1. I have corrected the e-mail settings so that outgoing e-mails from these forums should be sent now. If you tried to Register or Reset your Password, please try again!
    Dismiss Notice

Logarithmic Character Power Growth by Level and its Effect on MMO Game design

Discussion in 'EverQuest II General Discussion' started by Inire, Jan 4, 2018.

  1. Inire

    Inire Not really an evil duck, just misunderstood.

    From a great post by Trasak on the Pantheon Forums (link is here if you want to read the original)

    Logarithmic Character Power Growth by Level and its Effect on MMO Game design

    Logarithmic Character Power Growth, over linear or exponential power growth, enables a larger cross section of players to meaningfully play together, utilizes a much larger percentage of developed game world, removes the value of a mentor system, limits mudflation, and eliminates the need for continual level cap content development.

    Logarithmic Character Power Growth is characterized by a short period of very fast power growth, followed by a short period of linear power growth, ending with a long and very shallow power growth period extending to level cap. When coupled with an exponential increase in the number of kills required to level 80%-90% of character play time occurs while in the shallow power growth period. This makes designing game zones for the shallow power growth period the most efficient use of development time.

    To differentiate between the beginning and end of the shallow power growth period characters gain situational utility powers of increasing complexity rather than increasing the magnitude of primary offensive/defensive/healing powers. To make these utility powers meaningful Monster tactics and environmental effects would grow from simple tank and spank at the beginning of the period to extremely challenging dynamic battle field conditions and monster mixed unit tactics at maximum level.

    This focus on utility powers, over significant magnitude increases, for the shallow growth period has two primary effects. First while a fully developed character may have up to 20% higher magnitude over a character just beginning the shallow growth period the primary abilities that differentiate either end of the shallow growth period will not come into play when fighting content created equivalent to the beginning of the period. This will permit characters to play down to earlier zones within the shallow growth period without removing the challenge or danger, it will just be easier. Conversely characters at the beginning of the shallow growth period could meaningfully participate in content tuned to the end of the period, assuming they had the required gear to participate, but without the situational utility skills odds of death significantly increase and other party members will be required to cover for the combat responses typically covered by the under leveled player’s class.

    To further facilitate the natural progression of the logarithmic power growth the initial fast power growth period can be contained within the starter zone which doubles as an in-game tutorial. The starter zone can be designed for solo or small group play so that a player is introduced to each of the primary abilities that define their character class and how to use the GUI.

    The linear growth period can be sub divided into a beginning and end phase. The beginning phase geographically can take you from the tutorial zone to the closest city. This major city can be used to introduce common in game interactions and things such as trade skills. By the time a character is more or less done with the first city and it’s near vicinity the character can be encouraged to travel to the nearest capital to receive their final primary skills.

    The trip to the capital and the required class quests will mark the end of the linear growth period and the beginning of the shallow growth period. Ideally the final class quests will introduce challenging group content that will require characters to form groups to complete the quests. This simple grouping will hopefully prepare the players for the shallow growth period where virtually all content will require a group of some kind and the higher level content will require well balanced groups with increasing abilities and player skill.

    Most of the “paths” between the different capital cities and the nearest of the smaller cities should be tuned to the end phase of the linear growth period. This way characters at the beginning of the shallow growth period can travel solo to the small city they wish to adventure out from. Cities further from the capitals will likely require specialized skills or groups to reach safely. This structure will prevent the ghost town effect as player’s level out of the linear phase and into the shallow growth phase as the primary leveling areas are also the primary over land travel routes. Other than the tutorial zone, and its path to the nearest city, characters of maximum level would have compelling reasons to be in all the remaining zones in the game. Players who are also primarily interested in crafting, RP and trading would be able to stop leveling their characters at the beginning of the shallow growth period without isolating themselves to just the starting zones allowing for alternative play styles.

    From a game marketing perspective the trial period of game could extend up to but not through the finally class quest, doing the final turn in will require the account to be a full account. Additionally all further expansions can be broken down into new story lines and sequels to existing story lines. New story lines would signify a new sequence of zones and challenges from the beginning to the end of shallow growth period. Sequel expansions can add additional maximum challenge content and or new environmental and combat challenges while not increasing the magnitude of the character power at maximum level. A combination of the two expansion styles would be taking an already created sequence of zones and updating the look and feel as well as the in zone story lines while also introducing new styles of challenges at the end of the shallow growth period.

