On March 29^{th}, Blizzard decided to buff the proc chance of the Lightning-Imbued Chalice, a healing trinket that drops from Lei Shen. Just as a reminder, this is what version 1 of the trinket did.

- Static intellect: 1218/1467/1552/1657/1728*
- Smart heal proc: 46561/56071/59207*/63294/66816*
- 3 RPPM (real procs per minute) (here’s an explanation of what this means) (http://us.battle.net/wow/en/forum/topic/6893549789)
- Procs off direct or periodic healing spell
- Healing buff called “Restoration of the Infinite”, accumulated charges called “Infinite Power”

Recall earlier in the month around March 13^{th}, they buffed the proc chance on all of the trinkets together once. Therefore this trinket has been essentially buffed twice since we looked at it previously. Lets take a look at what the changes resulted in.

Here are some basic statistics about the logs I gathered:

Using the WoL import mentioned in one of my previous posts, I imported all of the information. All logs are in English and are full kill logs. I realized that including wipe logs would incorporate much more information, but in wipes, weird things happen especially towards the end and I can not quickly distinguish when the raid has given up so I left those out. A caveat of the analysis is that all of these logs are from around 5-6 individuals therefore there may be some bias in play style.

Our first step is to verify that our data makes sense. What I mean by this is longer fights for example, we would expect on average more healing done, more direct heals, etc. Lets check some of these points first.

The plot above shows the comparison between healing done and fight length. We would expect this plot to have roughly a positive slope which you can see here is true. This plot is interesting on several levels. Notice that the points are clustered together roughly according to group for some fights (ex. Horridon (H)). For every heroic fight, if you’re a DPS you can calculate on average how much DPS you will need to do to kill the boss before enrage. It is kind of interesting that you can tell from this boss around what healing you will need to do in terms of HPS to keep people alive through a boss. This number is of course extremely variable due to healing composition but the here is undeniable.

Here is a type of image called a dendrogram. This type of analysis which is a simple unsupervised hierarchical clustering is designed to identify similarities between two things. Imagine if you had a group of balls, some of which are red and some of which are blue. It would be very easy to distinguish these into two groups and in fact since you have no other information about them such as their size or any patterns they would separate into exactly two groups. But now suppose you had other information such as size and perhaps some balls have different patterns; to group these into similar groups would be a much more difficult task. What hierarchical clustering does is takes input, in our example it would be ball size, color, and pattern and identifies grouping based on these multiple input categories numerically. You can read more about the math behind it here but basically in a sense, the same action I’ve just describe to you can be achieved mathematically by the use of matrices. For example, we could denote different colors and patterns by values such as 1 for red and 2 for blue. Ball size is already a numerical value. Mathematically we can find the similarity between observations for one ball compared to another by metrics such as the ones stated on the Euclidean page. By doing this recursively we can find which balls are more similar to each other numerically and end up with a robust system of dividing the groups.

So what is this picture saying? This tree denotes a similarity structure where the longer the arm of the tree, the more different the two fights are from each other. Remember this is based on two factors, the healing done and the fight length. If we for example split this picture in to four groups, we notice the top group contains a lot of Dark Animus fights. This indicates that a majority of the Dark Animus fights have very similar fight lengths and healing done. We also notice in the second group, there is a majority of the Horridon (H) fights in the top half of the group. These are two groups where the two input variables were very similar among different logs. This could indicate many things. Perhaps this fight is relatively easy and everyone doesn’t need to heal a lot and therefore, difference in play style or raid comp don’t make a huge difference on healing. It’s also possible that these fights have very strict healing requirements and thus most successes in killing the boss have similar values.

Now lets look at a fight which doesn’t cluster well such as the Tortos fight. In my experience, Tortos is a very different fight depending on healing composition. Some ToT fights are very suited towards certain classes such as those primarily for AoE healing or single target healing. A paldin healing with a Monk and Shaman might not do as well as a paladin healing with a Disc priest.

Lets move on to looking at direct heals + HoTs since these are the spells which have the chance to trigger charges of Infinite Power. We would expect that a plot of this value versus fight length would be roughly similar to the one above.

The plot above shows the fight length by the Direct Heals + HoT ticks value. Recall that the LIC procs either on direct or HoT ticks. The purpose of this plot was to show that as the fight length went on longer, you would naturally have more direct heals and HoT values, regardless of how much healing was done. We would expect this plot to have a roughly positive slope and we do see that shape here. Once again notice how the fights are roughly grouped together indicating possibly that play style for these fights are all very similar.

