Abeness

Ah, point taken. My original post was essentially me saying that I didn't know enough about the fight, your gear, etc. to make any conclusions off of what was said. And I should have known that saying "never" would have gotten me in trouble . In a previous post, I believe I said that spamming that fast was unrealistic, but I was talking in terms of general gearing rather than considering single, hard fights.

 

Jackinthegreen

Your data is still useful, but the way you put it out could have used some work... Perhaps if you could modify the testing to factor in crit that doesn't come from Crit rating, as well as average cast speeds at the half second marks too. Heck, there might even be a way to make it an interactive spreadsheet or similar thing that allows one to at-a-glance see a relatively accurate view of how crit relates to Mp5 based on fight length, average cast length (for both HL and FoL and using half of each), and perhaps being able to switch from a 3.1 version to a 3.2 version. Using a parser that can break down the spell usage I'd say people should be able to acquire gear for certain fights based on how long it's expected to last, what the HPS reqs might be, and other things like that.

 

Abeness

Modifying the testing to factor crit from talents, base crit, buffs, etc. would make crit a little bit better, but when I ran some numbers it didn't seem worth it to redo all the equations. In an earlier post, I copied Endoscient's experiment to determine how many casts one gets at 20% crit, 21% crit, 50% crit, and 51% crit. His example showed that the number of casts gained between 20% and 21% was less than the number of casts gained between 50% and 51% by .2 casts of what my numbers predicted (using his 50k mana pool and 1k cost on Holy Lights). I used a much larger mana pool (254,800 mana) and redid the experiment to test the extreme cases. The final casts showed a .3% difference between my numbers of mana gained from crit, and the actual numbers (with an extreme mana amount and 30% crit increase). With a .3% margin of error, I called it a day. But there is a way to make it more accurate should that small margin of error make a noticeable change in the numbers. I do like the idea of having a spreadsheet display the relationship between Mp5 and crit so that all the extra variables could be accounted for and provide the at-a-glance comparison.

 

Endoscient

It was a lot more then 0.3% error, you should compare the gains to each other not to the starting amount of casts. If you computed vale of 1 crit rating with almost any formula you put it through would give a low margin of error with how you computed it. Going from 50% to 51% crit gives you around ~50% more casts then going from 20% to 21% crit. Which is quite a large error to just ignore, which your calculations for crit to mp5 does.

The value of crit depends largely on your mana pool and your initial crit rate, and you can't ignore them. Here is a chart that compares the mana gains of same item level amounts of mp5 and crit, for a 7 minute fight with a 150,000 starting effective mana pool at different initial crit rates. It uses the formula that Illumination increases your effective mana pool (counting all effects besides Illumination) by 1 / ( 1 - 0.6 * crit chance).

What you can see here is that mp5 scales with crit (like all other mana stats should), but that crit scales with itself at a large rate but starts out lower (depending on your exact mana pool). In this example mp5 and crit are around equal at a 50% crit rate, and that is not counting the extra benefit of critical heals. Which while isn't nearly as useful as the mana gains you can't just ignore it.

Here is another chart that compares them against different starting mana pools. It uses a 7 minute fight, and initial 50% crit rate.


These two graphs should clearly demonstrates crit's dependance on other factors that can a vary a lot from fight to fight and with different gear levels/strategies. While how many Holy Light casts per time period does sort of encapsulate the mana pool factor, actually having your mana pool displays the data much better and more accurately.

 

gcbirzan

First of all, there is a cap on the mana you get back from mp5's scaling. The reason it scales with crit is that it allows you to cast more HLs, getting more mana back from them, so if you can already spam HL constantly, mp5 will stop scaling with other mana stats.

 

Endoscient

Its assuming you are using all the mana that you have during the fight, its is only capped if that stops becoming true but then you no longer care about mana stats.

Its counting the gains from Illumination from the extra spells that it would let you cast as well. Since the 840 mana has a 50% chance to crit and restore 504 mana, and that has a 50% chance and so on.

 

gcbirzan

You might be able to spam Holy Light, but have to use Divine Plea on cooldown. In that case, more mana from other sources might allow you to use Divine Plea less.

 

Abeness

This has been driving me nuts because I could not figure out why my equations seemed to be off, when the way I did them should have factored in crit's scaling ability. I finally figured it out, and it turns out my numbers are correct. The thing missing from above is the cast time. Because as you're gaining casts (the above shows a gain of .2 casts), it takes you longer to get those casts off. In that extra time, Mp5 fills the gap. 20% crit gives 56.8 casts, so you've gained 6.8 Holy Light's worth of mana, which would give 6,800 mana using your scenario. Pick a random cast time...one cast every 5 seconds. It would take 284 seconds to get off those 56.8 casts. Divide the mana gained by the time taken to finish all casts and you get the mana per second. Multiply by 5 to get the Mp5 equivalent. Continue with the rest...