    I have made a google spreadsheet with nice graphs and break downs of the different power curves both for players and Monsters as an example of the background math.

    Thank you for reading the recap,

    *Edit end*

    I must apologize for letting my inner math nerd showing but game and system design is so heavily based on mathematical models that it is hard to talk about one without using the other.

    To my knowledge all modern MMOs and most gaming systems are either exponential growth or steep linear growth. Off the top of my head only original SWG had a shallow linear power progression before unlocking Jedi, GURPS has a logarithmic power progression and 4th Ed D&D has a moderate linear progression with a high Y intercept but every 10 levels had a step like power jump similar to the initial high y intercept.

    The problem with exponential or steep linear growth systems is that it is just not sustainable without an equal growth in challenge. I call this the “Jumping the Shark Paradox”, How do you keep something interesting without Jumping the Shark and making all previous material less entertaining by comparison? When challenges grow at an exponential rate only a narrow band of levels can engage the challenge without making it too hard or trivializing it. This in the end creates a lot of low to no return development time and each expansion negates the previous expansion content. This is all assuming that the goal is to reach the highest level as fast as possible and gear up as fast as possible, which to be fair is the mindset of most gamers.

    A basic example of exponential growth is if a character starts with 100 HP and can kill something in 10 hits with the same amount of HP then they do 10 damage a hit. If the character gains just 10% each level then at level 50 the character would have 10671HP and would do 106 damage a hit. (lvl 10 – 235 HP, lvl 20 – 611 HP, lvl 30 – 1586 HP, lvl 40 – 4114 HP)

    Moderate or Shallow linear growth can be much easier to control but over a long enough growth period you will still have a significant number of zones of content that are of no challenge to characters at the maximum level. If the character gains just 10% of the first level of power each level then at level 50 the character would have 590HP and would do 59 damage a hit. (lvl 10 – 190 HP, lvl 20 – 290 HP, lvl 30 – 390 HP, lvl 40 – 490HP)

    If you have not already guessed what is most interesting to me is logarithmic growth. For those less mathematically minded folks out there logarithmic growth can be split into three zones, a rapid initial growth followed by a standard linear growth then changing to an extremely shallow growth that trends toward no growth at all. Logarithmic growth also happens to be the most common type of growth in nature, partially due to supply and demand.

    A way to model logarithmic growth in a game would be as follows. You start at level 1 with 100 hp and each level you would gain 10*((Max level – Next Level)/Max Level) rounded up. This would play out to be the following scale; lvl 10 – 183 HP, lvl 20 – 256 HP, lvl 30 – 309 HP, lvl 40 – 342 HP and lvl 50 – 355 HP. If the majority of the content is tuned for level 30 characters then a total of 30 levels of play would be within plus or minus 20% of the targeted power level of the challenge. In this way a level 20 could group with a level 50 character without being completely out classed by several orders of magnitude.

    If the number of kills to level is equal to the HP values in the exponential growth example then 95% of kills required to reach level 50, 116391 kills, will be in the targeted level range. Very little of the game world will need to be dedicated to the lvl 1-20 range and could be restricted to the cities and newbie areas. Conversely areas tuned to level 50 characters will also be rare and intended to be handled by multiple groups of sweet zone characters to handle.

    When creating zones the monster level can be created as if looking at a topographical map of a mountain pass such that the main travel path is the lowest elevation and the lowest level mobs are close to the path. This way weaker groups can stay close to the roads to increase the chance of survival but groups consisting of higher characters level and or higher skill level can leave those lower elevations.

    Now comes the hard part, why level if you don’t increase in power? The answer is simple, complexity. Even if by level 20 you have all of your basic abilities and can really stand on your own in a fight that does not mean you are a master or can do anything with finesse. Knowing how to hold your spear and stand shoulder to shoulder in your shield wall makes you a soldier, it does not make you Cuhullin.

    Game wise while a level 20 spearman with a Steel Spear would do 25 damage and a Level 50 Cuhullin with the Fabled Gae Bulg would still only do 36 damage but Cuhullin would have so many more options. Cuhullin would know how to fend off multiple opponents keeping them at bay as he focused on a single target. Cuhullin would be able to move through his opponents spotting weakness and exploiting them and in so doing control the positioning of the battle. Lastly in his hour of need Cuhullin could choose to call down his battle frenzy knowing it could mean his life, but not before his enemies lay bleeding at his feet.

