Ranking the 40k Buffs


  • Reroll Ones: multiplier of 7/6
  • Chapter Master Rerolls: for BS3+ models, a multiplier of 8/6. This amounts to taking the normal expected total (6/6 of the total) and expecting two more die faces out of it (6 + 2)/6. This strategy applies to reroll failed wounds too, imagine you wound on a 4+. The multiplier is (6 + 3)/6. Reroll Wounds, to Wound of 6+? Multiplier of 11/6.   
  • Exploding Dice: The multiplier can be summarized as, take the sum of normally expected results and multiply it by the number of faces + 1 for each exploding face, and divide by the number of faces ie 6. So, Exploding on 6+s means a multiplier of 7/6, and exploding on 5+s means a multiplier of 8/6   
  • +1 to the Die Roll: count the normal number of faces that succeed; divide the normal sum of successes by that count; multiply that by the new number of faces that succeed. Example: Str 4 VS T3, 4 faces normally wound, now 5 faces wound, the multiplier is 5/4. 
  • Unmodified rolls of 6+ to hit produce 2 hits instead of 1: The formula is, number of faces that succeed + 1 divided by the number of faces that succeed. So BS3 has 4 successful faces on the die; the buff is 5/4. BS4 has a buff of 4/3. [Special explanation here: https://40kgamejournal.blogspot.com/2019/03/how-does-rules-like-unmodied-hit-rolls.html] With this modifier it is important to incorporate the modifiers to hit into counting the successful faces rather than relegating the power of the +1 to the die roll to its own modifier. 
  • Unmodified rolls of 6 automatically Wound, no need to roll to Wound: Depends on your To Wound Roll, and thus has 5 classes [The formula is addressed here: https://40kgamejournal.blogspot.com/2019/03/how-do-you-account-for-unmodifier-rolls.html]. The value of this force multiplier only depends on how many faces on the die count as a successful wound. (NumOfShots * BS-1 odds to Hit * odds to wound) + (NumOfShots/6) = Total Number of Wounds Generated.
Average expected outcomes: Logically it follows that Bolter Drill is capable of doubling the number of total shots, while Chapter Master will never excede the original number of shots. However this is a look at averages.

If you take your normal unbuffed expected outcome, if you use the following buffs the results on average will be multiplied by the given multiplier:
  • Chapter Master reroll misses is 8/6 (1.3333)
  • Bolter Drill exploding 5+s is 8/6 (1.3333) 
  • +1 to a hit roll is 5/4 (1.25) (For BS3+)
  • Bolter Drill exploding 6+s is 7/6  (1.166666)
  • Reroll ones is 7/6 (1.16666)
+1 to Wound Depends on Str VS Toughness, there are 5 classes
  • Normally Wound on 6+: 2/1 (2.0)
  • Normally Wound on 5+: 3/2 (1.5)
  • Normally Wound on 4+: 4/3 (1.33333)
  • Normally Wound on 3+: 5/4 (1.25)
  • Normally Wound on 2+: 6/6 (1.0, improvement not possible)
Reroll failed Wounds Depends on Str VS Toughness, there are 5 classes
  • Normally Wound on 6+: 11/6  (1.833333)
  • Normally Wound on 5+: 10/6  (1.666666)
  • Normally Wound on 4+: 9/6   (1.5)
  • Normally Wound on 3+: 8/6  (1.3333)
  • Normally Wound on 2+: 7/6  (1.16666)
Reroll Failed Hits, by BS
  • BS 6+: 11/6  (1.833333)
  • BS 5+: 10/6  (1.666666)
  • BS 4+: 9/6   (1.5)
  • BS 3+: 8/6  (1.3333)
  • BS 2+: 7/6  (1.16666)
+1 to Hit by BS
  • BS 6+: 2/1 (2.0)
  • BS 5+: 3/2  (1.5)
  • BS 4+: 4/3   (1.3333)
  • BS 3+: 5/4  (1.25)
  • BS 2+: 6/6  (1.0, improvement not possible rolls of 1 always fail)
+2 to Hit by BS
  • BS 6+: 3/1 (3.0)
  • BS 5+: 4/2  (2.0)
  • BS 4+: 5/3   (1.6666)
  • BS 3+: 6/4  (1.5)
  • BS 2+: 6/6  (1.0, improvement not possible rolls of 1 always fail)
Unmodified rolls of 6+ to hit produce 2 hits instead of 1, by BS (more here):
  • BS6: 2/1 (2.00)
  • BS5: 3/2 (1.5)
  • BS4: 4/3 (1.6666)
  • BS3: 5/4 (1.25)
  • BS2: 6/5 (1.2) 
  • with this modifier uniquely, you need to pick the BS your unit has as if any To Hit modifiers were applied to it. i.e. BS3 with a -1 to hit works like a BS4; BS3 with a +1 to hit operates like BS2. 
For unmodifed rolls to hit of 6 causing a wound automatically with no need to roll, the force multiplier depends on the class of roll required for damage and the BS of the attacking unit. (More here)

  • For BS3+:
    • 2+ To Wound has a force multiplier of 21/20
    • 3+ To Wound has a force multiplier of 9/8
    • 4+ To Wound has a force multiplier of 5/4
    • 5+ To Wound has a force multiplier of 3/2
    • 6+ To Wound has a force multiplier of 9/4
  • For BS4+
    • 4+ To Wound has a Force Multiplier of 4/3 (more to come eventually)
Rerolling Failed Wounds is one of the greatest Buffs in 40k, and is a driving force behind Guilliman's success as a unit. Considering defacto all Marines are BS3, the Chapter Master buff that Guilliman also has is usually a Buff of 1.33333; but the Reroll failed Wound Rolls is usually between 1.3333 and 1.83333.

If Ultramarines next to Guilliman are shooting Chaos Space Marines, the total Buff Guilliman confers total to 2 times normal production (8/6 * 9/6 = 72/36 = 2.0). Marines are literally twice as killy in his presence.

Comments

  1. An example of how this works is:
    Number of Shots * Odds to Hit * Odds to Wound * Odds to Fail Armor Save * Buff1 * Buff2 = number of unsaved wounds.

    So, Veteran Intercessors Rapid Fire 2, Bolter Drill, with Kantor + Lieutenant, shooting Orks who will get no Armor Save reads like this:

    40 * 2/3 * 1/2 * 1 * 7/6 (lieutenant) * 8/6 (Kantor) * 8/6 (Bolter Drill) * 5/4 (+1 to hit) = 35 wounds

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