Experience attenuation: a short primer on how it works and how it could work better

A detailed explanation of the attenuation system and my proposed changes can be found in the two papers linked on my web site at https://sotacalc.com/pages/sota_experience_attenuation.php. The video on the site is only for those interested in how I programmed my model, so they may reproduce it and experiment with it on their own.

Let's say a newish player has been playing the wonderful game Shroud of the Avatar for a little while now. They've got some exp under their belt, upgraded their gear from newbie gear to something decent, and started to understand the deck building system enough to have a decent deck running. We'll further assume that at this point in their career that they've got enough skills to kill enough mobs totaling one million experience every hour. If they're killing continuously the exp they gain verses time will look like this:



As you can see, we are just at the attenuation limit, so attenuation has not kicked in yet. This type of exp gain is psychologically very pleasing to gamers. We always gain at the same rate, no matter what time it is, so we never feel like we are wasting our time. This linear shape of exp gain is the ideal we should aspire to in the attenuation system.

Now assume our player has been working hard leveling, upgrading skills, gear, and their deck, to the point where they can kill twice as fast as before. Their exp gain verses time will now look like:



Here we see that instead of doubling their exp from before, they've only increased it by roughly a fifth. At first glace attenuation seems to be working, providing a soft cap of diminishing returns for experience. However, even at the relatively low value of base experience = 2 million per hour we see that the curve is starting to flatten out for the second part of the hour.

Now lets assume our unsung hero gets so powerful that they're killing enough mobs every hour to total four million unattenuated experience. Their exp gain verses time will now look like:



Now we're just barely over 1.3 million per hour at this insane amount of grinding! Going from 2 million exp worth of mobs to 4 million exp worth of mobs in an hour is a ton more killing, and we've gained around 100k extra exp for our efforts. Furthermore, if we just stopped at 15 minutes and forgo the rest of the hour, we'll only lose 1/13th of the experience we would gain if we leveled the entire time.

Here's some numbers for comparison:
Base gain = 1 million; Actual gain = 1 million
Base gain = 2 million; Actual gain = 1.256 million
Base gain = 3 million; Actual gain = 1.318 million
Base gain = 4 million; Actual gain = 1.351 million
Base gain = 5 million; Actual gain = 1.374 million
Base gain = 6 million; Actual gain = 1.391 million
Base gain = 7 million; Actual gain = 1.404 million

While its technically correct to say you can always earn more exp by burning faster, this is for all intents and purposes a hard cap on exp. Furthermore, just looking at the numbers in the table looses the information about 'when' the bulk of your exp is gained, which is captured in the plots.

Conclusion: Once you surpass the hard cap, getting higher level and killing faster only means more time spent every hour with very little progress and not more exp gained overall.

Now, what happens if our hero keeps leveling through attenuation? Let's assume they're very high level and can dispatch enough villains to total five million unattenuated experience every hour. After two hours their actual experience gained looks like:



Oh how far we have strayed from the highly pleasing linear shape in the first figure. We see that the second hour is basically a repeat of the first, and at the culmination of it we have gained roughly twice the exp we gained in the first hour, yielding a total of 2.678 million exp over the two hours. However, if you look very closely at the second hour you will see that the hump is not quite so pronounced, and the curve flattens out just a bit.

Now let's look at five hours of continuous grinding:



We can see that as time goes on the humps are getting less and less pronounced, approaching our ideal of a straight line. Finally, after fifteen hours of continuous grinding we have:



Conclusion: The current implementation of attenuation will eventually result in a nice linear gain of experience, but its hardly a smooth transition. It takes ten to fifteen hours of constant grinding to get there.

Now lets consider what happens if one takes breaks during the long, flat portion of the experience attenuation. For simplicity we'll compare our hero grinding continuously verses our hero grinding for the first thirty minutes of every hour, and taking the second thirty minutes off. Over a period of one hour the actual exp gained looks like:



Here we see that the the two earn the same exp until its break time, at which time the person on break stops gaining exp, while the person grinding continues to get another 100k or so for their efforts. However, this picture is misleading because it neglects to show us what happens once the person on break starts grinding again. Let's look at what happens over a two hour interval:



Even though the continuously leveling person was ahead at the end of hour one, when the other person comes back from break they very quickly catch back up. At the end of hour two, the continuously leveling person has a little bit bigger lead than they did at the end of hour one.

