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Kest

Level progression

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I'm curious to know what everyone thinks about typical RPG level progression. Specifically, opinions about exponential versus linear cost/progression. There are.. eh, four possible extremes, I think: 1. Exponential cost, linear improvement. 2. Exponential cost, exponential improvement. 3. Linear cost, linear improvement. 4. Linear cost, exponential improvement. These are not limited to character levels. They can also represent skill levels. Or even progression that wouldn't be considered levels at all. Which do you think is better for a game? Does it depend on linear versus open-ended exporation/gameplay? What about game length (short, long, never ending)? Anything else? My opinion: Exponential cost: Most games seem to go with this. The biggest problem I have with it is that the beginning of most games is already pretty exciting. Everything is new to the player, so it doesn't make a lot of sense to pile on a lot of progression there. Once the game moves along, the leveling aspect becomes so slow that it might as well be shut off. Exponential improvement: There's not much I can say about it. It's just pretty lame when a level 21 NPC/player can squish a level 19 NPC/player like a bug, regardless of how long it took them to get from 19 to 21. Linear cost: I like this one. The player's progress never slows down. That means very slow leveling near the start, but still leveling at that same rate while nearing a maximized character. The most negative aspect is that you're stuck with a beginning character for a longer time. Linear improvement: Pretty much the opposite of my complaints for exponential. A level 19 NPC/player can still get the upper hand on a level 21 NPC/player. That means AI enemies don't become useless/pathetic as quickly, and that the player can compete ahead of what the game expects with playing skills or strategy. What do you think?

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What do you think?

I think it is relative. If the monsters are just going to improve along with the player, then how fast the player improves is irrelevant, except as a reward (and only a perceived one at that as there is no actual improvement due to the fact that the monsters also improve at the same rate).

So it comes down to how often you want the player to be rewarded and how big you want those rewards to appear to be.

As for frequency, a constant rate of reward eventually weakens in its perception over time. So a linear rate of reward (linear level progression) will mean that as the game progresses, the size of the reward perceived by the player will be reduced. So this means that you have to give bigger rewards later in the game or the player will stop seeing the level up as a reward.

So to maintain the rewards effectiveness in the game, you will have to give bigger and bigger rewards for each level up, or have an exponential improvement if you are using a linear level up system.

If, on the other hand you are using a non linear reward rate (exponential cost), then as these are not regular reward periods, you don't suffer the effects of a diminishing returns (due to the psychology of humans). This means that you can get away with a linear progression (but can still use an exponential progression if you want).

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I think the big problem with "linear improvement" is what is called "diminishing returns." The amount that you increase may be the same when leveling up from 1 to 2 as it is from 99 to 100, *but* it makes almost no difference at levels 99. If your damage equals 5 * level, then you double your damage by getting to level 2. 5 damage to 10 damage is a big difference (10 hits to kill someone becomes 5 hits). 495 to 500 damage is hardly a change at all (if it took 10 hits to kill someone with 495 damage, it will at best take 9 hits to kill them with 500 damage). To double again, you must then reach level 4, then level 8, then level 16, then 32. Looking familiar now? Yeah, that's just like exponential cost and exponential improvement, but the levels are bigger.

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Original post by Ezbez
I think the big problem with "linear improvement" is what is called "diminishing returns." The amount that you increase may be the same when leveling up from 1 to 2 as it is from 99 to 100, *but* it makes almost no difference at levels 99. If your damage equals 5 * level, then you double your damage by getting to level 2. 5 damage to 10 damage is a big difference (10 hits to kill someone becomes 5 hits). 495 to 500 damage is hardly a change at all (if it took 10 hits to kill someone with 495 damage, it will at best take 9 hits to kill them with 500 damage). To double again, you must then reach level 4, then level 8, then level 16, then 32. Looking familiar now? Yeah, that's just like exponential cost and exponential improvement, but the levels are bigger.

But that's an unreasonable amount of progression (which plenty of games employ). You're creating too much of a gap. 5 damage to 500 damage? There's no conceivable way for a person to range from 5 damage to 500 damage with skill alone. Try something like 100 damage to 200 damage, or 50% damage to 150% damage. That will be much less obvious.