This is all strictly using just the quoted experiment. Now that we've taken cast time into account, we can compare the mana gain at the different crit percents. If the Mp5 of 51% minus the Mp5 of 50% (51% Mp5 - 50% Mp5) is larger than the Mp5 of 21% minus the Mp5 of 20% (21% Mp5 - 20% Mp5), then crit's scaling abilities could not be accurately expressed using the equations I used in my original comparison of Crit to Mp5. The difference between 51% and 50% is 6 Mp5. The difference between 21% and 20% is the same 6 Mp5 (if you're following along with your calculator, the numbers are not exactly equal due to rounding in the chart). Because a 1% crit increase gives the same Mp5 no matter what the initial crit rate is, my numbers representing Crit as Mp5 in the original post are acurrate. Crit does scale with itself, but because those extra casts take time it can be converted into Mp5 equivalent values. Also, this means that initial mana pool does not matter.
Edit: Initial mana pool does matter in the sense that it increases the total number of casts, but does not increase its Mp5 gain. Increasing mana pool just allows the player to keep that Mp5 from crit going longer.

This graph is inaccurate. As the player's mana pool increases, the amount of casts they can get off in the time limit is the same. Same amount of casts gives the same mana back. So the benefit from crit is actually a horizontal line just like the Mp5 gain.

 

Malleus

There's maybe nothing wrong with your mathematics, but your starting premises are faulty.

A Paladin in endgame content is not going to be casting HL once every five seconds on average (except on Vezax, but that's a special case) - that number isn't even within the range of possible outcomes. Realistically, you're looking at a HL every 2-3 seconds, faster in times of heavy burst damage. That decreases the total time to cast, which in turn increases the value of crit as MP5.

 

Jackinthegreen

You're forgetting Abe also has data for faster casts on the previous page. On there it shows that the regen from 100 crit is still decently replaceable by using Mp5 instead. What we really need to consider is the pros and cons of Mp5 and Crit in a given scenario, not whether one is just plain better overall.

 

Abeness

The 5 seconds used was just to show that a 1% crit increase always worth the same Mp5 at a given cast speed. The rest of what you are saying is what I have been as well. The faster you cast, the better crit becomes. If casting once every 2-3 seconds is realistic, then Mp5 is better. Also, the way you worded "faster in times of heavy burst damage" makes me want to say again that when seeing how much Mp5 one gains from crit, it's best to look at the average cast time over the entire duration of the fight. Using the average gives you the average Mp5 gained rather than looking at individual windows of increased cast time.

 

gcbirzan

Your mistake is that you're assuming your purpose in life is to cast a HL every 5 seconds, instead of trying to squeeze as many of them into 284 seconds as you can.

 

Endoscient

Abeness, as I said before fight time is fixed, gaining 1% more crit is not going to make the fight last 3 seconds longer like you say it would. Your numbers are never going to be accurate while you approach it that way. You can easily spend your additional mana without having it take you longer, by replacing FoL casts with HL casts.

gcbirzan, that is true about Divine Plea, but I that is not normally the case and is much more difficult to model with the relatively simple graphs I made.

 

Endoscient

Also is you really want to use a healing until oom model, which is a poor model anyway, representing gains as mp5 is extremely misleading and incorrect. Since how much mana they can return or casts they can increase can vary even though they say the same value (as you illustrated above), since it is essentially dividing the answer by a factor of itself. A better way to represent it is mana gained over fight duration, time it took to go oom, or total healing done.

 

Abeness

I'm not sure how I can get the point through that you can pick any cast time you want. Say the paladin was able to cast once every 1 second. That would allow him to get 420 casts off in 7 minutes. Now, if the paladin had 8,000,000 mana, he could still only get off 420 casts in 7 minutes.

The point is not that the fight lasts longer. The point is that a given crit percent ALWAYS yields the same Mp5 at given cast intervals. Pick any fight length, crit percent, cast time, etc. Find the mana back you gained from crit in that time, correlate it to my numbers, and the Mp5 equivalent will match up.

 

Endoscient

That is not what his point was either. He is saying that you should find out how many spells you can cast in a fixed duration instead of how long you can cast a fixed rotation of spells. Also your example isn't really useful since whenever you reach a point when you cannot cast anymore Holy Lights in a given time period then there is little value in additional mana. While healing you cast a mix of FoL and HL for the duration of the fight, gaining more mana means that you are casting more Holy Lights instead of casting Flash of Lights. So the duration of the fight can easily stay the same, while making use of additional mana.

