# Hammer of Math: The Cost of Overcharging in Warhammer 40k (Imperial Edition)

This week’s Hammer of Math takes a look at what price an Imperial player pays every time they fire an overcharged plasma weapon in Warhammer 40k. We’ll do a follow up at some point to cover the other factions.

In the 40k lore, plasma weapons are ancient creations of unparalleled value. Relics of the Dark Age of Technology, these devices are capable of unleashing incandescent destruction by firing pulses of highly charged plasma at a target that the Emperor/Chaos Gods/Boss wants dead. On impact they burn through armour and flesh with equal ease, but these power comes at a cost. Plasma weapons were designed with one simple idea; the weapon was more valuable than the being firing it. As a result they can overheat, and in lieu of becoming a bomb they instead vent the excess ionized gas into the surrounding area. That the surrounding area was previously occupied by a living creature is largely irrelevant, as the important thing is that the weapon remains intact to fire again.

In Warhammer 40k this overheating mechanism is represented by a mechanic based on the hit roll. Generally on a roll of 1 the target either takes a mortal wound or is killed outright, with no opportunity to save or mitigate the damage. The effective consequence is that every time a player fires an overcharged plasma weapon they are paying a price, that price being the product of the probability of overheat, the cost of the unit, and the amount of the unit degraded when the weapon overheats. For example a Hellblaster which costs 33 points firing an overcharged heavy plasma incinerator has a 1 in 6 chance of being completely destroyed, which means the cost per shot is 5.5 points.

The chart below shows all of the various plasma options for the Imperial factions. In addition to unit specific data (faction, name, type, wounds) the chart contains the weapons fired and the unit cost assuming just that weapon was purchased. The three columns on the right show the calculated results. The Probability / Average Losses column is either the probability of loss (if an overcharged result kills the target) or the average number of 1s rolled during an attack (if the overcharged result removes only some wounds). The Wounds Per Loss column is the wounds removed; often this value is equal to the Wounds characteristic of the firer because the model is destroyed. The Points Per Attack column on the far right is the final calculation; the average points lost for every attack made.