After five hours of this we get the following picture:



We can see this cycle just keeps repeating, where the continuously leveling person gains more exp while the other person is on break, and then when the person on break comes back they quickly catch up. The fact that at the end of each hour the continuously leveling person is further ahead demonstrates that they will eventually break away, but it takes so long for this to happen that it's practically meaningless.

Here are some numbers on exp gain. Note that the comparison is most fair at the half way point of each hour, since this is when the second person goes on break:

after 30 minutes: continuous = 1.2801 mil, break = 1.2801 mil
after 1 hour 30 minutes: continuous = 2.4908 mil, break = 2.4908 mil
after 2 hours 30 minutes: continuous = 3.6611 mil, break = 3.6611 mil
after 4 hours 30 minutes: continuous = 5.9925 mil, break = 5.9923 mil
after 6 hours 30 minutes: continuous = 8.1173 mil, break = 8.1110 mil

As you can see from the data, I chose a rather long break for this level of burn rate. As a matter of fact, at this rate one could get away with only leveling for 15 minutes every hour, which many avatars I know personally (including myself) have experienced first hand:



Conclusion: Once someone is able to burn exp fast enough, taking strategically timed breaks results in the same amount of exp gain as someone who levels continuously.

At this point I would like to point out how horrible this last conclusion is from a business standpoint. We actually have a system in our game which rewards hard work and effort on the part of the player by forcing them to play less and less the better they get.

Okay, so we know that forced breaks are a thing, and that they become more of a problem the faster you are able to dispatch mobs. We also know that the current attenuation system takes entirely too long to become a nice straight line which would represent consistent exp gain. What do we do about it? My answer is quite simple, we reduce the onset of attenuation to make it more gradual. How that's done is written up in my papers, but the results are as follows.

Let's go back to only considering continuous leveling (no breaks) and reduce our base exp by assuming we only kill two million exp worth of mobs per hour. The actual exp gain under the current formulation and the suggested formulation are as follows, where I also plot the unattenuated exp gain for reference:



We can see that for the first fifteen minutes or so all three curves are raising at the same rate. After this, the suggested formulation very quickly and smoothly transitions from the unattenuated constant rate of exp gain to a lesser but also constant rate of exp gain. Gone are the long flat stretches one is already beginning to see under the current implementation.

If we crank up our slaying to four million exp worth of mobs every hour, we get the following result:



And when slaying six million exp worth of mobs every hour we get:



We see that the suggested attenuation is very quickly and smoothly changing from one line to another even up to burning six million exp worth of mobs every hour. It is also significantly reducing the rate of experience gain from the unattenuated rate.

Huzzah! We have removed forced breaks from attenuation without abandoning the attenuation system altogether!!

To see just how well our suggested attenuation is working, lets look at what some attenuated rates of exp gain will be given an unattenuated rate of slaying mobs. The attenuated rates are calculated from times after the curve has settled down to the highly linear part:

unattenuated: 2 mil/hour, suggested attenuation: 1.200 mil/hour
unattenuated: 3 mil/hour, suggested attenuation: 1.500 mil/hour
unattenuated: 4 mil/hour, suggested attenuation: 1.714 mil/hour
unattenuated: 5 mil/hour, suggested attenuation: 1.875 mil/hour
unattenuated: 6 mil/hour, suggested attenuation: 2.000 mil/hour

This looks a lot more like a soft cap to me.

BEGIN EDIT

The above numbers still only give part of the picture. They give us totals for hourly experience, but don't show at what times we'll earn the experience. If you look at the above plots for the suggested implementation, it is clear that one will have to burn the entire hour if you want full exp. No longer can you burn for just a short portion of the hour and still gain 95% of your hourly exp.

Conclusion: While the suggested attenuation slightly raises hourly exp gain by trading the hard cap for a soft cap, one will have to level the entire hour to reach this amount of exp.

As a final nail in the coffin for the forced breaks, let's look at what happens if you do take some breaks under the suggested implementation:



This is the same burn rate for total exp from mobs that we were considering before when talking about breaks. Here we see that for a 30 min break one will immediately fall behind the person who doesn't stop. A short 15 minute break every hour does pretty well, but still noticeably falls behind on this time scale. Compare this to the plot above for the current implementation where the person who takes a 45 minute break every hour easily catches the person leveling continuously.

