Updated as of Megabonk version 1.0.7.


Each weapon has its own list of stats that may be included in an upgrade. The included stats are chosen randomly, so different stats may be included next time if an upgrade is skipped. A common weapon upgrade may select one or two stats, but the higher rarities always select two stats. Weapon upgrades only affect the weapon that it's for.


Each tome is associated with a single stat, so their upgrades will include only one stat regardless of rarity. Tomes affect the Character Stats shown in the pause menu, and Character Stats affect all weapons.

Upgrades are additive. A common Sword upgrade will always add +2 to the Damage (if the Damage stat is included). Likewise, a common Damage Tome upgrade will always add +0.08x to the stat.

Some stats stack multiplicatively. The Sword's Damage gets multiplied by the Damage Tome's multiplier to determine the final damage value. Other stats stack additively. See the Stat Formulas section below for a detailed analysis.


Rarity affects the size of the stat improvement:


For example, Sword upgrades will improve stats by the following amounts:


The rest of this guide will only refer to common-rarity upgrades since you can always multiply by the Rarity Factor to produce the other rarities.

This section lists the weapons' upgradable stats. Every weapon can upgrade its Damage.

Your character's current stats are shown in the pause menu and in every upgrade, shrine, chest, and shop screen. Character Stats are modified by many sources, including:

• All tome upgrades
  
• All charge shrine upgrades
  
• Specific character's initial stats
  
• Specific character's special abilities
  
• Many items
  
• Greed shrines

The following table includes all Character Stats in the same order as the pause menu. The Initial Character Stats shown are typical values, see the Initial Character Stats section for details.

The Initial Tome Stats shown are the effective values before you pick up any tomes. Picking up a tome immediately provides a common-rarity upgrade. Note that all tomes have an initial value of 0 except for the Damage Tome which has an initial value of 1x. The Damage Tome is known to be multiplicative, and all other tomes are very likely additive. See the Stat Formulas section below for a detailed analysis of how these different stat modifiers stack.

This section dives into the details of stat calculations. Expect it to be dense and complicated. I'm working on adding tables so you won't need to read this.

• A Weapon Stat is the value displayed in the weapon's upgrade menu.
  
  • Example: An upgraded Sword may have a Sword Damage value of 13.
• A Tome Stat is the value displayed in the tome's upgrade menu.
  
  • Example: An upgraded Damage Tome may have a Tome Damage value of 1.16x.
• A Shrine Stat is the sum of the Charge Shrine values displayed in the Shrine Logs section of the pause menu.
  
  • Example: If the Shrine Logs show "Gain 12%" twice, then you have a Shrine Damage value of 24%.
• A Character Stat is the value displayed in the stats section of the pause menu.
  
  • Example: The pause menu may show that you have a Character Damage value of 1.3x.
• A Weapon's Effective Stat is the result of combining the Weapon Stat and the Character Stat.
  
  • Example: If a sword's non-critical strike does 24 damage to an enemy, it has an Effective Damage value of 24.

• Initial Weapon Stats vary by weapon, see the Weapons section for details.
  
• Initial Tome Stats vary by tome, see the Tomes, Shrines, and Character Stats section for details.
  
• Since Initial Shrine Stats are not displayed, we take the convention that they all have an initial value of 0 or 0%.
  
• Initial Character Stats vary by character, see the Initial Character Stats section for details.

All upgrades have an additive effect on its associated stat. More explicitly:

• A Sword's Damage upgrade will add 2 to the Sword Damage stat, regardless of the stat's current value.
  
• A Damage Tome's upgrade will add 0.08x to the Tome Damage stat, regardless of the stat's current value.
  
• A Charge Shrine's Damage upgrade will add 12% to the Shrine Damage stat, regardless of the stat's current value.

• If a formula calls for a stat that is a percentage, divide the stat's value by 100 before plugging it in to the equation.
  
  • Example: 50% = 0.5
• If the result of a formula is expected to be a percentage, multiply the result by 100 to get the percentage.
  
  • Example: 2.4 = 240%

Damage is multiplicative! This has been carefully tested and validated:

• Effective Damage = Weapon Damage * Character Damage
  
• Character Damage = Initial Character Damage * Tome Damage * (1 + Shrine Damage)

Projectile Count is additive.

• Effective Projectile Count = Weapon Projectile Count + Character Projectile Count
  
• Character Projectile Count = Initial Character Projectile Count + Tome Projectile Count + Shrine Projectile Count

Not modified by Tomes or Charge Shrines.


Size is a mix of additive and multiplicative. This has been carefully tested and validated:

• Effective Size = Weapon Size * Character Size
  
• Character Size = Initial Character Size * (1 + Tome Size + Shrine Size)

The fact that these Weapon Stats are absolute (e.g. 4) while the Character Stats are relative (e.g. 1.2x) strongly hints that the Effective Stat is likely the product of the two.


Preliminary equations, requires more testing:

• Effective Crit Damage = (1 + Weapon Crit Damage) * Character Crit Damage * Effective Damage
  
• Character Crit Damage = Initial Character Crit Damage * (1 + Shrine Crit Damage)

Pickup Range is a mix of additive and multiplicative. This has been carefully tested and validated:

• Character Pickup Range = Initial Character Pickup Range * (1 + Tome Pickup Range + Shrine Pickup Range)

Given that the Initial Character Jump Height is absolute (e.g. 7) and the Shrine Jump Height is relative (e.g. 10%), this is likely multiplicative like Pickup Range. The lack of a Jump Height Tome and little variation between characters makes this difficult to test.


