Confessions of an XP Addict
Confessions of an XP Addict
Part 1: Exposing the Experience System like a Flasher Late at Night on a Street Corner
By Chris "Charista" Wilde
Part 0 Ramblings, Pramblings, Preamblings
Everyone that plays computer games has secrets, sometimes without even knowing we are keeping them. We make our decisions, play our way, and we do well or not. Some of us do better than others. Unless you notice that others are doing poorer than you and want to help them play better, you've got a secret helping you do better. Highly competitive players never give up their secrets, instead keeping them away from others so that they demonstrate their superiority, and feed their own ego.
I've been keeping secrets. Did I do it for my ego? Well, I did give them away to some trusted individuals, so maybe. But in my defense, if I had given them away, I might not have the data to prove they were better than others players' secrets. Or is that just an excuse to feed my ego? Who knows? Who cares?
Hereís the thing. Eventually, some of those secrets stop mattering. Once youíve used them, you may use them up, and then the secret doesnít help you anymore. What do you do then? Why, you tell the secret. To show off? Sure, Iíll admit to that, but also because a few people will be helped by it. Most wonít get past my perceived arrogance, though, but Iím used to that. Arrogant people are never actually smart, are they? Beware the arrogant smart guy, because you make yourself vulnerable to his intelligence by assuming heís stupid. And thatís all Iíll say on that one.
Well, what if they do still matter? I wrote this a month ago in preparation for passing L250, and while editing it for final release, they dropped Dungeon 13 and the Sticker Book on us. Suddenly, my secrets still mattered since they would work twice more, but I'd written the darned thing! Okay, I don't really mind if someone tries to use them against me. Really, it's time to come clean. I could tell just Zombunny, but some of them play in other guilds on other servers, so it would leak out anyway, and I wouldn't get the credit because people would put their name on this.
So what makes me expert enough to talk about this? Find Charista on your HoF. Look at my base Stats. These are a good indicator of how much money I have made. Now crack open some of the others of my level: you'll find them on the top page of the HoF. Iíve got the worst base stats of anyone of similar level. I am definitely doing something differently, and yet on Apr 30, 2011, I was #1 on the HoF, and repeated that three times in the next couple days. No, that doesnít mean I am as powerful as Bain or Alien53, but Iím not far behind. Somehow, Iíve done it differently and gotten to the same place. Some of the readers, a few anyway, will say thatís impossible, because long ago, someone ďprovedĒ stats are better than levels. Iím here because I proved them wrong simply by getting to #1 in competition with people that quested for stats that in the same time didn't even get to the top 15.
That is what this is all about. According to the most common theory about S&F gameplay when I began in June 2010 (I didn't start using shrooms until into July, so my effective start date is much later), what I just achieved was impossible. Stats were ďprovenĒ to be more effective, so someone that focused on experience only should never be able to compete. I found that highly suspect, and played differently. I did the opposite to common wisdom, and surpassed them all, and despite being 130 levels (and nearly 3 months) behind at start, reached a point where only 5 players had more levels, and the highest of those only 3 levels (or 18 days) more, and I was still able to compete for the #1 spot. the very fact that the most powerful players are the ones of highest level, not of highest stats, should have made that old debate moot. I honestly don't know if anyone still adheres to that tired philosophy.
I have been preparing to write this for a very long time. The Endless was built on some of these ideas (July-Nov 2010); however, Darstard and I (both Officers at the time) having realized that my attitudes on experience maximization were accurate decided that we would not write this document to prove my theories to the Endless. It was the advantage of the Endless, and we used it to gain on all comers, taking that guild from Rank 350 to Rank 4, with minimal personnel changes, and only four serious shroomers. Instead we just strongly recommended the theory and left it unproven. Writing this for the benefit of the Endless would allow it to leak to everyone, and spoil our advantage before we had used it to maximum effect. There was a limit to how far it could take the guild, though. Getting past Rank 4 required more than a few people leveling hard: it also took gaining more players of a competitive nature, and that was not to be. The Endless remains a powerful guild, but I cannot tell you how many are still using the maximized experience philosophy that otherwise would not (massive personnel changes, so I don't know if the idea survived my departure). "Fight Club" (our term for Maximum Experience when speaking outside the guild) remained in the care of the Endless all this time. Zombunny didnít need me telling them how to play, since many already played for maximum experience, or a high %age of maximum, anyway.
