The Maths of Multiplicative Modifiers in Delta Force.
A technical guide to understanding how recoil modifiers interact, with a practical example using the M4A1 Assault Rifle.
Recoil modifiers in this game are applied as percentages, reducing the recoil by a percentage of its current value rather than absolutely original value.
Each attachment reduces the recoil based on what remains after the previous percentage reduction.
How It Works: Example with the M4A1 Assault Rifle
Let’s take the M4A1 assault rifle as an example. It has an initial control value of 41. Control impacts five sub-attributes:
- Full-auto Vertical Recoil Multiplier
- Full-auto Horizontal Recoil Multiplier
- Single/ Burst Vertical Recoil Multiplier
- Single/ Burst Horizontal Recoil Multiplier
- Firing Stability
The recoil modifiers are applied multiplicatively to the sub-attributes, and different attachments impact different sub-attributes.
"Let’s examine the Silent Suppressor and the Blazing Fire Suppressor. Both have a +6 Control stat, but their effects on sub-attributes differ. We have to check in the details to see which Control sub-attributes they change.
A multiplier of 1 has no change to the current value. A multiplier of 0.76 means that the sub-attribute is reduced to 76% of its original value, or equivalently it represents a 24% reduction.
Reduction Calculation
Reduction = (1 - Multiplier) × 100
Reduction = (1 - 0.76) × 100
Reduction = 24%
Result: A multiplier of 0.76 represents a 24% reduction.
| Sub-attribute | Silent Suppressor | Blazing Fire Suppressor |
|---|---|---|
| Full-auto Vertical Recoil Multiplier | 1 | 0.88 |
| Full-auto Horizontal Recoil Multiplier | 1 | 0.88 |
| Single/ Burst Vertical Recoil Multiplier | 0.76 | 0.88 |
| Single/ Burst Horizontal Recoil Multiplier | 0.76 | 0.88 |
| Firing Stability | 0.76 | 0.95 |
With this in mind we can run an example with the Birdcage Flash Hider muzzle and the 416 Stable Stock stock showing how the multipliers work.
| Sub-attribute | Birdcage Flash Hider | 416 Stable Stock | Working | Reduction | Percentage Reduction |
|---|---|---|---|---|---|
| Full-auto Vertical Recoil Multiplier | 0.94 | 0.92 | 0.94 × 0.92 | 0.86 | 14% |
| Full-auto Horizontal Recoil Multiplier | 0.94 | 0.92 | 0.94 × 0.92 | 0.86 | 14% |
| Single/ Burst Vertical Recoil Multiplier | 0.94 | 0.92 | 0.94 × 0.92 | 0.86 | 14% |
| Single/ Burst Horizontal Recoil Multiplier | 0.94 | 0.92 | 0.94 × 0.92 | 0.86 | 14% |
| Firing Stability | 0.98 | 0.97 | 0.98 × 0.97 | 0.95 | 5% |
We start our M4A1 build with 100% recoil in each sub-attribute. Each attachment will reduce our recoil multiplicatively, not additively.
Why Each Attachment Has Less Impact
The Birdcage Flash Hider reduces the Full-auto Vertical Recoil Multiplier by 6%, bringing it down to 94% of its original value. When the 416 Stable Stock is added, it applies an additional 8% reduction, but this reduction is calculated on the remaining recoil, not the original value.
- Start with 100% recoil for Full-auto Vertical Recoil.
- The Birdcage Flash Hider reduces recoil to
100% × 0.94 = 94% - The 416 Stable Stock then applies its multiplier to the remaining recoil:
94% × 0.92 = 86% - The combined effect of these two attachments results in a total reduction to 86% of the original recoil, which translates to a 14% reduction overall.
Key Takeaway
Recoil modifiers are not additive (e.g., 20% + 20% + 20% ≠ 60% Instead, they stack multiplicatively 20% × 20% × 20% = 51%, making each subsequent attachment less effective. This ensures that you can’t reduce recoil to 0%, no matter how many attachments you add.
If this seems complex, don’t worry—I’ve built an attachment builder engine to simplify the process for you.
Try out the attachment builder engine for M4A1 (Operations Optimiser) or M4A1 (Warfare)
M4A1 (Warfare) Perfect No Vertical Recoil Build