Damage in the BattledomeElise Kozler
Chapter 1: The Problem
First, a warning. This isn’t intended for newbies, and isnâ€™t the easiest of reading. It’s long, but it will change the way you think about the battledome, and as far as anyone knows, no one has ever published this data before. Probably Majal_Kita, and a few others knew most of these secrets and kept them to themselves, but now they are out for everyone to see. There are excellent newbie guides to the battledome around, and if you cant find one, you can feel free to neomail me for a brief lesson anytime if I’m around.
The initial discussion for this came up when the IDB staff had an impressive looking function that rather dogmatically set out the range of damages one could expect to perform given a certain number of icons and a specific strength. It certainly LOOKED impressive, but given an engineering mindset, one would quickly see flaws in the model when looking at it. This was offset by some as “oh everything is plus or minus 15%”, and others still dismissed any criticism at all. This obviously didn’t satisfy me. What was especially worrisome was the fact that the error margin in many cases for the strength calculator was off by much more than 15%. IDB did an excellent job of identifying many of the so-called “strength-boosts”. The problem was in gauging what they did exactly. The original theory was each strength boost had an “x-factor” calculated to it. You would deal out a set # of icons, and the damage was calculated by multiplying the “x-factor” by the number of icons. Then you would take your opponents stance into consideration, and the result was some range of icons, depending on the opponentâ€™s stance. If the opponent too no stance, there was supposed to be an exact number. The problem was that that exact number was often wrong.
Chapter 2: Initial Contradictions
Since there was obviously a formula to be solved (though many thought it was better left unsolved… silly them ;P), someone needed to find it.
Finding no help from friends I took matters into my own hands and started testing myself. The so-called 55-strength boost is supposed to promise 1.5 hit points for every icon of damage. Of course, I had at the time, not one but TWO pets with that boost, and more often than not, even when the opponent wasn’t attacking, I was averaging well over 1.5 points per icon. What could be? So I started to test extensively, trying to control for as many factors as possible.
The classic testing point was to use a standard 10-icon weapon, on a frozen Punchbag Bob. The classic 10 icon standard weapon is of course the dark battle duck, and the results in fact confirm the tests.
Of course, the problem is very few people defend too often. I was then curious as to what the icon distribution would be of this same test without using defend… Not surprisingly the “x-factor” is much higher. Instead of being 1.5 it is instead 1.9.
I tried gingerly to point this out to people who had lots of power. No responses. Frustrated I went baiting in forums, posting a topic along the lines of “strength-boosts don’t exist”. I then posted the screenshot of my DBD doing not 15 but 19 damage… blowing the x-factor of 1.5 out of the water. I received a lot of testy replies immediately, which made me quite happy. Eventually reiksguardknight of IDB got a hold of me and after some reconciliation things were moving forward, and I was given license to test more.
The first conclusion to be drawn from those two crude screenshots is as follows: defense has roughly a 20-30% offset compared to any other ability. Nevertheless, since we are using defense as a base, we will do the rest of the calculations off of the defend option on a frozen Punchbag Bob, just for traditions sake.
So, we can say the 1.5 x factor is in effect. Surely whoever tested this originally used a dark battle duck right? My question is why didn’t ANYONE try at least one other 10-icon combination? Since I didnâ€™t have access to a radish bow or any other 10-icon weapons? I did some improvisation. The results put to shame all current theories. Simply put the original model assumes that all icon types are alike, and that 5 of icon A and 5 of icon B will do the same damage as 10 of either icon A or B. This is simply flat out wrong. I found it hard to find a 10-icon weapon that did all the same amount of damage (the kiln got upgraded after all, and finding a dark faerie collar to borrow would be… uhhh… difficult to say the least). What I COULD do, however, was to take a mud mixture and a caustic potion, which each did 5 earth icons for me, and use them together on defend. The result: The whole 1.5x factor theory is worthless.