Due to its size, I must break this into several posts. The subject matter is distinct in each, so I feel that breaking it up for debate and discussion will keep any arguments simpler and more on each particular topic.
After this preamble, I will describe the Experience and reward system of S&F. This will be mostly factual, and might better prepare you for the game youíre playing. Low level players especially will be unaware of some of the effects I will present, and will appreciate the forewarning, even if they donít like my analysis of how to manipulate the system in Part 2.
The second part will analyze the experience system and present techniques on how to optimize your gameplay. It may also be useful to you to see how to systematically analyze a system and this allows you to apply the techniques used to other games, possibly helping you in other RPGís. Knowing how is as useful as knowing what.
In the third part, I develop the counter-argument to the ancient fallacious argument that has hamstrung many players. Really, this is mostly unnecessary, since so few that know of it continue to play. Quite simply, I will endeavor to demonstrate that the best way to play this game is to select quests to maximize your experience and level gain. For some of you, you won't even understand why I am bothering with this discussion, since newer players don't know that old debate and seem to gravitate to maximum experience gain, simply to try to catch up. It seems obvious to them that maximum experience is mandatory. It seems that people that began playing after Sept 1, 2010 simply never heard that old pro-stats argument. Since in most games, level is more important than stats, they naturally choose to maximize experience gain. The old philosophy died, because many of the players that promoted it simply quit, or finally recognized that they had fallen behind.
Darstard once told a new recruit to the Endless, "Charista catches everyone." He wasn't lying, since I finally caught and passed Darstard himself in May 2011 (though, on the forthcoming Well model, my Quest Exp had passed his weeks before, and I was waiting only for the next Threshold to catch up on dungeons, see Part 2 for the terminology, and why I did it that way). He held me off for a very long time having adopted my own methods. So, how do I know for certain that I catch everyone, and people aren't just quitting shrooming?
I keep track of the competition. It's easy. It's called a spreadsheet. Log on each night, copy the Levels and Dungeon count of your competition, and you know if you're catching up, and why their Level jumps once in a while. It takes a couple minutes, and less if youíre tracking only one other person. (I tracked 12 at one point, but I'm down to 6 beside myself.) I have included the portion of that spreadsheet that covers only myself in the attached, "Charista Levels.txt".
So, here we go. On to Part 1. I hope you'll learn something.
Part 1 The Experience System Exposed
The Shakes and Fidget experience system is actually fairly complex, compared to similar systems. It has several distinct effects, and the more effects a system has, the more techniques you can use to abuse it. You need to know the details of each effect in order to determine what methods might work, so the first step is always to identify the elements of a system. S&F has some level-dependent effects, which is a problem for those that pass them first, since they can't see them coming and so can't abuse them. Since you donít know itís going to change unless someone that has been there tells you (or you carefully watch others like I did), you canít prepare to use the change. So, hereís the not-so-secret experience system, so that you can try and figure out your own methods, or understand the development of mine in Part 2.
1.1 Experience Basics and Definitions
Each day, you have 100 thirst for free, and if you shroom, you can increase that to 300. Thirst is, however, a useless term for this discussion. What is important here is that thirst equals minutes, and quests divide those minutes into what I call segments. A segment is the smallest amount of time you can spend on a single quest. For anyone over Level 15 with a 50 mount, a Segment is 2.5 minutes. With a 30 mount, a segment is 3.5 minutes. And so on. Without a mount, segments are 5 minutes. Quests use one to four segments. Quests have a minimum and maximum potential experience reward, with the maximum being approximately 4x the minimum. Quests also have a gold reward, for which the maximum is generally 4x the minimum. Segments are more useful for this discussion because it makes the discussion work for every reader, where using thirst depends on the particular mount being used.
I use "shrooms" and not "mushies" because the game is addictive.
XP is Experience, of course.
XP/level means the total amount of experience you need to reach the next level, not the amount of experince you need at the moment to get the next level. If you have 100000 of 150000 in a level, xp/level = 150000, not 50000. When you hover over your experience bar, it's the number on the bottom beside "Next Level", not the number on top.
xp/seg is experience per segment. It is synonymous to xp/monster.
ave_xp/seg is the average XP you're getting from a quest using your selection method, not the average of all possible quests.
days/level is the number of days it takes to gain a level. The inverse of this is levels/day, which is effectively synonymous with ave_xp/seg, since
ave_xp/seg x 120 seg/day = ave_xp/day (ave_xp/day)/(xp/level) = ave_.level/day and ave_level/day = level/day by definition
HLP is High Level Player.