FactionUnitTypeWeaponCostWoundsProbability / Average LossesWounds Per LossPoints Per Attack
Astra MilitarumCompany CommanderHQPlasma Pistol4040.1746.67
Astra MilitarumLord CommissarHQPlasma Pistol4040.1746.67
Astra MilitarumTank CommanderHQExecutioner Plasma Cannon175121.17117.01
Astra MilitarumTank CommanderHQExecutioner + Plasma Sponsons215121.58128.37
Astra MilitarumTempestor PrimeHQPlasma Pistol4540.1747.50
Astra MilitarumMilitarum Tempestus ScionsTPlasma Gun (RF)1910.3115.81
Astra MilitarumMilitarum Tempestus ScionsTPlasma Pistol910.1711.50
Astra MilitarumCommissarEPlasma Pistol3030.1735.00
Astra MilitarumMilitarum Tempestus Command SquadEPlasma Gun (RF)2010.3116.11
Astra MilitarumPlatoon CommanderEPlasma Pistol3030.1735.00
Astra MilitarumServitorsEPlasma Cannon1810.3115.35
Astra MilitarumSpecial Weapons SquadEPlasma Gun (RF)810.3112.29
Astra MilitarumVeteransEPlasma Gun (RF)1710.3115.19
Astra MilitarumVeteransEPlasma Pistol710.1711.17
Astra MilitarumArmoured SentinelsFAPlasma Cannon4060.31612.22
Astra MilitarumLeman Russ Battle TanksHSExecutioner Plasma Cannon130121.17112.64
Astra MilitarumLeman Russ Battle TanksHSExecutioner + Plasma Sponsons170121.58122.43
Grey KnightsBrotherhood LibrarianHQCombi-Plasma (RF)11550.17519.17
Grey KnightsServitorsEPlasma Cannon1310.3113.82
Grey KnightsStormraven GunshipFTwin Heavy Plasma Cannon165140.6717.86
Imperial KnightsKnight CastellanLoWPlasma Decimator595281.17249.58
InquisitionInquisitorHQPlasma Pistol6550.17510.83
InquisitionInquisitorHQPlasma Gun (RF)7050.31521.39
Titan LegionsWarhound TitanLoW2 Warhound Plasma Blastguns2000502.33193.33
Titan LegionsWarlord TitanLoW2 Sunfury Plasma Annihilators55001203.174580.56
Space MarinesPrimaris CaptainHQPlasma Pistol10060.17616.67
Space MarinesCaptain in Terminator ArmourHQCombi-Plasma (RF)10560.31632.08
Space MarinesCaptainHQPlasma Pistol8550.17514.17
Space MarinesCaptainHQCombi-Plasma (RF)9050.31527.50
Space MarinesCaptain on BikeHQPlasma Pistol10560.17617.50
Space MarinesCaptain on BikeHQCombi-Plasma (RF)11060.31633.61
Space MarinesPrimaris LieutenantHQPlasma Pistol8050.17513.33
Space MarinesLieutenantHQPlasma Pistol7040.17411.67
Space MarinesLieutenantHQCombi-Plasma (RF)7540.31422.92
Space MarinesLibrarianHQPlasma Pistol9540.17415.83
Space MarinesLibrarianHQCombi-Plasma (RF)10040.31430.56
Space MarinesLibrarian in Terminator ArmourHQCombi-Plasma (RF)11550.31535.14
Space MarinesChaplain in Terminator ArmourHQCombi-Plasma (RF)10050.31530.56
Space MarinesChaplainHQPlasma Pistol8540.17414.17
Space MarinesChaplainHQCombi-Plasma (RF)9040.31427.50
Space MarinesTechmarineHQPlasma Cutter8540.31425.97
Space MarinesTechmarineHQPlasma Pistol7540.17412.50
Space MarinesTechmarineHQCombi-Plasma (RF)8040.31424.44
Space MarinesTechmarineHQPlasma Cutter + Combi-Plasma (RF)9540.52449.19
Space MarinesCompany AncientEPlasma Pistol8040.17413.33
Space MarinesCompany AncientEPlasma Gun (RF)8540.31425.97
Space MarinesCompany VeteranEPlasma Pistol2520.1724.17
Space MarinesCompany VeteranEPlasma Gun (RF)3020.3129.17
Space MarinesCompany VeteranEPlasma Cannon3520.31210.69
Space MarinesVanguard VeteranEPlasma Pistol2420.1724.00
Space MarinesVanguard VeteranE2 Plasma Pistols3420.31210.39
Space MarinesSternguard VeteranEPlasma Pistol2520.1724.17
Space MarinesSternguard VeteranEPlasma Gun (RF)3020.3129.17
Space MarinesSternguard VeteranEPlasma Cannon3020.3129.17
Space MarinesServitorsEPlasma Cannon1510.3114.62
Space MarinesHellblasterHSAssault Plasma Incinerator3320.42213.90
Space MarinesHellblasterHSPlasma Incinerator (RF)3320.31210.08
Space MarinesHellblasterHSHeavy Plasma Incinerator3320.1725.50
Space MarinesRepulsor ExecutionerHSMacro Plasma Incinerator300160.58110.94
Space MarinesStormraven GunshipFTwin Heavy Plasma Cannon260140.67112.38
Black TemplarsPrimaris Sword BrethrenEPlasma Pistol2720.1724.50
Blood AngelsSanguinary GuardEPlasma Pistol3520.1725.83
Blood AngelsSanguinary AncientEPlasma Pistol11540.17419.17
Blood AngelsDeath Company MarinesEPlasma Pistol2320.1723.83
Dark AngelsInterrogator-ChaplainHQPlasma Pistol9050.17515.00
Dark AngelsInterrogator-ChaplainHQCombi-Plasma (RF)9050.31527.50
Dark AngelsInterrogator-Chaplain in Terminator ArmourHQCombi-Plasma (RF)10560.31632.08
Dark AngelsRavenwing ApothecaryEPlasma Talon10050.31530.56
Dark AngelsRavenwing ChampionEPlasma Talon7050.31521.39
Dark AngelsRavenwing AncientEPlasma Talon10050.31530.56
Dark AngelsRavenwing Black KnightsEPlasma Talon3530.31310.69
Dark AngelsRavenwing Land Speeder VengeanceFAPlasma Storm Battery11090.6718.15
DeathwatchDeathwatch VeteransTDeathwatch Combi-Plasma (RF)3020.3129.17
DeathwatchDeathwatch VeteransTPlasma Pistol2520.1724.17
DeathwatchDeathwatch VeteransTPlasma Gun (RF)2520.3127.64
Space WolvesBjorn the Fell-HandedHQHeavy Plasma Cannon17580.2214.86
Space WolvesWolf Guard Battle Leader in Terminator ArmourHQCombi-Plasma (RF)9050.31527.50
Space WolvesWolf Guard Battle Leader on ThunderwolfHQPlasma Pistol10060.17616.67
Space WolvesWolf Guard Battle Leader on ThunderwolfHQCombi-Plasma (RF)11560.31635.14
Space WolvesWolf Lord on ThunderwolfHQPlasma Pistol11570.17719.17
Space WolvesWolf Lord on ThunderwolfHQCombi-Plasma (RF)12070.31736.67
Space WolvesBlood ClawsTPlasma Pistol2320.1723.83
Space WolvesBlood ClawsTPlasma Gun (RF)2820.3128.56
Space WolvesBlood Claws (Wolf Guard Terminator Pack Leader)TCombi-Plasma (RF)3830.31311.61
Space WolvesGrey HuntersTPlasma Pistol2320.1723.83
Space WolvesGrey HuntersTPlasma Gun (RF)2820.3128.56
Space WolvesGrey Hunters (Wolf Guard Terminator Pack Leader)TCombi-Plasma (RF)3830.31311.61
Space WolvesWolf GuardEPlasma Pistol2420.1724.00
Space WolvesWolf GuardECombi-Plasma (RF)2920.3128.86
Space WolvesLukas the TricksterEPlasma Pistol8040.17413.33
Space WolvesWolf Guard TerminatorsECombi-Plasma (RF)3830.31311.61
Space WolvesThunderwolf CavalryFAPlasma Pistol4540.1747.50
Space WolvesSkyclawsFAPlasma Pistol1820.1723.00
Space WolvesSkyclawsFACombi-Plasma (RF)2320.3127.03
Space WolvesSkyclaws (Wolf Guard Skyclaw Pack Leader)FAPlasma Pistol2520.1724.17
Space WolvesSkyclaws (Wolf Guard Skyclaw Pack Leader)FACombi-Plasma (RF)3020.3129.17
Space WolvesLong FangsHSPlasma Pistol2320.1723.83
Space WolvesLong FangsHSPlasma Gun (RF)2820.3128.56
Space WolvesLong FangsHSPlasma Cannon3320.31210.08
Space WolvesLong Fangs (Wolf Guard Terminator Pack Leader)HSCombi-Plasma (RF)3830.31311.61

