Occasionally Attacks X

The new Magian weapons have jolted the interests of many, and in particular, those of the "Occasionally Attacks X" variety are highly discussed. As such, which Axe above is better for TP gain? Is it the Occasionally Attacks Twice (OAT) or the Occasionally Attacks Thrice (OA3) weapon?

Since both weapons have the same Delay, we need only concern ourselves with the distribution of multi-hit attacks. According to some sources, the OAT weapon has a 40 to 45% "Double Attack" rate while the OA3 has a 30% "Double Attack" rate and a 20% "Triple Attack" rate. Assuming the data above is accurate, we can then calculate the average number of attacks each weapon delivers per round.

Average # of attacks per round = (Frequency of Single Attacks * 1 attack/round) + (Frequency of Double Attacks * 2 attacks/round) + (Frequency of Triple Attacks * 3 attacks/round) + ... + (Frequency of "n" tuple Attacks * "n" attacks/round)

Note that the frequencies above must total to 100% or 1.0. As such, this formula determines the average number of attacks a given weapon delivers per round by enumerating the average number of attacks each n-tuple is expected to contribute.

Richardet's Axe (OAT)
Average # of attacks per round = (Frequency of Single Attacks * 1 attack/round) + (Frequency of Double Attacks * 2 attacks/round)
Average # of attacks per round = (0.60 to 0.55 * 1 attack/round) + (0.40 to 0.45 * 2 attacks/round)
Average # of attacks per round = (0.60 to 0.55 attacks/round) + (0.80 to 0.90 attacks/round)
Average # of attacks per round = 1.4 to 1.45 attacks/round

Richardet's Axe (OA3)
Average # of attacks per round = (Frequency of Single Attacks * 1 attack/round) + (Frequency of Double Attacks * 2 attacks/round) + (Frequency of Triple Attacks * 3 attacks/round)
Average # of attacks per round = (0.5 * 1 attack/round) + (0.3 * 2 attacks/round) + (0.2 * 3 attacks/round)
Average # of attacks per round = (0.5 attacks/round) + (0.6 attacks/round) + (0.6 attacks/round)
Average # of attacks per round = 1.7 attacks/round

Therefore, the OA3 Axe is better for TP gain, but the OAT Axe is often recommended over the OA3 weapon. Why? The reason lies in the amount of damage each Axe contributes over time. For simplicity, we will calculate the Damage per second (DPS) of both Axes without gear. Since the DPS rating represents a single round for a given weapon, we will multiply the DPS by the average # of attacks per round.



















Indeed, the OAT Axe delivers more damage over time (DoT), so therefore, choosing an Axe above is ultimately between WSing more frequently or dealing more DoT. Since most BSTs will likely parse better using the latter, an offhand OAT Axe is a good bet for many; however, the best Axe ultimately depends on your playstyle (and perhaps more mathematics).

Aside: "Double and Triple Attack" gear
One should note that your total "Double or Triple Attack" rate using the weapons above is not found by simply adding your gear and job trait values to the distributions above. From what I am told, it seems that "Double Attack" from gear and/or job traits reduces the number of non-double hits by said value and then adds the reduction(s) to your "Double Attack" rate.

For example, let us say you have 5% "Double Attack" from gear and the OA3 Axe:

• Shift 5% of your single attacks to double attacks. This means you have 2.5% less single attacks and 2.5% more double attacks.
  
• Shift 5% of your triple attacks to double attacks. This means you have 1.0% less triple attacks and 1.0% more double attacks.
  
• Recalculate your new single/double/triple attack rate: 50 - 2.5 / 30 + 3.5 / 20 - 1.0 = 47.5/33.5/19.