8) would be me smiling, but I don't do laugh tracks.
1.1.1 Converstion of Terms
If I use terms that discuss levels per day (level/day) or the like, assume that I am talking about someone using a 50 mount and 300 thirst. If you use a 30 mount and no shrooms for quests, then multiply time by 4. (Ie. "At L225, you gain 25% of a level per day." Someone on a 30 mount would convery that to 25% per four days.)
All of my times exclude the Sticker Album, which came out after this was written. This allows you to modify the times based on your own modifier.
1.2 Non-linearities in the Experience System
Few games have a truly linear experience system. A linear system would maintain a constant level/day (even if the xp/monster and xp/level changed), so if you spent 1 day to get a level at Level 5, you'd get 1 level per day at level 500. (I have been told that one dead MMORPG had a linear system, but can't confirm it since I never played it. It was Japanese in origin.) Most Linear systems do not include "Levels", instead increasing power through skills, powers, and stats only. In most RPG's, xp/level increases faster than xp/seg, so it takes longer to level up as your level increases, and that is what makes the system non-linear. There are ways a game can compensate for this and maintain a constant amount of real time between level-ups, but few do that. In real time terms, almost every system slows your advance as you level up. Why? For the life of me, Iíve never heard a really good explanation for why. The designers of S&F might say that it lets people catch up, but that doesnít explain why even pen and paper RPGís like D&D, GURPS, and countless others that pioneered the industry used the same method. I wonít defend this type of game design. It is the style the S&F developers have chosen, and thatís all there is to it. People tend to follow the crow when they lack a suitable explanation, but the previous system worked, and designers are no different.
So, that said, how exactly does S&F control your rate of level gain? Well, there are several effects in the S&F system to achieve this.
1.2.1 Diminishing Experience as a %age of Level
This is the most obvious effect in the experience system, and everyone experiences it in their first few days of playing. As your level rises, your experience gain per day as a percentage of level decreases steadily. That was a mouthful. It might be easier to describe like this:
the higher your level, the more quest segments it takes to level up.
This is due to average xp/seg increasing slower than the xp/level. Basically, when you are lower level, you might gain 3 levels per day. When you are Level 100, you may gain only 2 levels every three days. When you're L250, you'll gain only one level per week. (Yes, it was that bad before the Sticker Album, and it will get worse at L275, but I am getting ahead of myself.) This effect is common to 95% of all RPG's.
The good news is that this effect slows as you increase level, as it does in most systems (systems that don't slow the rate get to some absurd XP numbers). At L225, at maximum Exp gain, you make about 25% of a level per day. At L249, you make about 23.5%. You'll remember that in the early days of playing, you gained three or four levels per day, then 2, then 1.5, and 1, and... point is, it's a lot less now, but the rate of change is reducing to nothing for the HLP's.
1.2.2 The Threshold Levels
A lot of players donít notice this effect, but it really is significant. At L100. L125. L150. L175. L200. L225. L250. the experience rewards for quests and Guild Wars dramatically diminishes. At L249, you gain nearly 25% of a level per day. At L250, only 17%. I call these the Threshold levels. There isn't much more to say about this, except that the effect at L125 is smaller than the others, and that there is no sign it won't happen again at L275, L300 and every 25 levels thereafter...The most important part of this effect is to know that it causes a drop in xp/seg, not an increase in experience per level. (Ie. At L224, I had a maximum quest reward of 300000 exp/segment, but at L225, that diminished to 238000.) It is actually important that they did it this way, instead of bumping up xp/level, which could have achieved the same effect.
Are Threshold levels typical of the industry? No, but it can happen at particular points in time. When a game expands and increases the level cap, it rarely will use the same experience curve for the new levels, because the number of levels added is usually smaller than the number the game released with, and they want to keep those going for you until the next expansion. What is unique about S&F is that it came out with this effect already in place. The designers could have simply changed the curve on the diminishing effect in section 1.2.1 and flattened the effect out to be hidden, but they didn't. It's a Really Big Experience Reward Drop. You can see the effect in my "Charista Levels.txt" file. That can also give you an indication of how severe each drop is, but remember that I played those levels without Sticker Albums and the earliest part predates Guild Dungeons, so you need to convert the scale of the drop to your current advancement rate. These effects may halve the amount of time these levels take you.