Such as..
sword_scaler = sword_level / 25
damage_scaler = 0.5 * 1-sword_scaler + 1.5 * sword_scaler

If a certain sword caused 100 damage, it would be:
Level 1: 54 damage
Level 2: 58 damage
Level 8: 82 damage
Level 9: 86 damage
Level 24: 146 damage
Level 25: 150 damage

Climbing from 54 to 58 is not much better or worse than 146 to 150.

This type of progression is less noticable per level up, but that also means enemies and areas don't become outdated as quickly (instantly).

EDIT:

Actually, I think the point is that with linear progression, you need to start the player out at a humanly realistic scale. Not like your average out-of-the-box player character, who shoots a ranged weapon and misses by a 90 degree angle.

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I think it's not just as simple as which of these methods you use.
The way they fit into the game is what really makes or breaks the system.

You could design a game that works around all of these.
So it's really hard to say that one is definitively better.
(Although I agree with others that you want to avoid diminishing returns problem.)

I would say, however, that my favorite is exponentially harder levels with a linear improvement scale. Additionally, in my personal opinion, you don't really need a level cap if you fit the system into your game correctly.

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That's a very interesting discussion for me. I've been going through a lot of balancing in my RPG as of late. I've explored a lot of formulas for characters and enemy growth. I'm going to explain what kinds of formulas I chose and why. If you have any comments, be my guess, balancing is fun but hard. Tweaking numbers on an Excel sheet is one thing, but playing the thing in practice is different, because there is way too many variables to check, such as the number of foes per groups, the availability of shops (in case the player needs more potions) the enemy's AI, the specs of the characters, etc.

For level growth, I'm using a mix of an exponential and a quadratic function. (At low level it is quadratic because exponential scales too slowly and I don't want to player to score 10 levels in 5 minutes, after IIRC level 15 it becomes exponential) so I guess you could call it an "exponential cost" according to the TC's criterias.

However, I set the enemies' XP so that if you progress normally through my RPG, it feels actually linear, not exponential. Allow me to explain: what I do when setting enemies' XP is that for level X, I expect the player to kill Y enemies of level X, and the function for Y (average number of monsters I expect to be slain to go from level X to level X + 1) is linear. For example, to get from level 15 to level 16, it takes 4,372 XP and I expect the player to slay in average 25.72 level 15 foes, so the average XP for a level 15 enemy is 4,372 / 25.72 ~= 170.00. (±35%) So, thanks to the exponential XP function, my system puts a soft ceiling to levels by making it incredibly time-consuming to power-level past a certain point, but it also makes a low level character catch up really quickly. In my RPG, a character joins the party at level 2 in a level 8~11 area. After only two fights, I think she was already level 6. The high increase of an exponential function makes unusually low level characters correct very quickly, at any level. A linear cost growth would only work like this at lower levels, at higher levels, it would take a lot of time for a character 10 levels below average to catch up. I'm not saying this is bad, some developers might want this; it is simply not my case.


Concerning the growth in power, I'm still in the process of balancing, but I sure don't want linear damage progression. The diminishing returns here are too pronounced. Imagine a character does 20 damage on level 1 and gains an additional +20 damage per level. The damage increase between level 1 and level 2 would be 100%, then 50%, then 25%, etc... At low level, even-leveled enemies would become obsolete after one level. Then you tone down the scaling to 20 +5 per level so low-level isn't as crazy... Good now? Oops! Now the problem is at higher levels where player barely notice the effect of leveling.

For my part, I opted for a 3 variables which all increase linearly, and those are all multiplied together so that looks like an exponential improvements, though it's more a cubic one. Cubic and quadratic functions still have diminishing returns, but it's much less noticeable. Besides, I find a function with a *small* diminishing returns beneficial. On level 3, fighting a level 8 should be very dangerous, but on level 80, fighting a level 85 should not be a certain doom. Without diminishing returns it would be just as dangerous here.


EDIT: Split the wall of text in paragraphs. ;)

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Original post by Bearhugger
Concerning the growth in power, I'm still in the process of balancing, but I sure don't want linear damage progression. The diminishing returns here are too pronounced. Imagine a character does 20 damage on level 1 and gains an additional +20 damage per level. The damage increase between level 1 and level 2 would be 100%, then 50%, then 25%, etc...