That is the point, because that is the only reason that they do match up (read my previous post which you probably didn't see). It is an incorrect way to model fights anyway, since it doesn't represent what actually happens. When we gain more mana it means that in the same fight will be casting for the same period of time, but we will cast more Holy Lights instead of Flash of Lights. It doesn't mean we will tack time on at the end casting in the same "rotation" we have been using for rest of the fight.

Using the same fight situation I modeled in the graphs above, which are accurate and if you don't think so please show how they are not. At 20% crit 30 crit rating gives you 9.08mp5, at 50% crit it gives you 14.37mp5.

 

Abeness

Length of fight divided by time between casts gives you the amount of spells able to be cast in a fixed duration. That's why I include cast speed into the equations. To be honest, I'm kinda lost on the rest of your point. I think you are saying that once you cannot cast anymore Holy Lights in a given time period, then you wasted your stat points on mana regen and extra mana. But, what happens when you reach a longer fight? Then you switch back to saying that additional mana allows you to cast more Holy Lights (saying lots of regen is back to "good" status). This is true, but not in the same time limit. Crit does not increase haste speed. The casts you can get off in crit gear is the same as when you are in Mp5 gear.

Whether you model the mana gained from crit until the point where the player runs out of mana, or if you model it in a given time limit, my numbers match both scenarios. Are you trying scenarios where you're changing the spells cast? The rotation has to be the same when testing Mp5 gear and crit gear. So far, your point has been that more mana allows us to replace Flash of Light casts with Holy Light casts. Why would identical mana from Mp5 not allow us to do the same? Also, I did already quote one of your charts and pointed out that increasing the mana pool would not matter in a 7 minute fight (assuming the player does not go out of mana), which therefore makes the graph inaccurate. To quote yourself: "[...]whenever you reach a point when you cannot cast anymore Holy Lights in a given time period then there is little value in additional mana."

Again, you did not take time between casts into account (or total casts, if you're more comfortable with that term). Excuse the following numbers I use from "realistic" checks, they are only to prove the misleadings of the graph: What if the player casts one time in 7 minutes? Even at 100% crit rate, the most mana gained you could see is 765 from crit. In that same 7 minutes, Mp5 gives far more mana because it is not based on casts. So without taking total casts into account, you cannot hope to come up with a viable comparison.

 

gcbirzan

That's not how things work. What we are trying to say is that when you're healing in a fight, you don't think to yourself "I must heal every 2 seconds so that mana lasts me through the whole fight", you think "this tank is taking a lot of damage, I need to heal him more". The amount of healing you do in a fight is not limited by your haste rating (on most fights), but by the available mana.
To give you another example, what if the fight lasts 30 seconds and you needed to heal some moderate damage? Would you cast one Holy Light every 3 seconds, which is what on average the incoming damage should be, or spam it and be sure that you're not going to get gibs? And when you reach a longer fight, yes, mana stats are better for that fight. You cannot say this gear is better for all fights, just for these particular conditions.

 

Endoscient

You really do not understand what is going on or what other people are saying. How many spells you cast is determined by your mana pool, with an upper limit that depends on fight duration. The underlying assumption is that you are using all of your mana during the fixed fight duration. The only time is not true is when you are spamming Holy Light as fast as the cast time while let you for the entire fight, and still not running out of mana. Then extra mana has very little value, so it really doesn't matter how much mana crit vs mp5 would give you, since they won't change what you cast. When you are under that amount you are spamming a mix of FoL and HL spells for the fight duration, the exact ratio of two depends on how much mana you have. When you gain more mana you cast more Holy Lights at the cost of casting less Flash of Lights, but the total casting duration remains constant. So you see how you can use the additional mana you gain from mp5/crit to do more healing, while keeping how long you are casting the same.

The way you are modeling it, you say you cast a fixed amount of spells no matter what (1 Holy Light per 5 sec is your most common value). No matter how much mana you have you would still adhere to that rotation, which is quite useless and unrealistic. If you gain more mana, you are going to magically make the fight last longer, so you can still adhere to that rotation. If I have unlimited mana in a fight I am going to spam Holy Light as fast as the cast time lets me for the entire fight, not be limited by the arbitrary 1 per 5 sec (or whatever value) rule you model. While if I have less mana available to me I am going to cast less Holy Lights and cast Flash of Light instead, so I will be able to cast for the entire fight duration.