### Takeaways

• Should you be the kind of player who thought dual Sunfury Plasma Annihilators was cool when you played Adeptus Titanicus, and decided to field an identical Warlord Titan at 40k scale, every attack will cost you around 10% of the value of the Warlord or the equivalent of a Knight Valiant.
• The plasma decimator on a Knight Castellan will cost an average of 50 points to fire in terms of self-inflicted wounds.
• The most costly choices are ones that should be obviously avoided, most notably putting a combi-plasma on an expensive Space Marine character like a Terminator Librarian. The chances of rolling at least 1 on a two dice is 31%.
• The most costly non-character unit is the Inceptor Squad where each model has a pair of plasma exterminators. On average the plasma exterminators will get four shots resulting in a 52% chance that the 60 point model will kill itself.
• Hellblasters with assault plasma incinerators are also in a pretty bad spot, with each model costing around 14 points thanks to the high probability of self-immolation.
• The Astra Militarum truly embody the notion that the gun is more valuable than the man firing it; a poor guardsman rapid firing a plasma gun only costs an average of 2 points.
• Re-rolling hits is essential for mitigating the effects of plasma. When a re-roll is incorporated you can divide the points per attack by 6.

### Wrapping Up

While not a perfect analysis, particularly in the context of units with a lot of options like Space Marine characters, the numbers show that overcharging plasma weapons is often a surprisingly expensive choice. While some players are quick to make accusations of cowardice for not overcharging, the reality is that often it’s in your best interest to consider whether the benefits will outweigh the cost. This would be mitigated if overheating plasma weapons consistently inflicted a mortal wound on the bearer’s unit rather than destroyed the firing model depending on the gun and circumstances. This change would produce three effects:

1. It would eliminate the need to individually roll plasma hits to determine which model was destroyed, significantly speeding up play.
2. It would reduce the impact on character models.
3. In the case of a mixed unit would allow the wound to be transferred to another model, representing another warrior picking up the plasma gun from the charred remains of the previous bearer.

Hopefully the chart provides some useful insight into the models of your army. In a future article we’ll take a look a the Xenos and Chaos armies.

Thanks for reading! If you have any questions or comments feel free to drop us a note in the Comments below or email us at contact@goonhammer.com. That’s also the best way to suggest topics for future articles.