IMHO the idea, while interesting mathematically, is subject to Occham's Razor - adding a lot complexity for inconsequential in-game effect. Why?
1. The current autoshot accuracy averages the recoil in already, that's why it's lower than snap shot accuracy. Game-wise it doesn't make any difference if the separate bullets have varied or constant hit chances, as long as the average accuracy holds.
2. As Falko mentioned, the formula has problem with weapons where recoil is small or unknown - like lasers and plasmas. Maybe they work in reverse, shot tracing overwhelming the recoil effect and improving accuracy with every extra shot?
3. It is debatable what effect soldier's Strength, as in XCom Strength, can have on autofire accuracy. The Firing Accuracy parameter already covers how steady are shooter's hands.
4.Weapon's weight and construction has far more impact on recoil than soldier's (real-life) strenght. Human muscle system is nowhere as rigid as a metal tripod, it cushions a force, then counteracts (with delay).
5.Real life shows that proper weapon bracing has far more impact on accuracy than brute strength (again, Firing Accuracy stat in XCom, which already influences autofire accuracy).
6.The formula ignores the number of projectiles fired, thus dramatically reducing the accuracy of the final shots in a long burst, skewing the statistics.
But, to play devil's advocate...
A. A soldier in power armor should be able to brace the weapon much more effectively, thus measurably reducing recoil.
B. If we agree that Strength indeed has any measurable effect on accuracy, there is no need to calculate hit chances for every bullet, as (see 1.) the results are averaged anyway. Plus, if every bullet has different accuracy, the player is given false information about hit chances.
C. If a weapon had freely adjustable burst length - like in JA2 - a recoil formula would be needed, but again, a formula modyfying averaged accuracy would suffice.
Therefore, I'd vote for a much simpler solution:
a) Optional recoil parameter for a weapon. It is equal to required Strength to use the weapon efficiently. A soldier suffers [-2%?] autofire hit chance for every Strength point lower.
b) Optionally, they also suffer [half of that value?] when firing snap/aimed shots.
c) When kneeling, the Recoil parameter of any weapon is treated as [15?] points lower.
d) An armor can have Anti-Recoil parameter, which again, lowers the recoil of a weapon.
e) So, no need for complex calculations or gutting the mechanics, just a modifier to current Auto accuracy.
Actually I feel you're mis-applying Occam's razor in this case. Even the initial proposal has a distinct effect from rolling lower accuracy into auto shot, as it effects the likelihood the shot will hit 2 or 3 times. With a flat accuracy, the shot can potential hit 3 times rather often. If the second and third shots have lower accuracy however, then auto might become a bit less incentivised against high-health aliens. Also, even if it didn't have a gameplay effect, to be honest, it's a cool flavour option.
The point of simulating recoil is not to drop accuracy. You can have any degree of accuracy you want with or without simulating recoil. The point of simulating recoil is essentially that the faster you take shots, the more likely your aim is to be effected by the "kick" of your weapon. (basically, it gives a larger incentive to strategic positioning and aimed shots than currently exists, as opposed to a "bullet spray" strategy) Ideally, simulating recoil should actually make your initial shot in a turn more likely to hit, given the penalty.
Ideally, if you're adding recoil, it should apply to every subsequent shot on the same turn for the same soldier, not just to the second and third shots in an auto burst. Then it becomes a real tactical consequence, and having a soldier rush forward to act as a turret in subsequent turns doesn't work so well.
Thoughts:
Strength differential between the required strength and actual strength should ideally effect the recoil step rather than applying a flat bonus or penalty. Higher-strength soldiers will be able to bullet-spray more effectively that way. This should reinforce existing playstyles- in the early game you're trying to snipe off any aliens you can, in the late game you can sometimes go toe-to-toe with the weaker ones.
Walking shots with lasers resulting in a negative recoil makes sense realistically, but could have funky gameplay results. Worth trying it out.
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