Restraint revisited

According to the version update notes on December 14, 2011, the max Restraint damage bonus was reduced. After checking it with Spirits Within at 300 TP with 1249 HP and a 240-delay sword and lots of normal attacks (too lazy to count), the max bonus seems to be 30% (599 vs 778; 778/599 = 1.2988). This was repeated and I got the same result. For comparison here are the test server findings (a reminder that the final update may differ from that seen on the test server).

I also checked observed WS bonus per normal attack (taking the observed WS damage bonus and dividing by the number of normal attacks landed) versus weapon delay for both single-wield and dual-wield cases for linearity. WS bonus per normal attack appears to be linear with respect to total delay after accounting for dual wield delay reduction (acknowledging truncation of damage values). I'm just gonna throw the following data in here just to show I didn't make this stuff up:



BTW in the process of accounting for Fencer the TP bonus for tier V Fencer seems to be +50 instead of +55.

From regression I get -0.00001437022 + 0.00002596923*(delay). The intercept term is close enough to 0 that I would drop it, so each landed normal attack will add approximately an additional delay/385 to the WS bonus multiplier up to a maximum of 1.3. This assumes the bonus is independent of the number of normal attacks contributing to the total WS bonus. My understanding is that Ravager's Mufflers +2 doubles the bonus but the 1.3 cap cannot be exceeded (these findings suggest this).

Remember that if you have the average number of attack rounds per WS, you need to multiply this by 0.95 to get the average number of normal attacks that actually landed (missed attacks do not contribute to the Restraint bonus) to estimate the average Restraint WS bonus.

Are there multiple levels or tiers of Conserve MP?

I was recently looking into what exactly the proc rate is for the "Augments 'Conserve MP'" property of the full Goetia attire +2 set (5/5), which was estimated indirectly last year (a thorough overview of the set bonus, including the relationship between damage multiplier and the fraction of MP conserved, is presented at The Black Mage's Apprentice in two posts). This was done by estimating the effective rate of observed procs, or the product of the actual augment proc rate (which itself cannot be observed directly when the Conserve MP rate is not 100%) and the proc rate of BLM's Conserve MP trait, which is supposed to be 25%. If you believe the set proc rate is a multiple of 5, then 15% and 20% are plausible estimates.

While some of the reasonable assumptions underlying the analysis caught my interest, such as whether the occurrences of Conserve MP, resists, magic critical hits and the Goetia set bonus are all actually mutually independent (kind of similar to whether the Double Attack trait procs on two hits of a multi-hit WS; no one actively looks for these rare events so you have to use more clever methods of providing evidence of such), of greater interest was the suggestion that there are multiple "tier"s (or "ranks" or "levels") of Conserve MP.

I just checked wiki.ffo.jp for the Conserve MP article and found a claim of at least one more Conserve MP "rank" at level 76 for BLM and level 96 for SCH. The claimed Conserve MP rate was 33%, but I couldn't find any evidence supporting this. (But there must have been some reason for this to be posted?)

I then tried to look for evidence of another tier  on the BG forums. I totally forgot I already looked at the evidence for this last year (posts #154 and #155...), and test 1 showed that the estimated Conserve MP rate for BLM was well below the claimed 33% rate. (Due to the use of a non-MVUE for the conserve MP rate, which is a binomial proportion, for the sake of convenience and sanity, the nominal 95% normal approximation confidence interval based on the binomial proportion but plugging in the non-MVUE actually has a lower coverage probability, or 91% as I claimed previously...).   This was before the September 2011 version update raised the maximum job level to 95, so this doesn't rule out any new levels being introduced since then.

So as long ago as June 2011 there did not appear to be evidence of multiple tiers of Conserve MP. If this is to be checked again in the future, the data collection procedure as described on the BG forums (see the previous link) would be one way to amass evidence for or against multiple tiers.