Evasion is additive with a hyperbolic adjustment. This has been carefully tested and validated:

• Character Evasion = Internal Evasion / (1 + Internal Evasion)
  
• Internal Evasion = Initial Internal Evasion + Tome Evasion + Shrine Evasion

Armor is additive with a hyperbolic adjustment. This has been carefully tested and validated:

• Character Armor = Internal Armor / (0.75 + Internal Armor)
  
• Internal Armor = Initial Internal Armor + Tome Armor + Shrine Armor

This section dives into the details of stat calculations. Expect it to be dense and complicated. I'm working on adding tables so you won't need to read this.

Suppose you are given a choice between any common Revolver upgrade. Which upgrade will increase your DPS the most?

To answer this question, we first need an equation to show how DPS depends on the Revolver's stats. Revolver upgrades can improve Damage, Projectile Count, Projectile Bounces, Crit Chance, Crit Damage, and Projectile Speed. We can ignore Projectile Speed since it doesn't affect DPS. In broad strokes, we have that:

• DPS = k * Damage * Projectile Count * (1 + Projectile Bounces) * (1 + Crit factor)

where k is some constant of proportionality that is irrelevant to our analysis.

To fill in the crit factor, we have to take a moment to understand how critical hits work. We will assume for simplicity that the character's Crit Damage stat is 2x. (This stat is distinct from the weapon's Crit Damage stat). Thus the actual damage from a critical hit = Damage * 2 * (1 + Crit Damage). For example, the Revolver starts at 5 Damage and 0% Crit Damage, so critical hits do 5 * 2 * (1 + 0%) = 10 damage.

To work out the Crit factor in the above equation, we need to subtract and factor out the Damage (giving us just the bonus damage due to crits) and then multiply by the Crit Chance. This gives us

• Crit factor = Crit Chance * (2 * (1 + Crit Damage) - 1)

Putting it together, we get:

• DPS = k * Damage * Projectile Count * (1 + Projectile Bounces) * (1 + Crit Chance * (2 * (1 + Crit Damage) - 1))

To answer the question "which upgrade will increase your DPS the most?", we can ask a simpler question: "what weapon stats will result in any available common upgrade increasing DPS by exactly 10%?" (This will give us a Nash equilibrium of weapon upgrade strategies.)

Given that the Revolver has these upgrade values:


You can use the DPS formula above to verify that any upgrade will improve the DPS by 10% when the Revolver has the following stats:


The DPS Improvement Factor is straightforward to calculate when upgrading Damage, Projectile Count, or Projectile Bounces. It is equal to:

• Damage Upgrade / Current Damage
  
• Projectile Count Upgrade / Current Projectile Count
  
• Projectile Bounces Upgrade / (Current Projectile Bounces + 1)

For example, upgrading the Revolver's damage from 25 will yield a 2.5/25 = 10% DPS improvement, regardless of the Revolver's other stats. This aligns with our intuition that we get diminishing returns from each upgrade as the Revolver's damage scales up. Thus, if the Damage, Projectile Count, or Projectile Bounces is less than the values in the above table, then its upgrade will yield a DPS improvement greater than 10%.

Upgrading the Crit Chance and Crit Damage is more complicated though since each upgrade's effect on DPS depends on the current values of both Crit Chance and Crit Damage.

When you upgrade Crit Damage:

• 

When you upgrade Crit Chance:

• 

We can similarly see diminishing returns when either stat is upgraded in isolation. Thus we can conclude that our build is optimized when these stats have a Nash equilibrium, so we can simplify our lives by setting these equations equal to each other and solving:

• 

For the Revolver, this simplifies to Current Crit Chance = Current Crit Damage / 2 + 25%. As an example, if our Crit Damage is currently 100%, this tells us that we should upgrade Crit Chance until it is 1/2 + 25% = 75%.

While it is true that upgrading either of these stats in isolation yields diminishing returns, there is a bit of an oddity when they're in equilibrium at low values. The DPS Improvement Factor reaches a maximum of 10% when the Revolver's Crit Chance and Crit Damage are at 50%. This means that, until Crit Chance and Crit Damage reach 50%, upgrading these stats in equilibrium yields increasing returns. Thus it's not worth upgrading Crit Chance and Crit Damage at all until the other stats give less than 10% DPS improvement.

Putting this all together, we get the following table for the Revolver:


It is important to note that this analysis has several limitations, including:

• Charge shrine upgrades, items, and base stats of some characters can throw off the balance of these stats.
  
• This analysis does not consider the impact of rarity when selecting an upgrade. Optimizing for short-term gains does not always produce the best long-term outcomes.
  
• The equations assume that Crit Chance scales naturally beyond 100%. (E.g. at 200% every strike does the base damage plus double the bonus crit damage.) This may not be the case.
  
• The DPS calculation assumes that there are enough enemies to saturate the projectile count and bounces. A different strategy would benefit boss battles.