The problem is that you're adding 20 damage per level and starting at 20. If 20 represents a single learning step, your beginning character is worse than a complete moron. He's totally braindead. Something on the level of a newborn baby trying to wage war. Consider it. A 1 year old probably could do double the damage. And a 2 year old would probably triple it.

That's just not realistic. Humans can pick up weapons or dive into actions that they've never seen before and do a decent job with them. Don't start at the bottom.

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A very good point. Damage should never increase with levels. It is a function of physical strength, the weapon being wielded and possibly that character's skill with the weapon. The problem is the roleplay game designers are in love with number systems that have no relation to reality. Which creates for them all sorts of dodgy balancing problems. Bring the reality back, I say ;-)

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Original post by Kest
The problem is that you're adding 20 damage per level and starting at 20. If 20 represents a single learning step, your beginning character is worse than a complete moron. He's totally braindead. Something on the level of a newborn baby trying to wage war. Consider it. A 1 year old probably could do double the damage. And a 2 year old would probably triple it.


I have used these numbers for the sole purpose of magnifying the flaws of linear scaling. A real game would be, I dunno, 2 x (Lv - 1) + 20? The benefits of leveling in a linear system is never uniform. This is just a formula, this might be what a game designer wants, but in my project, I think that linear scaling would be flawed.

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Original post by Bearhugger
I have used these numbers for the sole purpose of magnifying the flaws of linear scaling. A real game would be, I dunno, 2 x (Lv - 1) + 20? The benefits of leveling in a linear system is never uniform. This is just a formula, this might be what a game designer wants, but in my project, I think that linear scaling would be flawed.

So your damage would be 22, 24, 26, 28, 30, 32, etc? What's wrong with that?

It should only be flawed in a system where enemies and challenges climb at an unrealistic rate. That might be the case when you go from figthing rats to fighting demons, but not with any reasonable progression.

I guess it's a personal opinion. I think enemies should become slightly less of a challenge, but not obsolete. They should still influence the game world, rather than being left behind. One benefit of it is that the player isn't limited to a few types of enemies at a time. Nearly all enemies in the game world could be fought with a reasoble chance to lose or win, at any one time.

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The character should be improving at a rate that keeps up with the world's increased difficulty, and gives the player a real sense of progress. The model that seems to be most effective is a constantly repeating experience of overcoming challenges.

You cross a bridge into a new zone, and the monsters are tough for you to kill, but you can do it if you keep up with the potions and the aggro management and the liberal use of magic buffs. As you live there and complete the local quests, you gradually use fewer potions, and fewer buffs, and when the time comes to cross the next bridge, you can squash the mobs here with your basic attack, without needing to heal in between fights. Then you hit the next zone, and you've got to drink (bigger) potions, spam (beefier) buffs and pull the baddies one at a time to stay alive, but you can do it. Repeat until you run out of continents, then release an expansion pack.

So the game experience is like a sine wave, oscillating between periods of "interesting challenge" and "satisfying ease". You can even have more "steps" than you need, so the players can go to an area that provides just the right amount of challenge for their mood. If they always want to be fighting bad guys who are three levels above thim, walking the razor's edge of "too damn hard", they can. If they want a cakewalk, to always be the biggest, baddest guy in town, they can adjust their pace through the world accordingly.

As for the exponential vs. linear debate, I've always favored linear/linear, or even exponential cost, linear improvement, in a world where getting juiced up to top level isn't the only way to succeed. I don't like games that encourage you to grind yourself a clear advantage (Final Fantasy is the obvious offender here) and then waltz through the rest of the game on easy mode.

If it's multiplayer, I favor exponential cost in any event, so that if two players are playing together, their levels will converge instead of maintaining a gap, as linear cost would.

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I didn't read all the replies, so sorry if someone already suggested this.
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Original post by Kest
Linear cost: I like this one... The most negative aspect is that you're stuck with a beginning character for a longer time.