We can estimate from each person’s logs their spell power very roughly. I was recently lucky enough to become the owner of the Thunderforged Hydra-spawn trinket. I am positive the absorb from this trinket is not affected by any holy paladin base talents such a Seal of Insight (1.05) or Holy Insight (1.25). Therefore, I can make an educated assumption that it does not affect the healing from the lightning-imbued chalice as well. This means that fights such as Jin’rokh (H) which give a healing bonus will not affect our calculation of spell power.

The LIC’s heal component is 56071 + 125% of SP for the 522 normal version. This value changes very little between the normal and normal thunderforged version which gives a base healing amoutn of 56286 and maintains the same SP coefficient but goes up drastically in the heroic and heroic thunderforged versions. Using this knowledge, and the crit coefficient of 2x because the heal from this trinket can crit, we can estimate the average SP.

Looking at the plot, you can see that a majority of the SP values are around 40,000 which I think is pretty much impossible even with Jade Spirit, Intellect Flask up continually. If you look at the outlying values which I plotted the fights specifically on to because the coloring was too close, they are both related to the Jin’rokh heroic fight. Thus we know that the healing from this trinket is affected by external fight mechanics. Is it possible that I was incorrect in assuming this trinket is not affected by holy paladin buffs like the Hydra-spawn trinket?

I replotted the values including both the innate holy paladin buffs and the values are a lot more realistic. The important thing from this plot we see is that the SP does not scale based on fight length which is what we expect.

I therefore have reasonable evidence to believe that this trinket is affected by both the Seal of Insight and Holy Insight buffs as well as any external boss mechanic healing buffs. I can also say that the general trend of our data from looking at these points is roughly similar to what we would expect in the typical raid situation.

**Buffed PPM Proc Rate ~6.4**

The first time I looked at this trinket, I made a mistake and took the proc chance from the number of procs of the actual heal and forgetting that the heal takes 6 charges to build up. I calculated the average proc for the heal to be around 105 seconds meaning that there was on average a proc ever 17.5 seconds. The original PPM value was therefore very close to the true value of 3 PPM. Let us not make the same mistake and look at the proc rate in the new data.

The plot above shows the total procs by fight length. The red points represent the buffed trinket and the blue points represent the original version. I have a fitted a linear model to the points because I expect the number of procs to go up linearly with fight length. By using R’s lm function which essentially takes a set of points and tries to find a linear line which will best describe the set of points. It does this by plotting a large number of lines with different plots and finding out how much error, or how far away the actual points are to the line. The sum of these errors which is the least is the line of best fit and R will return the slope of it.

The slope of the original trinket is 0.058208. The units of this value is procs per second. Therefore this trinket comes out to be around 3.49 RPPM. The slope of the new trinket is 0.107103 procs/second or ~6.42 RPPM. Essentially they buffed this trinket by almost two times so that in one minute it is very likely for the actually heal to go off once.

Notice the two red points close to the blue group. I suspected that these were actually non-buffed trinkets. Since the hotfix came in relation to the American time zone, I’m not sure whether the trinkets were buffed even though the log was recorded on the 29^{th}. I went back and checked the log dates and the dates for these two were clearly after the 29^{th}. However I noticed that in one log, the person survived only 70% through the fight and the other was around 56%. I suspect this is why these values are outliers.

**Haste**

I originally had tried to pull out information from the expression browser however that page is written with a javascript instead of HTML. Since I didn’t record the haste, I had wanted to calculate it from looking at Holy Light cases and deducing an approximate haste value from the time it took for the cast to finish. However I’m not familiar enough with HTML to extract a javascript source code so I went through and did it manually after making the URL which would find the page. I was interested in haste because from our previous analysis, it appeared to scale the best with PPM. However, the logs also have some lag which is different between different logs so I realized that this is probably not a viable method of calculating haste as there would be a lot of error in the value.

I feel like the only way to make a reasonable analysis of haste is for me to test it out on the trinket I came into possession of so we’ll hold off on this discussion for now.