 

Abeness

Nowhere do I say that the paladin has to adhere to a "1 cast every X seconds" rule. The time between casts is the average for the whole battle. So let's say there is a 5 minute fight. In the first 4 minutes, the paladin sits around day-dreaming; but in the last minute, he starts casting once every second. That would be 60 casts for the duration of the fight. Divide by the time (300 seconds) and you end up with an average of 1 cast every 5 seconds. So there is no rule to follow when casting. Find your average cast speed after a battle, then use that number.

Are you assuming that the paladin always uses his exact mana pool each fight so that he runs out of mana right at the fight's end?

 

Endoscient

I obviously meant adhere to the save average cast time for the whole fight after you gain the additional mana. Which entirely doesn't represent reality, and how you heal actual fights. When you gain more mana you cast more Holy Lights instead of Flash of Light, you do not keeping casting the same ratio of spells but for longer. The most obvious reason for this is that you have no control over fight length, gaining 1% crit won't give you 3 seconds longer fight duration to cast the same ratio of spells.

I just said I assumed you use your entire mana pool. While you will probably never end up at 0 because you can't predict the exact time, you should end pretty low. If you have a large amount of mana left over it means either that the fight is easy for your gear level, sp no point gearing for it, or you have too much regen stats for that fight.

Your model of the fight and showing gains as mp5 but over different durations of time misrepresent the value of each stat, and does not represent a real fight in game.

 

Abeness

Once again, there is no average cast time to adhere to. Take how long the fight lasted and divide by how many casts you did. There is no ratio to keep up; the ratio will likely change depending on the fight. By the way, I have been using casts of Holy Light this entire time because the Mp5 gained from crit is significantly lower than the Mp5 from Holy Light, and I was giving crit the best chance it could have. If interested in the Flash of Light numbers, there is an updated chart on the previous page. The fact that you "have no control over fight length" only strengthens mana regen as a stat. You say that a paladin has too much regen if they have leftover mana at the end of a fight. Using that logic, the same could be said that a paladin heals for too much if his heals have overhealing. The point of extra healing or extra regen is a buffer zone to keep the tank safe from unknown variables, like fight length.

Did you read through my methods or check my math? Every time you link the same old data and charts, I find something wrong with your logic. The only real argument thus far against my math has been people questioning if the cast times are realistic, which time and time again I have to tell them that I included different cast speeds for a reason. Go through the math, check my numbers. If you find that crit gives more mana back than the correlating Mp5 that my equations tell, let me know. If you do check the math, I cannot stress how much I encourage you to embrace the fact that crit's gain is based on number of casts in a given time limit, so they must be a factor.

 

Endoscient

This is totally incorrect with the data and formulas that you posted. In the table in this post each of different data points with different levels of mana maintains the same exact average Holy Light cast time (of 1 per 5 sec), while in reality you should have the same exact fight duration since it is trivial to get off as many Holy Lights as modeled in that time frame. Once you adjust for the large error, its quite easy to see crit scaling with initial crit chance. When you gain more mana it means you cast more Holy Lights in same time period, not that you cast the same amount Holy Lights in a longer time period like you model.

You haven't said at all how my data is incorrect, while I have pointed inconsistencies in yours and how it doesn't model real situations and is incorrect. Just because you can put numbers and formulas together, that doesn't mean they reflect real circumstances.

 

gcbirzan

I'm going to quote your first post here, to try to explain, again, why we disagree with you.

The problem here is that how often the paladin casts is a combination of the perceived fight length, your mana regen, and incoming damage. We can consider fight length and incoming damage as being constant, since we are trying to evaluate the value of crit/mp5 for a certain fight, their values will definitely change for different fights.

As a slight sidetrack, and to elaborate on your point of overhealing and ending a fight with 0 mana, your goal in a fight is, remember, to be able to outheal the incoming damage, and even if most fights aren't constant in the incoming damage, we can divide the fight into multiple mini-fights, each with constant incoming damage and consider each a problem we need to solve, the solution to the bigger problem (stat equivalence) being dependant on the solutions of the smaller problems. So we can just focus on solving a constant incoming damage throughout the fight problem knowing that it can be applied to a more complex fight. There are some constraints which make this not entirely true, like cooldowns, and these have to be factored in separately, but that's beyond the scope of this discussion.

To be able to outheal incoming damage (considering Holy Light spam is sufficient), you have to have enough mana for maintaining a high enough ratio of Holy Light/Flash of Light that the HPS is enough, anything above that will just reduce the chances of gibs, and our goal should be to maximise the buffer of HPS above incoming DPS.