16 damage and 10 icons on defend! What now? Well immediately some in forum tried to shoot me down, claiming that using two weapons might up the overall damage, and that the mud mixtures might do 5.3 icons instead of 5 icons… etc., etc., etc. Some of these people had a point, others that were claiming the fact that two weapons increased the amount of damage per icon didn’t deserve to enter in the discussion, because they were merely criticizing without doing any testing of their own.
What really blows the idiots out of the water though who didnâ€™t even try to look at alternate hypothesis, is that when you combine two OTHER weapons, with a vast array of icon types, (in this case I used a clockwork quiggle and a immense rubber axe of doom, you still get 10 icons… but look at the damage (or lack thereof!).
That screenshot right there destroys any theory that two weapons will do more damage per icon than 1.
Again that is another pet with the 55 strength bonus. There you can see 3 different icon types, and only 11 points of damage. Now you could round down the clockwork quiggle to maybe 3.5 icons, and consider the immense rubber axe only 5.5 icons, but that leaves 9 icons, and that doesnâ€™t equate to 11 hp of damage by any rounding scheme if the x-factor were to hold true. The only way you could round it out is if you were to take EACH set of icons and round them down, thus say the clockwork quiggles 2 earth were only 1.5 earth, and 2 physical were only 1.5 physical and so on, until you only did 7 icons of damage. This didn’t seem too logical, but what was starting to be clear was that icons didnâ€™t represent perfect amounts of damage. Things werenâ€™t nearly so neat as they looked.
Now the obvious conclusion to be drawn from this was that the more icons of one type you do, the better. This at first made sense to me. But I grew skeptical after running a few more tests. The DBD without an attack or defend did 19 icons as you saw. Dual Mud mixtures do 20 icons without an attack or defense (which would lead down this merry path youâ€™d think).
The problem becomes when one tries using a pumpkin stick on normal attack. Now a pumpkin stick on defend (8 icons) did 13 damage, which is above the 1.5 x-factor prescribed. I was feeling good about that, and even better when my kiln did 18 icons. All of the faith I had though I promptly lost, when making my pumpkin stick effectively a 10-icon weapon when by switching the mode to normal attack.
that looks a lot like 10 icons to me, and it looks a lot like 19 damage, same as the DBD. One theory was that the extra two icons from the jumping attack were somehow inferior, but that was pushing the boundaries. It was becoming clear that icons donâ€™t mean what they typically would, and that it would be possible to do fractions of icons, but since Neopets didnâ€™t have pictures for fractions of icons, it would merely either show all of the icon or none of it at all.
Sadly, 30 screenshots or so seemed useless. I was starting to test for every conceivable factor and was unsatisfied. I have learned that TRYING to defend at 0% doesnâ€™t reduce damage any, and a cautious attack adds no icons. Even more confounding is that a spider on a string did 12 points of damage on a cautious attack, while a immense rubber axe of doom did only 11 on that same cautious attack.
With that in mind, I was able to create two more iron clad facts:
- 1) A cautious attack means you are not doing any defense or offense in addition to the weapons you have chosen, and you are not diminishing the qualities of your weapons or defense.
- 2) Having 0% power is equivalent to being forced to do cautious attacks for the entire rest of the battle.
These two iron clad facts led to Sirhatter’s First Battle Theory
1) Under no circumstances is it ever a good idea to cautiously attack. The reasoning behind this is that any species ability will be an improvement over cautious attack in that it wastes none of your power, and doesnâ€™t expose you defensively or offensively while adding icons.
While on our original path, I was becoming increasingly convinced that icons were merely representations of numbers hidden away on a Neopets mainframe somewhere
Furthermore, what is the final nail in the coffin of icons representing exact amounts of damage is shown below,
Here on a frozen PBB, while trying to draw a comparison with a plain battle duck to a pumpkin stick, I inadvertently found something far more interesting.
In the first example, I do 6 icons and 11 damage, in the second example, I do 6 icons and 12 damage… same set of icons! Now usually with a pumpkin stick or DBD, you can test over and over and over and get the same results time in and time out. Since the plain battle duck is variable damage, it is clear that the icons are merely a representation of something else.
