[General] Monster Experience, Stat Growth, and Fodder XP

Discussion in 'Archived Guides' started by slope, May 29, 2013.

  1. slope

    slope Well-Known Member

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    Introduction
    The purpose of this guide is to explain the different ways in which monsters can progress in Puzzle and Dragons, and to empower readers to be able to decide how they can maximize the feeding of their monsters for the maximum short-term growth gains. This is particularly helpful if you want to have your team to always be at its peak regardless of whether you're just starting out in the game or building up a team for an end-game dungeon.

    The focus of this guide will primarily be on how to use one of the best tools we have available for evaluating monster growth -- the stats growth chart on the Puzzle and Dragon database (www.puzzledragonx.com). Somebody who has read this guide should be able to read and understand the graphs on that site.

    Who This Guide Is For
    If you've ever wondered what those pretty graphs on PDX are for, or if you've heard of people talk about "growth curves" or "stat growth" of monsters but didn't quite understand what all that meant, then this guide is for you. If you think you have a decent understanding of the subject but aren't sure about exactly how it all works, this guide might be for you as well. If you already know all there is to know about stat gains and growth curves - then you can stop reading now. :)

    The Basics
    The two core concepts behind understanding monster growth are the Experience Growth Curves and Stat Growth Curves or Stat Gain Curves. Both of these concepts can be understood independently of one another, but it is the combination of the two that provides the most useful information.

    The Experience Growth Curve
    In a nutshell, a monster's growth curve describes the amount of experience required for a monster to reach a particular level. For the sake of uniformity, these growth curves are named by the amount of experience required to reach level 100, as illustrated in this diagram from PDX --

    [​IMG]
    Source: http://www.puzzledragonx.com/en/experiencechart.asp

    In this diagram, the horizontal x-axis displays Monster Level, while the vertical y-axis displays the experience required to reach that level. So as a quick example, a monster with a 5M growth curve needs roughly 3M experience to reach level 80, while a monster with a 1M growth curve needs a little over 0.5M experience to reach level 80.

    The most immediate thing you'll notice from this is that lower is better - or rather, a monster with a 1M growth curve only needs 1M xp to reach level 100, while a monster with a 5M growth curve requires 5 times as much experience to reach that same level 100. Of course, though, the stronger monsters (i.e. Gods) tend to have much higher growth curves, particularly when they reach their final evolution form.

    The second most important thing to notice about these growth curves is that they grow exponentially. This means that as a monster levels up, it becomes increasingly harder for these monsters to reach the next level. For example, a monster with a 5M growth curve takes roughly the same amount of experience to go from level 75 to 100 as it did to reach level 75 in the first place.

    Each growth curve is defined by their exponential growth rate, which is essentially how quickly that curve starts ramping up towards infinity. In the best case of 1M, the exponential growth rate is slow enough that you don't really get to see its effects even at level 100. But in the worst case of the 5M growth curve, it takes you roughly the same amount of experience to take a monster from level 75-100 as it does to take that monster from level 1-75.

    Used by itself, a monster's growth curve is a great way to evaluate how much effort it will take for you to get the monster reasonably leveled up. But it's really only half of the equation if you actually want to draw some useful conclusions out of this. In order to make full use of the growth curve of monsters, one must understand the difference in stat growths for different monsters.

    Monster Stat Growth
    Monster stat growth can be described concisely as the amount of stat points a monster gains per level as they level up. By looking at a monster's stat growth (and later combining it with their exp growth curve), you can essentially determine the "bang for your buck" -- how much stats you're actually gaining for the levels that you're pumping into a monster.

    Unlike the experience growth curves, stat growth curves are not uniform across the game. They are different for every monster - and sometimes different for each stat within the same monster, but they generally fall under 3 categories: sublinear, linear, and exponential.

    Sublinear Stat Growth - "Early Bloomers"
    A monster sublinear stat growth will usually start out with very impressive stat gains in their first few levels, but start tapering off quickly in gains as you continue to level up. As such, you can sometimes refer to monsters with this stat growth as "early bloomers". Siren's RCV growth chart provides an excellent example:

    [​IMG]
    Source: http://www.puzzledragonx.com/en/monster.asp?n=202
    As you can see in Siren's RCV growth chart, Siren gains a hefty 100 RCV going from level 1 to level 26, but then requires another 40 levels to gain her next 100 RCV. And her RCV gain from her last 40 levels is well under 100 at around 70ish.


    Linear Stat Growth
    By far the most common growth rate in the game, a linear stat growth on a monster means that it gains exactly the same amount of a stat for each level.
    [​IMG]
    Source: http://www.puzzledragonx.com/en/monster.asp?n=230

    As you can see in FKK's ATK growth chart here, he gains roughly 100 ATK every 25 levels - all the way to level 100 for a total of ~400 ATK.