    Additionally from a game mechanic standpoint the complexity of mob AI, density and spawn rate of mobs, and manipulation of extreme environmental conditions by the mobs could all be functions of tuned mob level. The mobs in different areas could have various types of damage reductions and resistances and would require special gearing and tactics to defeat them. These challenging areas could be added both at launch and down the road without negating the areas already created. Each new area would need to have story and flavor reasons to face it but again that shifts developer work from making the next ride in the amusement park to writing immersive stories for the players to experience.

    Hopefully this post was worth reading and is not yet another thwak on the equine skeleton.

    • Like Like x 2
    • Informative Informative x 2
  2. Fuli

    Fuli Well-Known Member

    So, if I understand correctly...

    1. Ln growth to compact scaling
    2. Character power is more impacted by leveling into additional utility features?
  3. Inire

    Inire Not really an evil duck, just misunderstood.

    Correct, assuming for the second that the utility features has corresponding impact on the world/combat/other systems.
  4. Semperfidelis

    Semperfidelis Member

    Then there are those "girly" games that have no levels and focus on you learning skills like moving around the world, using your eyes to find items that don't glow, but are interactive, gathering materials and creating things from them (general sandbox stuff)... well ok now it's not girly anymore to do sandbox stuff, but for many years a game that focused on things you can learn to do with an interesting interface were "girl" games and called "non competitive." The worm has turned.

    Good post, thought provoking.
  5. Khendrask

    Khendrask Active Member

    I've never actually checked the player power increase vs. level in Lotro, but it is nowhere near EQ2's abortion, and all zones actually are populated, at least on the servers I play on there.
    The MOB's also don't just go from doable to impossible between expansions.

    It seems that EQ2 is even more than a simple logarithmic progression, and is nothing but a funnel to the end-zone boredom, while the other zones are ignored, except where absolutely necessary for "Pre Requirements" for the end zone.

    As I've said before, I've gone back to just running old zones to finish off deeds, and content that got skipped, and there is never anybody in them, except perhaps by accident.
  6. Inire

    Inire Not really an evil duck, just misunderstood.

    This is one of the issues that logarithmic power progress is meant to solve. gives reason to use the older zones.

    I always thought that it was a shame to have so MUCH content that is trivialized and ignored once the player approaches/hits the level cap. EQ2 has a HUGE wealth of zones, and I personally would have played in some of the better older zones for years if it meant I could have effectively leveled and contributed.
    • Agree Agree x 4
  7. Caam

    Caam Member

    One of the things that isn't factored into the model is population. The main challenge with releasing content at any point is that almost everyone starts at the same ability/power level. As such, everyone is trying to kill the same stuff. A perfect example is seeing PoM running 15 instances at some points over the holidays. The model works when there are people at different points in progression but fails when the population gathers.

    Content is not infinite (yet). As such, there has to be some way to scale for population that is both starting out and/or gathered at a point of near completion. The model doesn't account for this. I do like the concept, but until that can be addressed, I don't believe it is a practical concept.
  8. Inire

    Inire Not really an evil duck, just misunderstood.

    interesting. Your example of a system that does not use Logarithmic growth, i.e. everquest 2, points exactly at the problem discussed i.e. that everyone ends up in the final zones, doing final level stuff after an expansion, where in this model discussed, you could go back to Kunark, say, and fight mobs that are within a few levels of you, and still get XP.

    I THINK your point is based on having progression from GEAR, not progression based on experience based leveling and growth of skills/utilities? If that is so, or i missed your point, that's fine, clarify it for me.

    If your point was in regards to progression based on GEAR or STATS, then I would agree with you, the model discussed in the original post specifically addresses long term survival of games with power based off levels and abilities/utility, not specifically addressing gear. However, it could be completely possible to address gear/stat inflation at an inflection point (i.e. at an expansion) via a similar logarithmic methodology, with possible drops scattered throughout the other zones, i.e. possible to get the ring of current expansion awesomeness 01 from mobs of level cap-4 to level cap +4, and put it on the loot tables that way. This gives every zone the ability to be useful for loot.