You could always just use linear cost but make the gradient gentler at the start of the game and then have it become a bit steeper at a certain point.
You could even increase the gradient, say, every 10 levels or something, which might find you a nice middle ground between linear and exponential cost.

cheers,
metal

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Original post by Iron Chef Carnage
You cross a bridge into a new zone, and the monsters are tough for you to kill, but you can do it if you keep up with the potions and the aggro management and the liberal use of magic buffs. As you live there and complete the local quests, you gradually use fewer potions, and fewer buffs, and when the time comes to cross the next bridge, you can squash the mobs here with your basic attack, without needing to heal in between fights. Then you hit the next zone, and you've got to drink (bigger) potions, spam (beefier) buffs and pull the baddies one at a time to stay alive, but you can do it. Repeat until you run out of continents, then release an expansion pack.

I can play this type of game, but I'm not a fan of that style of progression. I prefer open ended worlds, where new areas can open up without rendering the old ones useless or pathetic.

Think Ninja Turtles. They're always going to new places and meeting new bad guys, but they're also always dealing with THE FOOT. Those poor ninja lackeys never become obsolete. The Turtles always have time for them. I like bad guys that don't give up just because I became stronger. If the game is dynamic and interactive enough, that shouldn't stop them from having a go at me. Just bring a few extra troops, or a bigger sword. Over a long enough time, it should also significantly enrich the game world and scripted story events, having a lot of bad guys to choose from to create each interactive plot.

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Original post by metalmidget
You could always just use linear cost but make the gradient gentler at the start of the game and then have it become a bit steeper at a certain point.
You could even increase the gradient, say, every 10 levels or something, which might find you a nice middle ground between linear and exponential cost.

That's my plan. Just a simple transition equation. Something like 75% cost at beginner level and about 300% cost at master level. I think Fallout used something similar to this with their skill costs, but they employed exponential character leveling on top of it. My game uses skill progression, but there are no character levels.

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Original post by Kest
Exponential cost: Most games seem to go with this. The biggest problem I have with it is that the beginning of most games is already pretty exciting. Everything is new to the player, so it doesn't make a lot of sense to pile on a lot of progression there. Once the game moves along, the leveling aspect becomes so slow that it might as well be shut off.


I think you're dismissing this option a little unfairly.

In reality, although the XP cost of leveling is exponential, the actual rate of leveling is often linear, or close to linear. This is because as the player increases in power, he gains the ability to take on more powerful enemies which offer correspondingly greater XP rewards. This also models the decreasing returns of battling trivial enemies; By the time I reach level 83, my character isn't going to learn many new things from farming level 1 goblins. I need to be taking on dragons and demons and big scary stuff like that.

With a linear cost to level, unless the XP reward for killing dragons is the same as killing goblins - which has it's own issues - you're going to level faster and faster as you go.

EDIT: Duh, I somehow managed to miss the fact that the first reply said the exact same thing.

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Original post by Sandman
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Original post by Kest
Exponential cost: Most games seem to go with this. The biggest problem I have with it is that the beginning of most games is already pretty exciting. Everything is new to the player, so it doesn't make a lot of sense to pile on a lot of progression there. Once the game moves along, the leveling aspect becomes so slow that it might as well be shut off.


I think you're dismissing this option a little unfairly.

Possibly. But I think that negative aspect is a big deal. I wouldn't want to change my character very quickly near the beginning of the game, then have that change become stunted as I get into the thick of it. I think it would be much better to spread the change out equally.

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In reality, although the XP cost of leveling is exponential, the actual rate of leveling is often linear, or close to linear.

That's similar to what I'm planning to implement. The player will earn experience at the same rate, regardless of skill levels, while the cost to improve skills will increase as the skill becomes better. The cost won't increase by a tremendous amount, but I'm not sure what scaler to use yet. Probably something between 200% and 500% at master level.

Quote:
This is because as the player increases in power, he gains the ability to take on more powerful enemies which offer correspondingly greater XP rewards.

If you're still referring to reality, I don't completely agree. This happens excessively in RPGs, but I don't think it's that profound in the real world. Regardless of how skilled you become with a sword or gun, anyone else with that respective weapon is still a moderate threat, who will offer decent combat experience. There's not really a ladder to visualize. You can become a better warrior, but that usually doesn't mean you can squish your old enemies. Likewise, just because you're unskilled doesn't mean you can't give the tough guys a run for their money. It gets easier, but it doesn't change from impossible to possible like a turn of a key.