    Exponential Stat Growth - "Late Bloomers"
    The exponential stat growth curve can typically be found in the strongest monsters in the game. They start off slow in stat gains, but as you begin to pump more levels into them, gain more stats per level. Thus, we can call them "late bloomers" because their stats don't really start to shine until their later levels.
    [​IMG]
    Source: http://www.puzzledragonx.com/en/monster.asp?n=188

    Awoken Zeus's HP growth chart provides an excellent example of exponential stat growth - he gains roughly 300HP in his first 30 levels, but nearly 1000 HP in his last 30 levels.

    The Growth Factor
    As important as it is to understand the rate at which monsters gain their stats. The growth curves can only inform you of how a monster grows, but they ultimately don't tell you how much a monster grows. The most important factor that you still ultimately need to look at is the differential between their min and max stats, because that will tell you how much you're ultimately getting out of max leveling a monster.

    Thus, we can sort of define growth factor to be (Max Stats - Min Stats)/(Levels) -- but since everybody caps at level 99, the denominator is the same for everyone, so we can just look at (Max Stats - Min Stats) in the numerator.

    For example, look at the comparison between Neptune and Mechdragon Hadar's HP growth curves:
    [​IMG]
    Source: http://www.puzzledragonx.com/en/monster.asp?n=391

    Even though Neptune has exponential HP growth while Hadar has a linear stat growth, the growth factor in Hadar's HP is so high that Neptune doesn't catch up even at level 100. It's probably worth noting though that if monsters weren't capped at level 99, Neptune would eventually beat Hadar in max HP, but because levels are capped in this game, we need to consider the growth factor as a serious element in comparing monsters.

    Ultimately, a monster's max stats are the only thing you really should consider when building your teams, but their growth factor and growth curves will at least tell you how you should prioritize growing your monsters.


    Putting It All Together
    Now that we understand how experience growth and stat growth works, we can put them together to truly understand how to get the best bang out of our buck when feeding our monsters.

    PDX has even made this easy by allowing us to examine a monster's growth curve by experience. By using the HP/ATK/RCV vs. Experience chart, we can see exactly what our investments get us, and where they start giving us high returns, or when they are really tapering off.

    As a fairly common example, let's examine the HP growth of everyone's favorite Meteor Volcano Dragon, which has a 4M xp curve and linear HP growth that earns roughly 1700 HP over 100 levels (or 17 hp per level).

    [​IMG]

    As the diagram shows, the first 1M XP you invest into a Meteor Volcano Dragon nets you a whopping gain of 1000HP... but it's going to take you another 3M to get him to max level.. for another measly 800HP. So this is a good indication that you may be interested in putting in about 1M XP into the dragon for that burst gain in the beginning, but you may not necessarily want to drop that remaining 3M xp afterwards for a much smaller gain.

    Contrast this with someone like Awoken Zeus, who, despite his 4M XP curve, has pretty decent stat gain per xp throughout the levels, thanks to his exponential growth rate.

    [​IMG]

    From this, you can think of XP growth and stat growth as counterbalancing forces to each other when it comes to calculating "bang for buck". A low XP growth curve can counterbalance sublinear/low linear stat growth, while high, exponential stat growth can in turn counterbalance a high XP growth curve.

    But if you take a high XP growth rate and sublinear stat growth, you end up with sort of the worst of both worlds - like so:
    [​IMG]

    As you can see, Siren the Enchanter is *really, really* not worth investing into past the first 1M xp, because your gains after the first 1M exp are absolutely horrible.



    OK, What Does This All Mean?
    As a general rule - the monsters you'll want to invest most heavily on are the ones that have the best max stats, lowest experience curve, and exponential growth curve. These are the cheap, late-blooming, ass-kicking monsters that... don't really exist, unfortunately. So we really should be looking at a case by case basis.

    All of this information should now help you look at each individual case-by-case basis and make fairly rational decisions about which monsters you should feed in order to get the highest stat gains for your team. Some monsters (like Zeus) are pretty much great bang for the buck regardless of what level they are, while other monsters (like Siren) are really not worth investing more than ~1M experience into. For the rest, you'll really want to look at their HP/ATK/RCV vs. Experience chart to help you decide, "Who should I level right now for the best gains?"

    Of course, stats aren't everything in this game. Active skills and leader skills can contribute way more to the effectiveness of your overall team than anything else. But if you find yourself in a position where it's simply a matter of dumping XP into Monster A vs. Monster B, you should now be well-equipped for making that decision.
     
