Tyr Damage Calculation Formula: Shell Math and Armor Guide
Master the Tyr damage calculation formula: exact order of operations, shell multipliers, effective sloped armor trigonometry, ricochets, and STK tables.
Tyr damage math executes sequentially: flat bonuses add to base damage first, percentage buffs pool additively, shell multipliers scale true damage, and armor sloped trigonometry reduces incoming alpha.
Tactical Overview of Tyr Combat Mathematics
Combat in Tyr is governed by deterministic formulas rather than random damage spreads. Unlike arcade shooters that rely on broad damage RNG (random number generation), every shell fired in Tyr evaluates a rigorous ballistics pipeline: flat talent additions, additive percentage scaling, shell velocity multipliers, armor impact angle trigonometry, and sequential defensive mitigation.
Understanding this deterministic sequence allows tank commanders to optimize component builds, calculate exact Shots to Kill (STK) against opposing chassis, and angle hull armor plates to create impenetrable ricochet angles.
The Complete Four-Step Damage Pipeline
Every projectile fired in Tyr follows a fixed mathematical sequence from firing pin strike to hull impact:
| Pipeline Stage | Mathematical Operation | Practical Example (105mm Gun) |
|---|---|---|
| Stage 1: Flat Base Sum | Base shell alpha + flat talent and component bonuses | 200 + 10 (Talent) + 5 (Duplicator) + 7.5 (Charger) = 222.5 |
| Stage 2: Additive Percent Pool | Sum same-type percentage buffs into a single scalar | 222.5 × (1.0 + 0.05 + 0.10) = 255.88 |
| Stage 3: Ammunition Multiplier | True shell damage × loaded shell type modifier | 255.88 × 1.20 (High Explosive) = 307.05 Muzzle Alpha |
| Stage 4: Armor & Defense Chain | Sloped armor absorption + sequential defense components | 307.05 × (1 − 0.08) − 3 (Micro Plating) = 279.48 → 279 HP |
Stage 1: Flat Base Stat Accumulation
Flat bonuses from mounted components and tech tree nodes add directly to the weapon’s base shell alpha. For instance, testing a frontline medium tank with standard armament:
200 (Base Alpha) + 10 (Shell Talent) + 5 (Duplicator) + 7.5 (Shell Charger) = 222.5 Base Alpha
Flat modifiers are always computed before any percentage scaling takes place. Because flat bonuses increase the foundational base number that later multipliers act upon, mounting flat damage components produces the greatest relative return on high-fire-rate, lower-caliber cannons (such as 76mm and 90mm guns).
Stage 2: Additive Percentage Stacking Rule
A foundational rule of Tyr combat engineering is that percentage buffs of the same category never compound multiplicatively. Multiple items or talents granting percentage increases to firepower or hit points pool into one combined additive factor before applying to the base sum.
Health Pool Scaling Example
Consider maximum health calculations on heavy chassis:
- Chassis Baseline: 2050 HP (Atlas)
- Flat Durability Node: +200 HP
- Pre-Percentage Subtotal: 2250 HP
- Bulkheads Component: +8.5% Maximum Health
- Final Health Pool: 2250 × 1.085 = 2441.25 HP
If flat additions and percentage modifiers are mixed in incorrect order, tanks would experience erratic balance drift. The additive pre-percentage rule ensures predictable balance across all 18 vehicle weight classes.
Stage 3: Ammunition Modifiers & Ballistics Profiles
Once true base damage is established, the loaded shell applies its dedicated damage and velocity scalar. Different ammunition types present distinct ballistic trade-offs:
| Shell Type | Alpha Damage Multiplier | Penetration Characteristics | Tactical Trade-off |
|---|---|---|---|
| Standard AP | 1.00x Baseline | Balanced baseline penetration | Reliable muzzle velocity and standard normalization |
| High Explosive (HE) | 1.20x Buff | Fixed low penetration (no normalization) | Vulnerable to spaced armor and heavy frontal plates |
| Gargantuan Shell | 1.20x Buff | Enhanced module damage | Significant dispersion penalty and increased aim time |
| Momentum Shell | 1.30x Buff | Penetration increases over flight distance | Requires minimum 200m engagement distance to activate |
| Unstable Payload | 1.10x Buff | High splash radius | Reduced maximum flight velocity |
Applying a High Explosive shell to our Stage 1 example:
222.5 True Base × 1.20 (HE Modifier) = 267.0 Muzzle Alpha Damage
Stage 4: Sloped Armor Trigonometry & Ricochet Limits
When a projectile reaches the target vehicle, the game engine calculates armor penetration before applying hull hit-point reductions.
Effective Armor Thickness Formula
Armor plates in Tyr are modeled with physical thickness and angular slope:
$$\text{Effective Armor} = \frac{\text{Nominal Plate Thickness}}{\cos(\theta)}$$
Where $\theta$ represents the impact angle relative to the plate normal (perpendicular axis):
| Impact Angle ($\theta$) | Cosine Value | Nominal 100mm Plate | Nominal 160mm Plate | Nominal 260mm Plate |
|---|---|---|---|---|
| 0° (Flat Impact) | 1.000 | 100.0mm Effective | 160.0mm Effective | 260.0mm Effective |
| 30° (Moderate Angle) | 0.866 | 115.5mm Effective | 184.8mm Effective | 300.2mm Effective |
| 45° (Optimal Diamond Angle) | 0.707 | 141.4mm Effective | 226.3mm Effective | 367.7mm Effective |
| 60° (Extreme Angle) | 0.500 | 200.0mm Effective | 320.0mm Effective | 520.0mm Effective |
| 70° (Ricochet Threshold) | 0.342 | Automatic Ricochet | Automatic Ricochet | Automatic Ricochet |
The Ricochet and Overmatch Rules
- Armor-Piercing Ricochet Limit: Any standard AP shell striking at an impact angle $\ge 70^\circ$ automatically ricochets, dealing zero damage regardless of incoming penetration value.
