budget for First-Round Hits at 600 and 1,000 Yards

A Monte Carlo error budget for a 12-inch plate at 600 and 1,000 yards: wind call, range, velocity spread and rifle precision, solved with the engine. The wind call accounts for more of the miss than the other three combined.

6 min readSolved with the Ballista engineUpdated October 2026

A 6.5 Creedmoor with a 1 MOA rifle, a 10 fps velocity spread, a laser rangefinder and a shooter who calls the wind to within 2 mph hits a 12-inch plate at 1,000 yards with the first round 21% of the time. Give that shooter a perfect wind call and nothing else, and the rate climbs to 62%. Give them perfect ammunition instead, with no velocity spread at all, and it reaches only 23%. That’s what an error budget shows: which error is costing you hits.

The four errors and their sizes

Bryan Litz built this kind of analysis into his weapon employment zone (WEZ) method in Accuracy and Precision for Long Range Shooting: list every uncertainty a shooter has, simulate many shots with all of them at once, and count the hits. We did the same for four errors, each a normal distribution with this standard deviation:

• Wind call: 2 mph. The true wind is 10 mph. Your call is right on average, and off by more than 2 mph about one shot in three.
• Range: 5 yd. A laser rangefinder on a plate, allowing for a reading off the berm or a mistyped number now and then.
• Muzzle velocity: 10 fps standard deviation from shot to shot.
• Rifle and shooter: 1 MOA average 5-shot groups. A 5-shot group’s extreme spread averages 3.06 times the per-axis standard deviation of a round normal pattern (we checked it with 200,000 simulated groups), so this is 0.34 in per 100 yd in each direction.

Everything else is assumed known: the BC is trued, the zero is good and the scope tracks.

How the simulation works

For each rifle and distance we asked the Ballista engine how far the impact moves per unit of each error. A 1 mph wind error moves the 6.5’s impact 6.8 in sideways at 1,000 yd (and 0.37 in vertically, from aerodynamic jump). A 1 fps velocity change moves it 0.27 in up or down. Ranging 1 yd long means dialing the come-up for the wrong distance, which puts the shot 0.53 in high. We got each number from engine runs on either side of the true value: ±10 fps, 9 and 11 mph, and the come-up 5 yd short and long.

Over errors this size the effects are close to proportional, so we drew 200,000 shots at random, gave each shot its own wind error, range error, velocity and group dispersion, added up where it landed and counted how many fell inside a 6-inch radius.

At 1,000 yd the wind call alone spreads the 6.5’s shots 13.7 in sideways at one standard deviation. Range, velocity and group dispersion together come to 6.2 in. Because independent errors add as the square root of the sum of squares, the biggest one swamps the others even more than the raw numbers suggest.

The ranking changes with distance. At 300 yd the rifle and shooter are the biggest term, 63% of the 6.5’s miss measured as share of the variance, with the wind call at 31% (48% for the .308). Group dispersion grows in proportion to distance while the wind and velocity terms grow faster, so by 1,000 yd the rifle’s share is down to 10%. A more precise rifle pays off most at short and middle distances. Past that, the hit rate is set mostly by how well you read the air.

Which error to fix first

The wind call dominates at both distances and for both rifles. Removing it lifts the 6.5 from 73% to 97% at 600 yd. Removing any other single error moves it by 1 to 9 points across the four columns.

Halving the wind error is worth more than any equipment change here. Going from a 2 mph to a 1 mph wind call takes the 6.5 at 1,000 yd from 21% to 36%. Perfect ammunition takes it to 23%.

The .308 pays more for the same call. It drifts 11.2 in per mph at 1,000 yd against 6.8 for the 6.5, so the same wind call costs it more. It hits 55% at 600 yd and 11% at 1,000.

Range and velocity errors act up and down. At 1,000 yd the range error spreads the 6.5’s shots 2.7 in vertically and the velocity spread 2.7 in. On a round plate that’s minor next to the wind. On a target that’s wide but short they’d matter more.

Using an error budget

1. Put your own numbers in. Your group size, your chronograph’s SD and a realistic wind error. The ranking of errors is what to take away, more than any single percentage.
2. Spend practice where the variance is. For most shooters past 600 yd that’s reading wind, and watching where misses land so the second shot corrects it.
3. Pick targets for the odds you want. If the first-round rate at a distance is 20%, plan for a correction shot, or move closer.
4. Don’t chase velocity SD past the point it pays. Going from 10 fps to 0 bought the 6.5 2 percentage points at 1,000 yd in this budget. A wind call 1 mph better bought 16.