1.2.3 Player Dungeon Experience
The rewards from Player Dungeons are constant values, and are unaffected by Guild bonuses or your level.
If you convert the reward to be a percentage of your current level, the reward decreases as you increase level, becuase the reward stays constant in numerical value, but xp/level increases. (In division, increasing the divisor decreases the result -- 5/6 is less than 5/8.) So, remember that if a Dungeon gives you 5 million exp at level 175, it will still give 5 million exp at level 200, but Level 200 takes a lot more xp/level and so it will fill less of your XP bar.
1.2.4 Guild Instructor Bonus
The Guild Instructor bonus provides a multiplier to the quest reward of each quest. Thanks to Guild Dungeons, that bonus can now range from 0% to 200%; however, it is unlikely anyone will see the maximum bonus. Thanks to the ever decreasing level/day gain, it may take years to finally kill the last dungeon at L540. (Edit: Sticker Albums provide a hope that it won't take as many years now, but it will take another major exp boost to bring the target for L550 down to a reasonable timeframe.)
Some kind HLP's will help lower level guilds by temporarily helping with dungeons, but sorry, don't bother asking me. Right now, no one is doing it regularly anymore.
1.2.5 Guild War Experience
Guild War Experience is affected by the Threshold Levels in equal measure to Quests. I won't talk about this much, because it is affected by which guild you select more than anything else. You can effectively treat Guild War experience as quest experience, except that it is not affected by Instructor Bonus.
While it is claimed that the Losing guild's honor and the difference in honor between winner and loser affect the XP reward for Attacker Victory, I have not seen these effects to be significant enough to use in any way. If the effects were significant, I could tear them apart and totally abuse them, so they better not "fix" the "bug," or I'm going to do things that will inspire them to return to the current system, if I can recruit enough other competitors.
1.2.6 The 300 Thirst Reward
With a 50 mount and 300 thirst, the very last quest of the day can be exceptional. Instead of dividing the reward by the actual number of segments remaining, that final quest can give a 4 segment reward for a 1 segment quest.
Months ago, with a 30 mount, this effect could happen on the last quest of the bar, every time, so using 10 shrooms on additional thirst and only spending one at a time to use up the entire bar 11 times in one day could give you many exceptional quests per day. This effect may have been corrected, but I cannot confirm that it has, since it required a 30 mount and I haven't used one since June 2010. With that many shrooms, you are still better off getting a 50 mount than using them for thirst in this way, unless you don't play every day.
For players with inconsistent play time, buying a 50 mount and not using it every day is less effective thn using the shrooms as supplemental Thirst when they do have play time. Basically, if you play 11 days out of 15, buy the 50 mount. If you play 10 or less, use them as thirst. Shrroms for thirst with a 30 mount are about 75% as effective as a 50 mount, but wasting a 50 mount by not playing reduces that effectiveness and eventually the definite gain of Thirst when you can use it becomes more efficient.
1.2.7 Mount Buying Day
On the day you buy a mount, you can find the first quest that day to have a very short segment length. If all you do is extend your mount, youíll never notice this effect. It doesnít happen every time, and I canít always cause it to replicate, so I canít tell you how to force it. Both times it happened to me, I got a 1:30 minute segment length. Using this to maximum effect requires not letting yourself get a 1 minute quest to end the day: the system would not execute one that short for me.
1.2.8 Guild Dungeons
I havenít gone to the trouble of determining how Guild Dungeon experience is calculated, or if it is affected by Threshold levels. Itís such a small part of your overall experience, itís not worth the trouble trying to figure it out.
1.2.9 Sticker Album
The brand new Sticker Album adds to your Instructor bonus. (Trust me, it does, and I proved it already in another thread.) This can increase your total bonus to 300%, for up to a 4x multiplier on quest experience reward compared to someone that is guildless with no Sticker Album . I will include pointers on how to optimize your Sticker acquisition rate in Part 2.
Note that quest reward from this modifier is set at the time the quest is created, so adding stickers between quests will not increase the reward for the current quest, but will for any quests generated after completing the current quests.
