Tau Hammerhead Cluster Attack Analysis

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By now, just about everyone knows about the rule changes coming in Warhammer 5th Edition. One change drastically affects on the Hammerhead's cluster attack is resolved. In 4th edition, the attack would either directly hit, or completely miss. Now in 5th edition, this attack, along with all other template weapons, can drift. Therefore the cluster attack will land somewhere. Using probability, it can be determined if this attack is better or worse in 5th edition, then it was in 4th edition.

In 4th edition, the attack would hit directly 67% of the time and completely miss 33% of the time.

Probability of a Direct Hit

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In 5th Edition, the cluster attack will inflict a direct hit if either the scatter die comes up with a cross-hairs and/or the 2d6 roll results in a 4 or less. Using the inclusion/exclusion principle, The probability of a direct hit will be:

Probability of Event 1 + Probability of Event 2 - (Probability of Event 1)(Probability of Event 2)

Event 1 - Probability the Scatter Die will roll a cross-hairs: .33

Event 2 - Probability the 2D6 will roll a 4 or less: .167

Total Probability = .33 + .167 - (.33)(.167) = .45 or 45%.

Therefore, the probability of a direct hit is lower.

Probability of a Decent Hit

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Even if the cluster attack does not directly hit, it can still inflict quite a bit of damage. For this calculation, I am going to assume that the average squad radius is around 3". Therefore, if the template drifts less then 3", a sizable portion of the squad will still be hit. This event will occur if the scatter die comes up with a cross-hairs and/or the result of the 2d6 is 7 or less. Therefore:

Event 1 - Cross Hairs: .33
Event 2 - Roll of 7 or less: .583

Total = .33 + .583 - (.33)(.583) = .71 or 71%

Therefore, there is a higher probability of dealing damage in 5th edition.

Probability of a Glancing Hit

The large blast template has a radius of 2.5". Therefore, as long as the template drifts less then 5.5 inches, it will probably hit a figure. For this calculation:

Event 1 - Cross-hairs on Scatter Die: .33
Event 2 - Rolling a 9 or less on 2d6: .83
Total = .33 + .83 - (.83)(.33) = .89 or 89%

To finish up, while the probability of a direct hit is less in 5th edition, then in 4th edition, the probability of inflicting damage is higher in 5th edition.



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