    Additionally, growth of itemization should be logarithmic as well in this case, which is not something that is currently true for everquest 2, and was in fact one of the reasons i stopped playing.

    Hope that this makes sense?
  9. Caam

    Caam Member

    My point is that the assumption of the model is that nobody will ever reach the "limits" of the content. Just as people are facing right now, the content of PoP was played and "completed" by a lot of people within a few months. Unless the plan is to generate content so fast that nobody can ever complete it, there will be times where players reach the practical limit of the content, not the model. Each time that occurs, you'll have a gathering of players near a specific level due to the content. Once new content is available, they will move forward together and the content will be the same for everyone so there will be a need to provide playable content for everyone at that time.

    Folks generally do not want to go back and run old content when they run out of new content to play. I started by beta-testing in 2004 so I've seen all of the content in this game except for a few raids that I was not able to achieve. I don't want to go back and run it again and I think most will agree.
  10. Inire

    Inire Not really an evil duck, just misunderstood.

    in terms of limits of the content: Expansions of Successful Games create a future for those games where the content will possibly be growing faster than the limits of the players near term. Far term, growth options in utility and ability can be used on all content, old and new, which gives greater depth/play-ability for the game.

    In terms of running old content when new content is out: Sure, that's why EQ2 discontinued the TLE Servers, and why WoW is discontinuing the WoW Classic release, and why EQ1's Event servers never had anyone on them. /sarcasm

    Perhaps not for you, but for a number of other players, going back and running old stuff is fun.

    This type of growth model in the original post allows the ability for younger players to be involved with events/things right from the start as well. they may not be able to contribute completely, but it avoids the issue of having to grant level caps and giving items right at the door of the expansion.
  11. Fuli

    Fuli Well-Known Member

    I like the idea of logarithmic scaling. I also like leveling schemes that are more interesting than metely increasing pools and acquiring gear.

    That being said, Caam has a good point in that any game that wants to stay relevant and interesting needs a constant stream of new content.

    For a game like Pantheon (which to me is just a modern eq1 grind game), this will likely work well.

    For a game like LOTRO, probably not so much - different designs entirely.

    However, I could see how a game like ESO could add stuff like this in just fine.
  12. Semperfidelis

    Semperfidelis Member

    There's more to a game than power, levels and old v new content. One of the brilliant parts of Lotro is an interesting and funny fishing system that is then incorporated into annual events and has its own little buffs and bonuses you can collect. There are graphical amusements such as the smoke your character blows turning into a ship or a flock of birds that go beyond simple cosmetics. The graphics of carrying a chicken are hilarious especially when jumping, hence the carry a chicken to... series of just for fun quests. I can't say I participate in the animal whacking quests but I appreciate that others do. When person is confronted by grinds such as are found in Lotro and Eq2, having these amusements (and others) breaks up the monotony. The key to the amusements is to offer something valuable, but not essential from them. Something nice to have, but not something that causes anguish if you don't have it.

    The essentials should be in the content. The nice but not essential bonuses should be found in amusements. Therefore, I'd rather the current PG rewards should be earned by several currencies, starting with KA or Thallumbra. Populate the vendor wares with temp adorns that are nice but not essential, cosmetics, temporary jumping bonus, weaker versions of totems and other buffs, similar items to what was offered via Dungeon Marks, and move all essential things into the Signature quest and status vendor in CoV/Nye'Caelona/Maldura.

    One of the biggest bummers is that the essential items are received via Achievements and rare drops, and weird grindy tasks not relevant to the rest of the game. They keep wanting us to "explore" and "experience" but then they give us endless grinds of the same episode of PGs? How can a person explore if they are stuck there? Sure you only ever have to do that once for your main. But that's ground zero for not being alt friendly.

    Another difference with PGs and the Marks from Lotro big battles or skirmishes is variety. The solo skirms and battles have many forms. If I get bored with some of them, I can do others. If that's even too much, I can buddy up and do a 3 man instance with two of us. And much of the loot can be sold. So my server-mates get some benefits out of my time... and I get some benefit from their time.

    It's funny, I think this game is one that tells the story I want to hear. But that one has the better structure. I've been stuck like that for a long time. Between two games, both mildly unsatisfying.
    • Agree Agree x 2

Share This Page