Again, the lesson is we donâ€™t know nearly as much as we should, and that much more testing needs to be done. In some cases (points towards the clockwork quiggle) the representation of icons might be an outright lie. In other cases there might be a variability factor missing. Lastly it seems clear that some weapons are better than others, even if they do identical icons. Icons do not determine damage points, and the formula is far less cut and dried than initially anticipated. I posted a teaser with along the lines of quot;Dark battle ducks are overrated” in forum, and again was delighted at the lively responses I got, some of which were well informed, others belonging to people of which I could only wonder “Who helped YOU log on?”
Chapter 3: Calculating Damage…Finally a Formula
From here, I was convinced that icons didnâ€™t mean as much as they initially were supposed to. What was interesting though was I was no closer to solving my original dilemma of finding an easy way to calculate expected damage done. The IDB formula was way off. I needed someone to test on. Punchbag bob is a perfect opponent in this regard. He had no weapons, and wouldn’t block icons.
I had to choose weapons. At this point it was clear I needed to use a constant damage weapon, or testing would be impossible due to the variability mentioned above. I had 3 constant icon weapons: a portable kiln, a dark battle duck, and an oh-so-underrated pumpkin stick. While the pumpkin stick is a personal favorite of mine, it seemed inadequate for these purposes. The reasoning was more icons would clearly be better. This was also a reason for rejecting a spider on a string or a lost desert dagger. For example if I did 12 damage with a LDD on normal attack and 20 on fierce with all other things equal, the actual percentage increase from normal to fierce could be 66%, but it could be 70%, or 65% quite easily. With two high icon heavy hitters though, these differences would be more pronounced, and my range of error would be much smaller.
I had finally promoted a pet to the 85 strength boost, and was delighted to see that the boost actually existed. (leaving my other pet at strength 80 seeming woefully underqualified). My final pet to test still didnâ€™t have the 55 boost, so I had the 3 distinct levels of intermediate pets to test with, and a spreadsheet of data and a free night to test it. With my kiln in one hand and my evil duck in another, I sent sirhatter (with the 85 boost against Punchbag Bob. At one point I had 20 screenshots here, but that would be over-the-top. I will instead gladly cut and paste the results into a table here for you to read. The numbers indicate how much damage I did. Each row and column corresponds to the attack stance I took and Punchbag Bob took, and note that it took a while to fill all 25 spaces with multiple cases of data (to confirm that constant icon attacks did the same amount of hit points each time). I didnâ€™t include normal attack in this table, though I tested it independently. Punchbag Bob will never normally attack you it seems, so that is why you donâ€™t see that row here.
|85 Boost||My Attack|
*Denotes that Punchbag Bob doesnâ€™t actually ever attack berserk, and these results were extrapolated by a method shown below
*** Denotes that Punchbag Bob is either attacking cautiously or is frozen for the sake of these damage/icon calculations. Of course when Punchbag Bob defends the illusion is that he blocks ALL icons, when clearly that is nowhere near the case.
I was very happy with myself upon completion of these tests. In addition to being able to rack up another kill on PBB within 20 seconds of finishing them (I took full advantage), there was a clear pattern emerging. You could switch the charts axis and the result was EXACTLY the same. What does this mean exactly?
Well, basically it means that when Punchbag Bob fiercely attacks you, itâ€™s the equivalent of giving you a free fierce attack, even if you didnâ€™t do it before. Thus the percentage of damage you expose yourself to is identical to the percentage extra damage you deal. The lesson? Anytime you wish to really add on damage by doing fierce attacks, be prepared to receive the same proportion extra of damage upon yourself. Fiercely or going berserk with only one weapon is a bad idea, because if your opponent goes uses two similar weapons, youâ€™ve given him a berserk attack for TWO weapons, while u only get the damage bonus for one. Meanwhile he can either berserk attack himself (and exponentially increase your pain!) or use an ability for free, gaining you berserk attack as a free expense.