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  2. slope

    slope Well-Known Member

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    RE: [Team Building] Monster Experience and Stat Growth

    Monster Fodder/Feeding XP Values
    By request on this thread and as a result of a conversation in a different thread, I went ahead and did some more looking into monster fodder XP values, and made a spreadsheet (in a section below) to show the XP conversion ratios for the common monsters we use as fodder.

    This section was derived primarily from the tables listed in PAD Wiki:
    http://pad.wikia.com/wiki/Monster_EXP_Curves

    These tables tell us a few important things -- what the XP Fodder Multiplier/Growth rate is for certain monsters, and what XP curve these monsters are on. They also show us that the Fodder XP Growth Rate is linear for *all* monsters, which makes the calculations a lot more straightforward.

    Without further ado...

    The Big Fodder XP Table
    Here's the spreadsheet I compiled containing the monsters we might generally use as fodder --
    https://docs.google.com/spreadsheet/ccc?key=0Ah1NjACTDodGdHo2V0lQUHQ1SDZ5QWRnU1hzYVBLaFE#gid=0

    There are 3 sheets - one for 1M XP Curve monsters, one for 1.5M XP Curve monsters, and one for 2M XP Curve monsters.

    Reading the Numbers
    The way you want to read this spreadsheet is primarily by looking at the Fodder Multiplier (the higher this number is, the better) and by looking at the XP GAIN column. The multiplier tells you how much fodder XP value a monster gets per level. XP GAIN tells you how much XP you actually gain from feeding the monster to level up -- that is, the amount of additional XP OUT you get for your Fodder Monster subtracted by the amount of additional XP IN that you have to invest to level him.

    As long as the XP GAIN remains positive, you'll be getting an incremental net positive amount of XP from leveling your Fodder Monster.

    As soon as the number goes negative, that means that you'll start losing experience for pumping the Fodder Monster any further. Once you reach this point, you will earn more experience from just directly feeding your monsters rather than feeding them to each other.

    What Does It All Mean?
    A few basic conclusions can be drawn from these tables and from the spreadsheet:

    Generally speaking, you don't want to directly feed stuff that's below level 6. If they're below level 6, there's an untapped "growth potential" of XP that you can gain from pumping a few levels into them first. Note that even in the most aggressive 2M XP Curve, it only takes 1176 XP to get to level 6.

    The most optimal way to use fodder is to pump them while they're within the green zone - that is, as long as your XP GAIN is greater than 0, because this means that at least you'll be getting MORE XP than you were putting into that monster.

    To summarize the spreadsheet's green zones, you basically don't want to pump these fodder monsters past these levels:
    Pengdras - Level 9 / 1904 xp (if directly feeding)
    T2 Carbuncles - Level 6 / 588 xp
    T2 Knights - Level 6 / 588 xp
    T2 Ninjas - Level 8 / 1364 xp

    Moltdras - Max these guys. They're that good. / 3834 xp
    T2 Ogres/Devils - Level 6 / 882 xp
    T3 Devils - Level 7 / 1391 xp
    T3 Ogres - Level 7 / 1391 xp

    T1 Chimeras - Level 5 / 673 xp
    T2 Chimeras - Level 6 / 1176 xp

    (TX = Tier X = X'th evo form)

    Update 11/15/2013: Thanks so much to Kelbesque for pointing out the error in my original spreadsheet model. I made updated the spreadsheet to be a lot simpler to understand thanks to his post. :)
     
  3. 38thdoe

    38thdoe Old

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    RE: [Team Building] Monster Experience and Stat Growth

    Nice work slope! Although I'm sad that you had to make Neptune look bad. Wish I started playing early enough to get mechdragons.
     
  4. slope

    slope Well-Known Member

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    RE: [Team Building] Monster Experience and Stat Growth

    Ha! Thanks. :D I'm quite fond of Neptune myself (I started this game with a 6* Neptune roll and he carried me very, very far)... I was originally going to use him for a good HP example, but at some point looked up Mechdragon Hadar and saw how much crazier *that* guy is... (at least in terms of HP growth)
     
  5. Marty

    Marty Meow?

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    RE: [Team Building] Monster Experience and Stat Growth

    Awesome explanation slope!!
     
  6. calorie

    calorie パズドラオタク

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    RE: [Team Building] Monster Experience and Stat Growth

    Thanks for the great guide!
     
  7. Trix

    Trix New Member

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    RE: [Team Building] Monster Experience and Stat Growth

    Awesome job slope!

    Quick question. Can you explain how is this a Team Building guide? It sounds more like a General guide to me.

    But yeah, it's really awesome!
     
  8. slope

    slope Well-Known Member

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    RE: [Team Building] Monster Experience and Stat Growth

    I was debating about the label actually, so I just took a look at the guides in the Guides section and for some reason concluded that it was a Team Building guide.

