TP bonus of Fencer

(Edit: This is for WAR at level 75. I didn't consider the possibility of "increasing levels of mastery" bullshit.)

Saw this dumb shit so I thought I would act a dumb shit too by wasting my time figuring this out. (Figuring out the critical hit rate bonus did not waste that much time as I was sleeping while the data was being collected...)

One way to characterize the TP bonus of Fencer is to see how (and whether) the damage of the weapon skill Spirits Within varies with TP in the presence of Fencer and then compare the results to the damage-TP relationship of Spirits Within without Fencer. (Then you assume the findings can be generalized to all weapon skills and hope your observed damage with other weapon skills is consistent with the findings from Spirits Within testing.)

Some preliminary considerations

The problem is that the latter has not been fully characterized to account for flooring, so after retrieving Spirits Within damage observations between 100 and 300 TP without Fencer (using a Trainee Sword with store TP +5 for 6.7 TP and given 1000 current HP), I came up with a formula that matched the observations exactly.

Let D denote Spirits Within damage, H denote current HP and T denote current TP. Then Spirits Within damage appears to follow the piecewise function


This function describes the TP modifier (the fraction) increasing with TP in increments of 1/256 (other increments, such as 1/128 and 1/1024, result in calculated damage values that disagree with the set of actually observed damage values), so perhaps the TP modifiers at 100, 200, and 300 TP are better described as 32/256, 48/256, and 120/256, respectively. (Note: the inner bracket is there to ensure TP values are floored for the purposes of damage calculation, as TP values, while discrete, need not be integers.)

Now, with the same 1000 current HP and 6.7 TP, we can then observe how Fencer affects Spirits Within damage in terms of modifying base TP. We assume the TP bonus is additive and hope it is constant.

Actual TP bonus determination

The actual TP bonus (assuming it's additive and constant) was determined by a step-wise process of elimination by identifying "candidates" for the TP bonus as follows:

Step 1: For 100.5 TP, the predicted Spirits Within damage is 125. The observed damage is 148. The TP bonus could be 38, 39, 40, 41, 42, or 43. (At this point, 40 is the most plausible candidate as one would expect SE to make the TP bonus a mutiple of 5 or 10.)

Step 2: For 120.6 TP, the predicted Spirits Within damage is 136. The observed damage is 160. The TP bonus could be 37, 38, 39, 40, 41, or 42, but only 38, 39, 40, 41, or 42 are consistent with both observations.

Step 3: For 147.4 TP, the predicted Spirits Within damage is 152. The observed damage is 175. The TP bonus could be 35, 36, 37, 38, 39, or 40, but only 38, 39, or 40 are consistent with all three observations.

Step 4: For 140.7 TP, the predicted Spirits Within damage is 148. The observed damage is 171. The TP bonus could be 35, ..., 41, but, again, only 38, 39, or 40 are consistent with all four observations.

Step 5: For 154.1 TP, the predicted Spirits Within damage is 156. The observed damage is 183. The TP bonus could be 40, 41, 42, 43, 44, or 45, but only 40 is consistent with all five observations. Assuming the TP bonus is additive and constant, Fencer adds +40 TP to the current TP for WS damage calculation.

At this point, we should make sure adding 40 TP to the current TP allows us to predict correctly Spirits Within damage when the "net" TP exceeds 200 TP (so that damage is calculated based on the other part of the function).

For 167.5 TP, the predicted Spirits Within damage, based on 207.5 TP, is 207, which is also the observed value.

For 174.2 TP, the predicted Spirits Within damage, based on 214.2 TP, is 226, which is also the observed value.

For 180.9 TP, the predicted Spirits Within damage, based on 220.9 TP, is 246, which is also the observed value. (Note that you cannot floor the current TP to 180 and then add 40, which would give a predicted value of 242 based on 220 TP, which is wrong.) At this point, it seems reasonable to conclude that there is a 40 TP bonus from Fencer between 100 and 200 TP.

Now what about between 200 and 300 TP?

For 201.0 TP, the predicted Spirits Within damage, based on 241.0 TP, is 300, which is also the observed value.

For 227.8 TP, the predicted Spirits Within damage, based on 267.8 TP, is 375, which is also the observed value.

Finally, to make sure the actual TP for damage calculation is actually min(TP + 40, 300), for 300 TP, the predicted Spirits Within would be 578 given 340 TP, but the observed damage is 468, which is consistent with the 300 TP maximum.

Conclusion

Fencer gives a constant TP bonus of 40 TP for weapon skills independent of what the current TP is.

Critical hit rate bonus of Fencer

(Edit: now with information on Fencer with dual wield.)

Fencer is a new job trait from the July 21, 2010 version update that is available to the Warrior job at level 45 and the Beastmaster job at level 80. It has the following help description: "Increases rate of critical hits when wielding with the main hand only. Grants a TP bonus to weapon skills." The critical hit rate bonus was estimated using the following procedure.

Methods (brief)

An estimate of the critical hit rate bonus was obtained by auto-attacking overnight a level 69 Ul'hpemde, which has AGI 65 (source). WAR75/MNK01 was used. The following equipment was used to obtain STR 57, DEX 64, and an accuracy score of 276:

• Trainee Knife (240 dagger skill)
  
• Walahra Turban
• Dusk Gloves
• Snow Ring (STR -2)
  
• Swift Belt (Accuracy +3)
  
• Aurum Sabatons (DEX +3, accuracy +5)
  

STR 57 ensures 0 damage to any Ul'hpemde, and DEX 64 ensures (with 4/4 critical hit rate merits) a 9% critical hit rate before the effect of Fencer (source). kparser was used for automated data collection.

The level of the targeted Ul'hpemde was inferred by comparing the predicted hit rate for a level 69 Ul'hpemde (.92) against a point estimate of the hit rate of 5628/6133 = .9176 , with 95% confidence interval (.9105, .9244). The observed hit rate is consistent with the prediction.

Estimation of Fencer's effect with dual wield was also done with a Trainee Knife/Trainee's Needle combination, but the Ul'hpemde was level 68. (Critical hit rate is "directly" independent of level, but not AGI, which depends on level to some extent. But for both level 67 and level 68 Ul'hpemdes, the AGI is 65.) The following image summarizes the final base attribute values for this particular trial:

Results

Single wield: A point estimate of 802/5628 - .09 = .0525 was obtained for the critical hit rate bonus, with a 95% confidence interval (.0434, .0619).

Dual wield: A point of estimate of 464/4983 - .09 = .0031 was obtained for the critical hit rate bonus, with a 95% confidence interval (-.0048, .0115).

Interpretation and conclusion

Since critical hit rate has statistically been shown to take only integer percent values, assuming that the bonus is additive, the critical hit rate bonus of Fencer is either 5% or 6% with 95% confidence.

For the dual-wield case, suppose there were a 5% bonus for the main hand and none for the off hand. The effective bonus would then be 2.5%. Yet the observed estimate is much less than 2.5%, which should be taken as evidence that Fencer has no effect when dual wielding.