The second thing that jumps out at you is just how irrelevant icons are. The DBD is a strange weapon in that you gain just as many additional icons from a jump/attack as you would a fierce attack. The kiln only gives one more icon. Thus between the two, even with a fierce attack only does one more icon than a jump and attack. So why just not jump and attack you ask? Well the reason is icons in this case have very little to do with the amount of damage you deal. Ignoring the defend column (which has that offset that will be talked about later), we can see that the average damage per icon varies fairly large. If we only had a few icons we might attribute this to round numbers, but itâ€™s clearly not just a rounding error. This is clear-cut when you gain FIVE extra points of damage from fiercely attacking (as opposed to jumping) for just one more icon when Punchbag Bob cautiously attacks (the default). If all of the other icons are only doing 2 or 3 points of damage, why is that last icon doing 5? The answer is because the icons are merely representations. If one were to believe in icon theory you would expect the fierce attack to do maybe 69 or 70 damage, but it jumps instead from 67-72.
Thus we can see they are representations. What the final thing, and most important discovery of this exercise was is that there is NO RANDOMNESS in the amount of damage done if PBB takes an attacking stance; itâ€™s the same each and every time. Punchbag Bob could not take a berserk attack stance, but since the table perfectly mirrored, I felt very confident in using my berserk stance, and flipping the data across, to represent Punchbag Bob’s stance… The results are in line with the next discovery I made. Itâ€™s the same each and every time. You can try it yourself if you don’t believe me. What this results in is a clear-cut discovery of exactly how damage is calculated. The neutral stance (any cautious attack, species ability I tested, or faerie ability) represents our base case. All numbers with hard data to back them could then be calculated in relation to the neutral stance… What does this mean in English you ask? First, hereâ€™s the table
Percentage Increase resulting in taking an attack stance
The results are clear:
Attacking like berserk increases the amount of damage done by 50%****
Attacking fiercely increases the amount of damage done by 40%
Jumping and attacking increases the amount of damage done by 30%
Normal Attack (not shown here) increases the amount of damage done by 20%
Defending REDUCES the amount of damage done by 20%
Thus if you wouldâ€™ve dealt 10 points of damage normally…
Berserk attacking deals 15, fiercely deals 14, jumping will give you 13, normal attack will give you 12, and defending will only give you 8. This would be critical to know. If the round before, your opponent didnâ€™t use any shield, and with a fierce attack you did 42 points of damage, and now your opponent only has 30 points left, you donâ€™t need to expose yourself any by taking an attacking stance, (assuming your opponent wont burrow or something like that), and that could be the difference between a win and a draw, as you can easily and crudely within 1 hp calculate the amount of damage youâ€™ll do next turn with each option.
Since the table mirrors, the defensive weaknesses apply to you as well.
If your opponent would normally do 20 points of damage, and you attack like berserk, he will now do 30 points. Thus if he’s been using those same two dark battle ducks throughout the battle, and has done 20 points each time, and you only have 27 hp left, you better not fiercely or berserk attack or you will die if you donâ€™t block those icons. If both sides decide to attack like berserk, the increase in damage isnâ€™t 50% + 50%, but rather its exponential, so its 1.5*1.5 or a 125% increase. Thus scrolling up and looking at the table, you can see when neither side takes an attack stance you will see I dealt 51 points of damage. But if both sides went berserk, those same two weapons would deal 115 points of damage, not 102. Thus one can easily calculate the maximum amount of damage they could conceivably do by finding a frozen opponent, use your two best weapons + whatever faerie ability you like (that doesnâ€™t do additional icons), and with that number multiply by 2.25 (or 2.1 if you can only fiercely attack) to calculate how much damage you could do.
This was a significant discovery. While I was happy, there was much more to be done. I went and transferred my precious weapons away from my str85 pet to my one with the 55 boost (and prayed that no pant devil would steal them… which would set me back millions!)