Now, for where you went wrong. You're listing different values of crit/mp5 equivalence, for the intervals between Holy Light casts, but those intervals are themselves determined by your mana regen. So while your math is certainly not wrong (I didn't actually verify it), the assumption you make at the beginning that how often a paladin casts Holy Light is something static and not something determined by their mana regen is flawed, and what's causing us to consider your numbers wrong.

This is exactly what we've been saying. It is a factor, but if you look at it independently from the other fight details, you will not get any relevant information. I don't care mp5 is better than crit tenfold if I cast it once every minute, since I don't do that because I can get a higher degree of safety my tank won't get gibbed because they sat down if I cast it as fast as my mana pool allows me.

 

Abeness

That post you linked was not to model my original equations. That was proving that the crit increase of 1% always gives the same total mana, and that my original equations do not have the margin of error I predicted a few posts earlier. Your counter-arguments say that crit will allow the player to get off more casts than Mp5 would. Which makes no sense. "When you gain more mana it means you cast more Holy Lights in same time period." So mana gains give haste now? I've proved that the mana gained from X crit is equivalent to a Mp5 value that my equations predicted. Because the linked post shows that a 1% crit gain always equals a constant Mp5 value (with varying cast speeds), crit does not have a scaling property when viewing it in terms of Mp5. It does scale in that it gives more casts per crit percent stacked, but those extra casts take time to get off. The extra time it took to cast the extra casts gained, the Mp5 equivalent was able to catch up. That linked post did not use my equations at all. I looked strictly at the mana gained from crit (converted it to Mp5), and showed that a 1% increase at 20% gives the same Mp5 as at 50%. Because extra casts gained take that extra time, converting crit rating into Mp5 includes crit's scaling abilities.

I'll admit that I have been so caught up in proving crit can be represented as a static Mp5 value that I forgot to mention that the increased mana casts gained by stacking crit does increase the total mana back. But in an earlier post, I found that when a paladin has 254,800 starting mana, and get a 30% crit increase (even though the normal crit percent gain from gear would be more around 15%), the mana gained from that crit increase was .912 casts, or 1162 mana. So, even when a paladin has a ridiculous initial mana amount, and is gaining another ridiculous amount of crit percent, the scaling ability only awards 1162 mana to the total effective mana pool. All this means is that the more crit you have, the longer you could keep the Mp5 from Illumination up. Again, even in this case using a mana pool and crit percent way larger than what would be normal, stacking crit would only allow the player to keep the Mp5 from crit for a few seconds longer (the faster you cast, the faster the paladin will use up that 1162 mana...woo! less than one Holy Light!). For instance, if the paladin was casting once every 2 seconds, that tiiiiny increase in the effective mana pool from crit would only allow the player to keep up his Mp5 from Illumination for less than 2 seconds longer. Knowing this, there is no way that crit's stacking benefit would be worth it.

It does give ~50% more casts, but so does the Mp5 equivalent. You cannot show how much crit gives and exclude what Mp5 would have given. When one factors in the extra few seconds that the Mp5 from stacking crit gives, the number of casts gained is very small (.912 in the experiment I talked about above). Which as I factored was something like a .3% margin of error. I now understand that the margin of error lies within the total effective mana pool predicted, not with the Mp5 values (and yes, I checked the numbers again, that experiment would lead us to believe that the player's effective mana pool is .3% less that it would be thanks to the scaling crit). Jackinthegreen has the right idea with an interactive spreadsheet. If you combine my equations with different fight lengths, that margin of error can be dwindled from "almost not there" to "actually not there."

When I run your numbers, they rarely match up with what they should be. And the graphs you use are misleading and wrong (see my previous posts to read my comments on them). All the "inconsistencies" you have pointed out always turn out to be misunderstandings on your part of what my math shows, or how I came about doing that math. You rarely (usually not at all) even make comments about what I've said about your work. Generally, you will pick one part of what I have said, try to loophole it to death (or get caught up on arbitrary numbers), and mostly ignore the point. I have had to re-say a lot of my information and prove my numbers in several ways just for you to "nuh uh" it. And most of the time, the comments in your replies lead me to believe that you basically skim over my posts and assume my math is wrong without actually testing it.

Once again, I'll say that a paladin will never cast at a static speed. The times I use represent the average time between casts throughout the whole battle. That number will change from fight to fight. When I said that Mp5 is way better when only casting once in the battle, it was only to demonstrate that the amount of casts needs to be considered. I think we're half-arguing. I am still trying to get the point out that my math is right, while you are already discussing what the math means. I may have jumped the gun in some of my conclusions (seems like I was saying Mp5 is always better). I would love to get away from the topic of "is the math right" and on to how we can use it.