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This also models the decreasing returns of battling trivial enemies; By the time I reach level 83, my character isn't going to learn many new things from farming level 1 goblins. I need to be taking on dragons and demons and big scary stuff like that.

I'm considering something a little different - the mixer system I posted about a while back. Players learn more by mixing it up. So at level 83, if the player hasn't fought goblins for an eternity, goblins will provide decent experience for them.

That's a scaler on top of rewarding them based on the enemy threat level, though. Fighting demons will still provide better general experience, but only because demons are a tougher fight than goblins, gameplay wise, rather than character wise.

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With a linear cost to level, unless the XP reward for killing dragons is the same as killing goblins - which has it's own issues - you're going to level faster and faster as you go.

Probably. But in an open ended world, "as you go" simply means "how crazy you are". You can face many things that are below and above your expected level. Fighting above it will train you up faster, but it will also be more challenging. Some players may enjoy safely combating lackeys, while others go straight for dangerous glory.

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Original post by Kest
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With a linear cost to level, unless the XP reward for killing dragons is the same as killing goblins - which has it's own issues - you're going to level faster and faster as you go.

Probably. But in an open ended world, "as you go" simply means "how crazy you are". You can face many things that are below and above your expected level. Fighting above it will train you up faster, but it will also be more challenging. Some players may enjoy safely combating lackeys, while others go straight for dangerous glory.


The best way I can think of to combat the levelling up faster and faster as you go while retaining differing amounts of experience gained is simply to keep the amount of experience required to each level the same, yet scale the amount of experience a monster gives dependant on level. It would work in this formula (example where 1000exp is what's required to level up):

Experience Gained = 10(Monster_Level/Player_Level)

In that way, fighting 100 monsters of the same level as the player has the same effect as fighting 50 of twice the level, 25 of four times the level, etcetera. However, on a traditional scale of levels, this may be a little severe to make any real difference to the levelling process, and still slows down levelling at higher levels, if less. To combat this, we can use:

Experience Gained = 10((Monster_Level/Player_Level)^3)

If we assume a scale of levels from 1 to 100, that means that a level 1 (noob) that defeats a level 2 gains 80 experience, while a level 70 that defeats a level 81 gains 15 experience. To suit the system for a particular game, we simply change the formula to:

Experience Gained = x((Monster_Level/Player_Level)^y)

I hope this helps in some way.

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That reminds me of one of the Tactics Ogre games. Every level requires 100 XP to get, but the XP you get from an action depends on your level and your target's level. If you hit a guy who's your level, you get 20XP. For every level above you, you get a 5xp bonus, up to 100. For every level below you, you get a 5xp penalty, down to 1. So if you're hammering on little guys, you need to perform 100 successful actions to level, or you can go toe-to-toe with a scary dude and learn a lot while getting your ass handed to you.

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Original post by Kest
I'm curious to know what everyone thinks about typical RPG level progression. Specifically, opinions about exponential versus linear cost/progression.

I know quite a lot about creation of PnP RPG system. However, what do you mean by a level?

A word level might mean quite a lot of different things. (For example skills could be separated from level.)

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I think Bearhugger cut closest to the matter here. But don't tangle yourselves up with finding a mathematical expression for the XP between levels right away. XP and levels are just arbitrary tools used to keep the player motivated. There is no right and wrong. If you manage to keep the player motivated throughout the game you've won. If you don't you've failed. It all comes down to challenges and rewards, and to determine how many challenges a player needs to complete before he is rewarded and what kind of reward he gets.

Try this method as a thought experiment:
1. Imagine your character at the beginning of the game. Determine what the typical challenge is. Determine how many of those he must complete before he improves. Don't determine the nature of this improvement yet.
2. Imagine your character after his first improvement. Determine the typical challenge. How has the the nature of the challenge changed? Is it equally challenging or more? How many of those must be completed before the next improvement? If he had taken on these challenges at the beginning how many would have been needed to improve? The same amount or less? If he keeps going with the earlier challenges, how many are required to improve again? The same amount or more?

Define each of these improvement steps as a level, beginning at lv. 1. Repeat this process for a few more levels and make a table of the resulting number of a) challenges per level - 1, b) challenges per equal level and c) challenges per level + 1. Decide if the number of levels throughout the game should be limited or not. Extend your list to as many levels as you can but concentrate on spreading out the control points. Begin for example with every tenth level, then every fifth level and so on. If any levels are to be special you need to take this into account when setting the challenge numbers around those levels.