END EDIT

The final point I'll make is a subtle one. If you look at two plots up you can see that even the suggested implementation is starting to flatten out a bit in the neighborhood of one hour. This is because what is considered 'gradual' attenuation is highly dependent on one's burn rate. In the last figure the burn rate is getting high enough so that even the suggested attenuation is not completely gradual, it is starting to look like a hard cap. Under the suggested implementation it takes a burn rate of around ten million exp worth of mobs every hour to see this really pop out:



Even at this extreme amount of exp gain, look how much better this is than the current implementation at a paltry base rate of two million exp worth of mobs an hour!

As the game grows and new episodes are released, its natural that the base exp gained per hour from slain mobs will increase. Thus, what is a good gradual attenuation now may look like a hard cap later on. The solution to this is easy, just reduce the attenuation even more once this becomes an issue:



Everyone gets a boost of exp across the board with the lessened attenuation, and the high end players are no longer running into walls where they are forced to take breaks.

Congratulations! You have reached the end of my 'short' primer on attenuation. You deserve a hearty pat on the back.

 

I'm curious what Chris's thoughts are on this. Seems like there's community interest in modifying attenuation. A variety of players have contributed their 2cp, but your proposal well reasoned and substantiated with data, some of which is over most of our heads, but the graphs here are easier to grasp.

 

The whole reason it was put in place was to stop the gap between newer players and veterans. It has done just that. As a veteran player I think it's doing exactly what it was designed for.

 

Because new players are hitting +100 in weeks, while veterans who can gain 24mil if uncapped can't level into thee 200s etc quickly because of attenuation. Which is why people are complaining. Numbers mean nothing.

 

@Chrystoph Reis and @Antrax Artek

This thread is not about 'why' attenuation is in the game, nor is it about whether attenuation successfully addresses the reasons for 'why' it is in the game. This thread is about 'how' attenuation works, and 'how' it could work better. Please kindly redirect all comments about 'why' attenuation should or should not be in the game to other threads.

 

I was intrigued to know the motivation of @Chrystoph Reis (which I do not agree with).
Let's keep it clean so.

 

I will leave this thread with this Mimner.

I think it is a valid point to make, because your changes would defeat the purpose of it. You can't make something BETTER that is accomplishing what it set out to do. I know it's a sore point with a lot of players, but I see it working to perfection.

Letting new players get to competitive levels quickly, while making those with unlimited time not out level the newer players coming in. I thought of all the groups this would appeal to the most would be the PVP community. Newer players get to compete without feeling like they can NEVER catch up, with the veterans being held in check.

I would also feel that even the PVE crowd can see the benefit of this as there is ALREADY a lack of end-game content. The attenuation only punishes those well into the 100 levels and SERIOUS grinders.

I ask, and then what? Quit the game?

 

I apologize for jumping on you like that. Its just that I worked really hard on this post and I'm sensitive about it getting off topic. You've offered an insightful perspective on many attenuation posts, and I want you to know that I appreciate it.

Washing clothes and dishes by hand accomplishes what it set out to do. Washing machines and dish washers make the process better while still accomplishing the task at hand. I'm not suggesting removing attenuation. If you read my post you'll see my suggested implementation still leaves experience heavily attenuated. So what's the problem?

I have never suggested changing attenuation from 1m to 6m an hour.

 

Cutting through all of the misunderstood stuff, this is a sound proposal and I'd love to see if we are missing a reason why the current attenuation model has to flatten so drastically each hour as opposed to a smoothed curve. @Chris will know.

However... Whilst mathematically sound there is an assumption at the heart of this proposal, that is that a significant number of players experience, dislike, are impacted by and notice the forced breaks. I don't. I play a lot, enjoy the game but never attenuate as I kill, gather, harvest, explore, make coffee, talk to the cat...

I'm sure those that spend hours and hours in high exp gain locations hit the soft cap within each hour and are frustrated that they can't continue. But I would say try something else in the game or maybe accept that it's going to take you a bit longer to get to 140 and solo swarms of dragons.

I say this as even with the proposed new exp attenuation curve, all it does is maybe improve satisfaction and remove frustration as it does not gain you significantly more experience per hour or per day no matter how many mobs you kill per hour.