    You're most likely right - I'll change it to General for now, until I can think of a more appropriate label (or perhaps General is the most appropriate).

    Thanks for reading!
     
  9. Trix

    Trix New Member

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    RE: [General] Monster Experience and Stat Growth

    Hehe, alrighty then!

    Gonna move this to the Guides due to its awesomeness~
     
  10. slope

    slope Well-Known Member

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    RE: [General] Monster Experience and Stat Growth

    Sweet! :) Hope some folks will eventually find this useful. I was certainly frustrated when I started with not being able to find any info on exp curves even though they get mentioned everywhere.
     
  11. Dubby

    Dubby Dubulubu ♥

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    RE: [General] Monster Experience and Stat Growth

    SWEEEEEET~

    Thanks, was wondering how these factor on PDX (never actually really deeply cared to get into this) but now it makes sense. I was always using the "Show stats on level X" function in 2 tabs in my browser comparing monsters... LMAO! >.<" Andn ow we got them curves. easier.. so much easier :D

    Thank you!! :)
     
  12. bangbang

    bangbang Light Mage

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    RE: [General] Monster Experience and Stat Growth

    Nice write up for us number crunchers.

    I'd love to see the formula for the curves to really compare the monsters. Of course the linear ones all you need is slope and starting point.

    I'm curious if gungho kept the other curves simple and gave them all the same base. If that's the case the stat growths would be very easily comparable. Someone with a lot of free time, go use datathief and pull off all the curves from puzzledragonx, fit the equations and tell us what you get :).

    Actually if someone has the data from puzzledragonx in a txt file, send them my way and I'll fit them and see if the curves are easily classified (or at least rank all the curves and give everyone the results).

    This would be great information for picking which monster to level next. Ultimately, we should make an applet where you can input your teams and levels, how much exp you have to spend, and it'd output the atk, hp, and rcv you'd gain from investing it certain ways, and tell you what would be ideal.
     
  13. slope

    slope Well-Known Member

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    RE: [General] Monster Experience and Stat Growth

    The curves shouldn't be hard to figure out. I imagine that the superlinear stat curves are really just parabolic - that is, they're just ax^2 + bx + c.

    BetaTester (the owner of PDX) certainly has the formulas or he wouldn't be able to generate them on the site and provide the stat calculators per level. In the worst case, you should be able to reverse engineer the formulas just from taking two or three points.
     
  14. rod-

    rod- I just want to stand on land.

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    RE: [General] Monster Experience and Stat Growth

    If only you'd been there a little bit earlier for me! My highest-level monster is (you guessed it!) Siren the Enchanter! (Lol).

    I knew the stat gains were mediocre, but I had literally ZERO other playable blue cards, so I figured that 1.5x exp was more important than the alternative...which upon reflection is untrue.
     
  15. Cel

    Cel New Member

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    RE: [General] Monster Experience and Stat Growth

    XP = C * 10^6 * ((level - 1)/98)^2.5

    C = 1, 1.5, 2, 2.5, 3, 4, 5 depending on the monster. Their monster curves

    Stat = (stat@99 - stat@1) * ((level - 1)/98)^K + stat@1

    K = 0.7, 1, 1.5
    0.7 - Siren curves
    1 - linear
    1.5 - most god curves.

    something like that

    IMO, Gods just make you put in more XP to get the desired stats. Sirens are better, since you gain the most bang for your buck early on, but yeah it diminishes greatly at higher levels.

    You can use calculus to figure out the best +egg stat gain per monster. For example, Princess Valk has horrible stat gain. At level 35, she gains as much +eggs/xp as Ancient Light dragon does at level 99.
     
  16. iAMFogal

    iAMFogal New Member

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    RE: [General] Monster Experience and Stat Growth

    Nice. The only thing this thread needs now is a list of popular monsters and at what point their xp falls off so i can be lazy and not look it up myself :D
     
  17. IronH

    IronH Paralysis by Analysis

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    RE: [General] Monster Experience and Stat Growth

    Great work, Slope! I am branching out in all directions/colors at the moment. Recipe for disasters I know, but hopefully the information on stat growth will help mitigating the problem.
     
  18. darkshabow

    darkshabow New Member

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    RE: [General] Monster Experience and Stat Growth

    Nice work,helped a lot understanding the game
     
  19. frotes

    frotes New Member

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    RE: [General] Monster Experience and Stat Growth

    Nice work. Now to compile some break points for popular monsters or for each growth curve. That would be sweet
     
  20. Zyrax

    Zyrax New Member

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    RE: [General] Monster Experience and Stat Growth

    Not sure how you'd envision break points making sense but I would be down with managing a monster list down to the exact XP and letting a tool show me what the expected returns are with any fixed amount of XP feeding I designate.
     

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