**Direct Heals + HoTs scales with number of Procs**

Here we see a comparison of procs (of Infinite Power) and direct heals and HoTs. From the description of the trinket, we expect this relationship to be positie. Here we can see that relatively this is true. Up to around 4000 DH+HoT, the value of Procs is consistently increase. After a certain number however, the number of procs become extremely varied. If you look at the number of DH+HoT for people who received 60 procs, the number rangse between 2000 and 6000. Perhaps this haas something to do with the fight?

We see a slight grouping of the type of fight. For example, Horridon (H) points are once again grouped together. The relationship is however not extremely clear. We do notice that Megera (H) fights have a lot of DH+HoT but on average, less procs than other fights where paladins used the same number of DH+HoT.

I therefore conjectured that the fight might have ore to do with fight length after a certain point. First off, I want to point out something quite striking, we see essentially the same rainbow pattern consecutively from left to right indicating number of procs is very closely associated with fight length. From a vertical point of view however, it is almost like the number of procs you get is unrelated to the number of heals you do. Therefore, any class who has a higher active time from HoTs or something such as paladins or druids will not benefit from this trinket over classes which have lower active times such as priests. This is of course expected since the healing from this trinket is unaffected by how many times you cast. The equation could easily have told you that.

**Healing Done from Trinket is ~1% Greater than Unbuffed Version**

When reading the next second, remember the number of data points in each set and just keep this in mind.

This is a plot of the percent of total healing taken by LIC by item level and version. As you can see the previous version of the trinket was healing under 1% for the normal version and around 1.5% for the thunderforged version. The difference between the normal and normal thunderforged version is actually quite large. While this the difference between normal and normal thunderforged decreases, we can see that in the last two for the buffed version, t he average healing is around the 2-2.5% range. This is approximately 1% better than the older normal version. The thunderforged version of the buffed trinket has a shorter bottom quantile meaning while the average of this trinket versus the normal version of the buffed trinket is similar, the chance for a higher % of overall healing is a lot higher with the thunderforged version whereas the normal buffed version even reaches down below 1%. Even though the buffed version of the normal trinket has the most datapoints, it has the longest tails. This means that the variability of this trinket is still extremely large. While the old normal version only had 7 samples, you see that the range of values is surprisingly small.

**Summary**

The buff to this trinket is quite noticeable. The trinket is proccing a lot more and thus healing a lot more than the old version. There is no denying it’s an improvement, but the source of argument is whether the buff was enough. Let’s put things in perspective. Our spell daybreak heals approximated 1-4% each fight. This is a paladin spell. We are talking about a trinket which provides on-par healing with a paladin spell. I don’t think there should be any argument about how good this is if it on average can provide an addition 2.5% healing.

However…this trinket still has two problems. The first is the overhealing. As expected we see an extremely positive trend in the data when comparing healing vs procs.

Look however at this plot for overhealing vs healing.

This plot shows the effective healing from the trinket by the over healing percentage. This kind of negative trend strongly indicates that the decrease in healing from this trinket for some people was mainly due to overhealing. Of course we expect to see a trend because the more effective healing you do, the more overhealing you do. What would be ideal would be if the overhealing % was relatively independent of effective healing.

The second problem I saw was that for the new version of the trinket, the number of procs is highly variable. Some people using the trinket reported numbers around 1.5% which from our data is perfectly viable. But this value is not much different from what the old version was giving. Of course people are going to complain that the new version didn’t buff anything.

Therefore, what I think will solve this (and I’ve said this before) is if we decrease the SP scaling or the base heal amount AND make the number of procs more consistent. I realize the model for RPPM is fairly dynamic and dependent on play style but I would argue for a method to make the value less variable or dependent on so many variables. With more consistent procs and less healing per proc, I think the overall amount of healing would increase.

Ultimately I would use this trinket if it dropped for me. Despite my frusturations at it, I feel like the trinket is better than say Relic of Chi-ji. As people gear up, we are already noticing the trend towards using less spirit simply because the fights are not as mana intensive. I personally think sitting around 15-16K spirit unbuffed will last you through most of the heroic fights. The main problem now, is not that we’re going OOM but during damage heavy damage phases, we won’t be able to keep people up because our heals are not strong enough. Therefore this trinket with its static INT would be the go to choice with Horridon’s Last Gasp as the preferential spirit trinket. I suspect in the following days, we will see some buff to the Stolen Relic. That one is currently and was before the worst performing trinket. We’ll have to se what they do to it because unlike this trinket and the Hydra-spawn bag, the trinket is an on use item and if changed properly could end up being stronger than both LIC and the IHS.

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