- HEAT Ricochet Limit: High-Explosive Anti-Tank (HEAT) warheads maintain penetration up to an extreme $85^\circ$ angle before deflecting.
- Caliber Overmatch: If incoming shell caliber exceeds three times the nominal plate thickness (e.g. a 152mm shell striking a 40mm roof plate), the shell ignores ricochet angles and guarantees full penetration.
Stage 5: The Sequential Defensive Mitigation Chain
If a shell penetrates effective armor, the receiving vehicle’s defensive components process sequentially. Unlike attacker buffs which add together, defenses compound multiplicatively:
Damage Received = (Incoming Alpha × Component 1 Reduction × Component 2 Reduction) − Flat Plating
Defense Calculation Walkthrough
Consider a 267 incoming shell striking a heavy tank equipped with Adaptive Hardening (-8% reduction while spotted) and Reactive Modules (-10% reduction following component damage), backed by Micro Plating (-3 flat damage reduction):
Step A: 267.0 × (1 − 0.08) = 245.64 HP
Step B: 245.64 × (1 − 0.10) = 221.08 HP
Step C: 221.08 − 3.0 (Flat Plating) = 218.08 → 218 HP Final Damage
Notice the compounded reduction: $0.92 \times 0.90 = 0.828$, yielding a total damage reduction of 17.2% rather than an additive 18.0%.
Comprehensive 18-Tank Armor & Shots to Kill (STK) Lookup Matrix
The table below provides the definitive tactical benchmark for all 18 chassis in Tyr. It maps nominal armor values, effective angled frontal armor, total health pools, and baseline Shots to Kill (STK) required when engaged by standard 105mm cannons (250 Alpha) versus heavy 130mm Siege cannons (650 Alpha):
| Tank Chassis | Combat Role | Base HP Pool | Frontal Armor (Nominal) | Effective Front Armor (45° Angle) | 105mm Gun STK (250 Alpha) | 130mm Gun STK (650 Alpha) |
|---|---|---|---|---|---|---|
| Alecto | Light Scout | 1150 HP | 45mm | 63.6mm | 5 Shots | 2 Shots |
| Kestrel | Aerial Scout | 1100 HP | 40mm | 56.6mm | 5 Shots | 2 Shots |
| Tempest | Flank Scout | 1250 HP | 55mm | 77.8mm | 5 Shots | 2 Shots |
| Helio | Shield Support | 1300 HP | 60mm | 84.9mm | 6 Shots | 2 Shots |
| Rook | Light Brawler | 1425 HP | 80mm | 113.1mm | 6 Shots | 3 Shots |
| Phantom | Infiltrator | 1450 HP | 75mm | 106.1mm | 6 Shots | 3 Shots |
| Deadeye | Sniper Medium | 1500 HP | 90mm | 127.3mm | 6 Shots | 3 Shots |
| Fuse | Missile Medium | 1550 HP | 120mm | 169.7mm | 7 Shots | 3 Shots |
| Maul | Rammer Medium | 1600 HP | 130mm | 183.9mm | 7 Shots | 3 Shots |
| Corsair | Tank Destroyer | 1600 HP | 110mm | 155.6mm | 7 Shots | 3 Shots |
| Valor | Brawler Medium | 1650 HP | 160mm | 226.3mm | 7 Shots | 3 Shots |
| Arbalest | Siege Destroyer | 1700 HP | 140mm | 198.0mm | 7 Shots | 3 Shots |
| Atlas | Frontline Medium | 2050 HP | 150mm | 212.1mm | 9 Shots | 4 Shots |
| Vanguard | Assault Heavy | 2150 HP | 200mm | 282.8mm | 9 Shots | 4 Shots |
| Sentinel | Defense Heavy | 2200 HP | 220mm | 311.1mm | 9 Shots | 4 Shots |
| Bastion | Fortress Heavy | 2300 HP | 260mm | 367.7mm | 10 Shots | 4 Shots |
| Paladin | Support Heavy | 2400 HP | 240mm | 339.4mm | 10 Shots | 4 Shots |
| Goliath | Siege Heavy | 2500 HP | 280mm | 396.0mm | 10 Shots | 4 Shots |
Frequently Asked Questions
Can two identical percentage buffs stack together in Tyr?
Yes, but they combine additively into a single pool rather than multiplying. Two separate +10% firepower buffs result in a clean +20% damage increase over baseline.
How does module damage calculate against tracks and engines?
Critical hits against internal modules calculate independently of hull hit points. Once effective armor is pierced, shell caliber and module damage talents determine if the component breaks or jams.
Does angling my hull reduce high-explosive blast damage?
Direct armor plating mitigates splash damage based on plate thickness at the detonation point. Angling decreases the risk of direct penetration, but high-explosive shockwaves still apply partial splash damage to surrounding tracks and optics.