Reference

Numbers & Formulas

Everything numeric in one place. Each row links back to the page that explains it.

On this page

Costs
Caps and limits
Combat
Timers and durations
Reward formulas
Class cadence formulas

Costs

What	Formula / value	Page
Normal upgrade level	`10 × level²`	Upgrades
Class upgrade level	earned by flying	Upgrades
Revive	`wave × 10`	Waves
Reinforcement Clone summon	`wave × 100`	Reinforcement Clone
Premium ship unlock	200,000, +100,000 per ship already owned	Ships
Charge buff (escalating)	100,000, +100,000 per paid buff owned	Charge Skill
Doppelgeschoss	400,000 flat	Charge Skill
Reinforcement Clone unlock	300,000 flat, each	Reinforcement Clone
Decal	100,000 flat	Cosmetics
Afterburner colour	50,000, +50,000 per colour owned (Blue and Orange free)	Cosmetics

Caps and limits

What	Value
Stronger Bullets / Faster Bullets / Health Increase max level	100
Additional Bullets max level	9
Common-upgrade levels shared across ships	50
Class max level — Healer, Shielder, Bomber, Assister	30
Class max level — every other ship	50
Decals equipped per ship	30
Decal preset slots per ship	3
Buff-ball stacks per type	10
Buff balls on screen	10
Assister-spawned assist balls alive	6
Players in co-op	4
Enemy soft cap (reduced effects)	120 (70)
Concurrent explosions (reduced effects)	16 (2)
Custom playlist songs	100

Combat

What	Value
Base bullet damage	10.0
Faster Bullets, fire rate per level	+4%
Lv100 bonuses — explode chance / radius, flat fire rate, wave-clear heal	10% / 10 px · +10% · 5–10 HP
Bullet fan spread per extra bullet	5.0°
Focus Fire spread	2.0°
Player radius	32 px
Arena	800 × 800
Chain-lightning range / hops (assist ball)	300 px / 10
Chain-lightning hops (Tesla class)	20
Chain-lightning hops (Tesla Clone)	5
Enemy speed scaling	1 + (wave − 1) × 0.02
Boss contact damage	wave × 2
Boss-gun bullet damage	10
Boss-gun volley size (wave 50+)	1 + (wave − 50) ÷ 10

Timers and durations

What	Value
Boss dive countdown	wave × 25 s (Twirly wave × 20 s)
Revive window	10 s
Band-buff vote countdown	10 s
Vote intro / decide pause / result hold	1 s / 1.5 s / 2.5 s
Assist ball lifetime	30 s
Gold ball lifetime	30 s
Buff ball lifetime / buff duration	15 s / 120 s
Mastery XP	+4 / wave, +20 / boss, +4 per elite kill (50%)
Mastery ability level	1 + floor(√XP), capped at 30 or 50
Mastery rank thresholds	0 / 25 / 75 / 175 / 350 / 650 / 1100 XP
Stardust value	100,000 gold
Stardust drop	boss 5%, elite 2% (×2 on Elite Hunt)
Stardust idle decay	1 per hour away
Elite spawn rate	4% from wave 4
Elite health / size	×6 (×1.6 more if tough) / ×1.7
Wave event chance	20% on non-boss waves from wave 6
Fever	combo 15+, 8 s, ×2 coins
Beat damage to a boss	×12 effective damage per beat
Debrief record bonus	200 gold × wave, per record beaten
On-beat crit multiplier	×2
Crit chance off-beat	+2% per combo, capped 50%
Band-buff pierce	±1 enemy, floored at 0
Zone assist ball	100 px, 4 s, 3× damage every 0.5 s
Beat-synced spawns	up to 4 enemies per beat
Party Damage	+50% for 30 s
Charge Doubler	2× for 30 s
Focus Fire / Doppelgeschoss	100 volleys
Reinforcement Clone duration	wave seconds
Reinforcement Clone HUD button visible	wave > 6 (from wave 7)
Reinforcement cooldown between summons	120 s / 30 s with the Pass
Reinforcement ally lifetime	300 s / 600 s with the Pass
Reinforcement HUD button visible	60 s
Reinforcement lock after an empty pool	30 s
Goldie lifetime	wave × 15 s
Buzzby puzzle window	wave seconds
Beat hit window	±35% of a beat (±194 ms at 108 BPM)
Chompy / Mama Spider respawn after death	10 s
Tesla max-level stun	2 s

Reward formulas

Source	Formula
Boss gold ball	`wave × 500 × dive-timer fraction remaining`
Goldie	`wave × 200 × lifetime fraction remaining`
Mini boss / level-10 boss kill	`wave × 10` / `wave × 20`
Buzzby solve (word / perfect)	`wave × 200` / `wave × 300`
Rhythm pot per input	`200` per ball or charge, `100` per free tap
Rhythm every-10 extra	`50 × wave`
Song-end payout	`combo × wave × 5`, only above combo 10
Daily total	`max(highest wave, 10) × 1,000`, split 40 / 20 / 40
War liberation	`100,000`
Buzzby failure damage	`wave ÷ 5` to every player

Class cadence formulas

Ship	Interval	Lv1	At cap
Laser	`max(0.1, 50 ÷ level)`	50 s	1 s
Tesla	`max(1, 51 − level)`	50 s	1 s
Oktopodia	`max(2, 100 ÷ level)`	100 s	2 s
Flare	`max(0.5, 25 ÷ level)`	25 s	0.25 s
Pinball	`max(1, 26 − level × 0.5)`	25.5 s	1 s
Flying Sky Whale	`max(10, 30 − 0.4 × level)`	29.6 s	10 s
Horridus	`max(5, 15 − level ÷ 5)`	14.8 s	5 s
Flammenwerfer	`max(5, 15 − level × 0.2)`	14.8 s	5 s
Einfrieren	`max(5, 15 − level × 0.2)`	14.8 s	5 s
Clavier	`60 ÷ BPM (one note per beat)`	—	—

Healer, Shielder, Bomber and Assister have no interval — they roll a level % chance on every kill. Gemini has no interval either; its drone is permanent and its damage is level ÷ 50 of yours.