Now, that I have completed testing the 55 boost with berserk, the results are to be found here.
|55 Boost||My Attack|
*See below for explanation
**Again this assumes the opponent is frozen or in a non-attack/non-defense pose.
***From 3 paragraphs above: Some have claimed berserk increases damage by 60%. This data shows that is clearly not the case. However, my pet is at level 50 by the slimmest of margins, and there exists some possibility that Neopets might have tiered the berserk ability, so that as you reach a very high level berserk becomes more powerful.
As I was testing with my pet at strength 55, it became tempting to fill in the numbers on the opposite end. It was obvious what they would be right? Alas, towards the end, when I was defending and when Punchbag fiercely attacked, I did LESS damage than when Punchbag was defending and I fiercely attacked. I already etched in stone that this would do the equivalent amount of damage. So why the 1 hp difference? The answer has to do with rounding and the order in which they calculated damage done. If you have a messy number such as 26 and multiply it by 1.4 (increase from fierce attack), you get 36.4. This rounds down to 36. Then you multiply that by .8 and you get 26.8, which becomes 27. If you were to reverse the order of these multiplications, you get different rounding offs, and thus that can explain a small difference in this case of 1 hp, and I felt relieved and happy to move on.
Before I did though, I felt the need to compare the 55 boost to the 85 boost across identical categories. The one that stares right at the reader is the fact that at a 55 boost when both sides fiercely attacked with the weapon set I had youâ€™d deal 80 damage. On the 85 boost it was 100 damage, an increase of 25%. I looked at all of the other numbers, and within 1 percentage point either way, the damage dealt increased by 25% across the board. Thus that boost increased strength increases by 25%… Yet the damage done per icon was still variable. The latter was a problem to be tackled later. For now I named my boosts, 24 and 30 (the 55 and 80 boost respectively). Eventually we will find a better designation for these boosts.
I then moved on to my pet that was still a few points away from the 55 boost. Same drill as before. Same weapons, same boring combo. By now I was getting quite tired. But I dutifully calculated out all the numbers.
Here they are if you are interested: I elected not to extrapolate to berserk, because this was my lab pet and seeing level 50 seemed like a distant reality. Furthermore, unless you owned a pet with less than 55 strength and used a kiln/DBD, it would be of little value for you.
|25 Boost||My Attack|
The only thing left to do was to calculate the difference between the 25-85 boost and report it. When both sides fierce attack, one would expect 60 points of damage. I was thus disappointed to see 59 damage, but it may be a rounding error, or merely that the 100 damage from the 85 boost was really 99.7, and the 80 damage was really 79.5, and this is only 59.4. Who knows? Otherwise though it is clear that jumping from the 25 boost to the 55 boost increased all stats across the board by a third. Thus we can rename our three boosts as follows:
25 boost –> lvl 18
55 boost–> lvl 24
85 boost –> lvl 30
The boost from 55 to 85 is smaller proportionally, but the same in terms of pure arithmetic.
Now that the boosts were calculated, there were only a few problems left to be solved. This had to do with the pesky issue of damage done per icon from weapon to weapon. It was clear that taking single case studies was in effective. The DBD showing only 9 icons for a jump+attack and also 9 for a fierce attack is deceptive if not an outright lie. At this point some fatigue was setting in. Rather than transfer all the weapons numerous times, I stuck with my strength 55 pet (who had no berserk attack, and geared up for one final round of testing weapon by weapon.) Some people swear by certain weapons, not knowing that they like them but just that they do. People would coldly say, it doesnâ€™t do enough icons. Well that may be true, but icons have major rounding issues. I decided to take my pumpkin stick, kiln, and dark battle duck and stack them up. We have already seen how variable icon weapons can be troublesome in that they do different damage with the same number of icons. The results here are similarly troublesome.