Keeping this list as a reference to check against you could begin deciding the nature of the improvements per level and how the challenges are going to match this. Setting an XP base at a first level challenge you can also begin calculating the XP needed to progress to level 2, level 3, etc. Keep checking back with your list to make sure it's consistent. You'll probably have to make some adjustments to fit and your challenge counts will probably end up with some decimals.

When this is done you'll most likely have some quite irregular XP scores for the levels. Decide whether to keep them this way in a discrete list, perhaps rounded off a little to make them more appealing, or to find a continuous or piecewise continuous mathematical function to approximate them.

This may seem like a lot of work but it is essential that you know and understand every bit of the progression system you're making. At some point you will find that it is unbalanced or broken and needs to be adjusted. Then, if you've cut corners during the design you will live to regret it.

Anyway, at the heart, it is the amount of challenge between each reward that the player will perceive and either like or dislike. The rest is just arbitrary numbers.

Oh and Kest, don't fall into the trap of trying to make character development 'realistic'. Try to think of ways to give the player what he would expect from a game or what he finds intuitive and rewarding, not what would be realistically accurate. Otherwise you'll end up with a simulation, not a game.

Take care.
Staffan

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Original post by Delphinus
The best way I can think of to combat the levelling up faster and faster as you go while retaining differing amounts of experience gained is simply to keep the amount of experience required to each level the same, yet scale the amount of experience a monster gives dependant on level.

Personally, I think simply increasing the cost of improving a skill based on its current level will be adequate. I may be wrong. I need to do some testing before I can be sure. In my specific game, players will earn experience faster as they fight more complex enemies. But unlike traditional RPGs, fighting more complex enemies will be more difficult, regardless of your character's abilities. In other words, enemies become harder to fight, rather than just owning higher arbitrary numbers.

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Original post by staaf
Oh and Kest, don't fall into the trap of trying to make character development 'realistic'. Try to think of ways to give the player what he would expect from a game or what he finds intuitive and rewarding, not what would be realistically accurate. Otherwise you'll end up with a simulation, not a game.

I use realism as a guide, not a rule. It makes a great guide. When I dislike existing or mainstream ideas, I use realism to break away from them. But I'm all for traveling away from it when it improves the game. For example, my characters earn generic experience that can be used to train any skill. That's not very realistic, but it allows players to spend their gaming time doing whatever they like best, instead of repeating specific mundane tasks to improve associated skills.

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Original post by Raghar
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Original post by Kest
I'm curious to know what everyone thinks about typical RPG level progression. Specifically, opinions about exponential versus linear cost/progression.

I know quite a lot about creation of PnP RPG system. However, what do you mean by a level?

I mean any type of character advancement. It's an open-ended discussion; not specific to any exact progression type. As far as I know, the rate and style of cost and improvement will relatively have the same effect on any of them.

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Well a character advancement in RPG is influenced by the story. From a meek nice guy, a hardcore criminal in five days. It's not just about these numbers.

As for these thinking about damages. Fallout was somehow unbalanced in this respect, it however felt more real than Hellgate: London. It's up to the game developer if he would like to imply real world damage, and obtain real world tactic, or make puzzle game.

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Original post by Kest
I'm curious to know what everyone thinks about typical RPG level progression. Specifically, opinions about exponential versus linear cost/progression.


Exponential progression only works if you control the exact number of encounters (which no one really wants). If there are random encounters, or any other form of grinding, then it won't work. What happens is that the xp for killing mobs rapidly diverges from the imagined level progression.

There have been attempts to make "exponential" xp work by adjusting the xp awarded based on character level. This is no longer exponential xp levelling, borders on self-deception, and makes it difficult to understand and debug levelling problems.

If we are looking for a good way or a better way or some form of improved way, then I have a comment here as well: For each level of character class, how many kills of which types of monsters do you envision being necessary for a level-up? Map this out for the entire level progression. Don't cheat and use math, actually think about how many of what kind of monster is necessary to level up.

Related (but controversial) page: What if xp doubled each level?

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