I appreciate the suggestion is aimed at removing frustration and improving satisfaction in exp gain despite of attenuation and not a case for removing attenuation, however for me the elephant in the room is attenuation.

But attenuation is NOT UNIQUE TO SOTA. Many MMO games have a variation on it. In some it's harsh - no more exp gain today, you've burned it up. Others not quite so overt but still harsh - your full exp gain today has been used up, you are now on low exp gain. You have to stop playing for the 'blue bar' to refill and enable optimal experience egain to recommence... Until the blue bar depletes again. Which is basically - go away and stop playing or stop killing or grinding craft for a week and your blue bar will be full.

The raging against attenuation is by players who are only interested in maxing exp per hour for hour after hour after hour......

The casual or indeed average player who also does other things in game doesn't experience it at all or only rarely and doesn't have an concern about it.

My point is should anything be changed regarding attenuation which is a pretty decent and fair implementation compared to other exp soft cap models I have played with, for a small, vocal minority of exp gain min maxers?

 

Mimner, I thoroughly appreciate and enjoy your detailed, well structured, and data driven analysis. It is outstanding analytical work and regardless of which side of the attenuation issue a person stands, you should be recognized for its depth and for your efforts.

Well done.

Fenris

 

@Steevodeevo

Thank you for your kind and thoughtful post. Some of my responses will stray away from factual analysis given above and into the realm of my own personal opinions.

I would actually argue that a small but still significant proportion of our player population is really experiencing the forced breaks issue. SotA encompasses a vast variety of play styles. Power gamers are only one of many pillars of our outstanding community.

I do not believe it is good game design to have the game itself limit the options of the players. While I am personally amenable to the argument that it is good for us to take breaks, I do not like that the system forces these choices upon us.

In this thread I do not wish to address whether or not attenuation is a good or bad mechanic, merely how to make it function better at its intended task.

I certainly hope you did not get the impression that I am raging against attenuation!

I couldn't agree more. It is also true that for power games, forced breaks (notice I did not say attenuation) is deeply unsettling to our play style.

Some game design decisions are painstaking in that they require choosing between a mechanic which benefits one play style and frustrates another, or another mechanic which does the opposite. My suggested change does not fall into this category. I have shown how to eliminate the forced breaks, while keeping the core of attenuation in place. In your own post you elude to the fact that the change only results in a modest exp gain per hour by changing the hard into a soft cap, but it does provide the psychological benefit of removing the forced breaks. This is really a have your cake and eat it too solution. So, why not?

And if you're concerned about spending developer hours on this change, I can assure you the work required is quite minimal. All that's needed is to update the attenuation formula, which amounts to changing a few lines of code. Also, they will need to multiply the base exp for all mobs in the game by 1.5 to deal with some issues on the low end of exp gain which I fully detail in my paper. The technology for this is already in the game as evidenced by the double exp they used to turn on and off. If they want to get really crazy they can replace the incredibly misleading, binary attenuation light with a slider which visually depicts how attenuated you currently are. They could also just remove the light completely and leave the changes behind the scene. The fix is so subtle that I bet no one would even notice, except the power gamers of course.

Look, I know you're not a power gamer, so why should you care about our plight? Simple, the diversity of the player base is what makes this community the best I've ever seen in gaming. It is this diversity of players which adds so much spice and life to Novia. Power gamers are only one component of our player base, but it is my opinion that every component is important. I'm tickled to death that they're adding new features for dungeon builders though I'll never build a dungeon myself. I so love running past all the beautifully decorated homes in my town while I run to my little row lot shack with nothing more than a few boxes on the ground. I want to keep rocking out at dance parties where everyone's showing off their newest armor skins, while my stuff all looks completely default. (But you know it has some bad ass stats!) When I play Everquest the player base there is a monolith. Power gamers abound, and man is it boring!

As for us power gamers, we give back by shepherding those of other play styles through dungeons: guiding them, protecting them, and giving them a chance to face the meanest baddies in the land. We can also help people who are casual but wish to try some pvp by teaming up with them. Finally, we can usually help to answer peoples questions about game mechanics.

It is my humble opinion that we should all be concerned with any issue that a pillar of our community experiences, even if that doesn't fall in our particular play style. That way our player base stays diverse, inclusive, and hopefully ever growing.

 

Please note that I have edited the OP to include a section discussing what would happen if you took breaks under my suggested implementation of attenuation.