In each case I was using just a cautious attack, the base measure. I recorded what Punchbag Bob did to watch the fluctuations in icons. Chapter 5 will address the minor flaws in this study.
|PBB Attack||Pumpkin Stick||Portable Kiln||Dark Battle Duck|
|Icons each does||8||11||10|
Immediately I knew something was fishy about the Dark Battle Duck. The others averaged exactly 2 icons per damage on a neutral setting. The dark battle duck was averaging only 1.9 icons. This was no rounding error either. Clearly it should be doing 20 damage, instead it did 19. Across the board, it was doing less damage per icon than the rest of these weapons. Mind you the difference wasn’t huge, but it’s enough to think of the DBD as a 9.5 icon weapon instead of a 10-icon weapon in the old vernacular. I propose a new methodology of grading weapons though, that would basically be to take the neutral/neutral setting, and then grading weapons based on that. The best way to do this would be to take a pet with a maximum boost (700) and divide by 10, and round to the nearest tenth or hundredth. Incidentally the 55 boost is exactly 10 times weaker than the 700 boost in theory, and the 700 boost may make the DBD shine in a better light, especially if on the 700 boost it does 194 icons, (which divided by 10 is 19.4 rounded down to 19), than just the 19.0 it shows right now. I suspect it will make the pumpkin stick look slightly less good than the 16.0 score its receiving right now. All of the tests that have been measuring icons dealt are proven to be a waste here. The kiln, as the tests show, maintains an impressive score of 22. Obviously the exact score wont be known until we can find a pet with 700 strength willing to test these for us.
Chapter 4: Some Thoughts on the Defend Ability and What Defense Does
Now we know a lot about offense, and know we still need to learn a lot more.
I focused my sights to defense. I have a friend in maximus_goatimus who owns a pet thatâ€™s easily in the top 100, that is not surprisingly absurdly strong. He also has his hands on a seasonal attack pea, also known as the all time best constant icon weapon known to man. I put up two pets, one with defense 80, and one with defense 23. I had already claimed that defense has no impact on the defend ability, that the defend ability lowers your offense and your opponents offense by 20% regardless of the situation. I lined up my pet with the pitiful defense, and maximus_goatimus clobbered the poor thing for 504 hp of damage. I then lined up my defense 80 pet, and let him try again. I again crouched into the defense stance, and he again took his SAP and went berserk. The result? 504 damage. This would lead you to believe that there is no correlation between defense ability and the defend tactic, and that defense might have a much more limited use
Chapter 5: What Still Needs to be Done
There is still a lot to be done
One of the biggest things is that along the way, maximus_goatimus let me tee up on his pet. I took my str_85 pet, and told his pet to take the defend posture (I had tested my kiln+dbd on berserk on various frozen opponents till I was satisfied it did the same damage across the board)
I was expecting identical results to PBB, and I got them… for only 2 of the 5 positions I took. The other 3, this pet with insanely high defense did WORSE than PBB. This is an anomaly that needs to be observed.
Also, as mentioned, the bigger the numbers you have, the less rounding error. If someone has a pet with str 700, please let me know if youâ€™re willing to do some testing for the good of the whole.
Also, some weapons need to be tested that are constant damage. Itâ€™s clear that the icons alone are no longer a measure of how strong a weapon is, but merely a representation. It is clear though that constant damage weans are exactly that… constant, and thus they can be graded completely objectively. Again testing should start immediately.
Variable damage weapons need to be looked at closely, and I didnâ€™t even begin to touch how defensive items affect things. Needless to say going by icons is a suckers bet.
Roughly speaking it seems that multiple icon weapons (that do many types of damage) fare slightly worse than good ol constant icon weapons. Again this is not a fact set in stone quite yet, not until we get the last bits of data.
Finally, there are some exciting features down the road we can make here. We can recreate the battledome perfectly, and simulate battles as they would actually happen eventually, so you can know your odds of winning a given fight before fighting it for real. (This will also allow you to pit one pet you own against another without actually having to swap it out of the pound). That will be a ways away of course. We can also push for newbie friendly changes like representations of partial icons, and a variety of other features that will be mentioned at a later date.