1.3 What's important out of all of these?
Most of the effects are constant and not going to affect the analysis. The important things to keep in mind are that xp/level increases and days/level increases, but eventually days/level stops rising from the diminishing effect in 1.2.1, and Threshold levels take over to cause days/level to drasatically increase at particular levels.
Last edited by Bullbound; 05-27-2011 at 10:45 PM. Reason: Fixed name to reflect merged thread
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Confessions of an XP Addict: Part 2
Confessions of an XP Addict
Part 2: A Dime Bag of System Abuse
by Chris "Charista" Wilde
Part 2 The Addiction of Abusing Things
Okay, I've established that I have played differently, and I think that I've done a pretty good job of figuring out how the experience system works. So, it's time to figure out how to manipulate that system to maximize our level gain and seek absolute power! Binky, we're going to do what we do every night, try to take over the World!
Yes, that's why the signature moreum created for me (when I was in the Endless) included Brain and plans on a chalkboard. My nefarious intent is never well hidden.
Anyway, to analyze a system to find its holes, you must be able to view it from multiple perspectives, and just as importantly, identify when you're switching perspectives. That's the hardest part. Lots of people jump back and forth between perspectives when making an argument, without even realizing they had different perspectives in mind in the first place. We call these perspectives "models". Not understanding the model you are using, and not knowing when you've changed models will muddy the argument, and though you can still get to the right place because of the simplicity of a detected effect, that doesn't make your argument inherently accurate. Inspiration can tell us a correct answer that we then have to try to explain, so with Inspiration but without accurate modelling, we can have the right answer and the wrong explanation.
Segment = Amount of time used for the shortest possible quest on current Mount
SP = Experience
xp/level = total experience required to level up
level/day = how much of a level you gain in one day's questing
days/level = the number of days of questing that it takes to level up
xp/seg = XP reward from one segment, often synonymous with xp/monster
ave_xp/seg = the average XP you get from questing, based on the chosen method of selecting quests. Excludes quests you don't choose. Synonymous with level/day.
Charista = my addiction
All times are for a 50 mount and 300 thirst, so you may need to convert for your own style.
2.1 Models of the Experience System
Knowing the numbers isn't enough. The experience system needs perspective in order to compare various solutions. There are three useful ways of looking at the experience system. (Really, there are!) When analyzing a system, it is important to identify which model youíre using and when, and to not switch between them accidentally.
2.1.1 The Level Model
In the Level Model, we normalize (oops, mathematical termÖ it means to modify everything to be proportional to a standard value) all of our numbers to a percentage of the level at which they are applied. People are now swiping their hands over their foreheads.
Okay, that just means we talk in terms of %age of a level, not the original experience numbers. In this model, 1/10th of a level is the same at Level 250 as L10, despite the real experience numbers they represent being astronomically different, and the amount of time required to gain that much being drastically different. So, we are always comparing Levels, levels/day, segments/level, and so on. We never refer to a real experience value in this model: we normalize that value to %age or fraction of a level.
So, if I make 30 million experience and my xp/level is 150million, under the level model, I made 30/150 = 0.2 levels. If my xp/level is 60 million, I made 0.5 levels. Normalization, in this case, eliminates the term experience by converting it to levels.
This model is most useful for examining whether we are gaining power on someone else. With this model, if I gained ľ of a level today and you gained Ĺ of a level, you caught up to me by ľ of a level. You may be level 100 and me level 250, with an enormous power gap, but you really did catch up a little in terms of power. Every four days, you catch up one level, and that will last until one of us hits the next Threshold. (In actual fact, Iím making 1/6th of a level per day at L250, so a L100 is catching up by at least a level per day if they are 50 mount and 300 thirst since they're making 1.5 levels per day. I'm crawling and they're racing along like a thoroughbred.)
2.1.2 The Well Model
This model views the experience total as a well with various watermarks indicating where levels are gained. This system is more commonly associated with pen and paper RPGís, but is equally valid in S&F. S&F only shows you the amount of experience you have in the current level, and doesnít show you all of the experience accumulated over all your time playing, whereas in many RPGís, you have a running total of all experience and a target for the next level. The Well is the model most people would use to prove that you canít actually catch up to someone that uses the same leveling method as yourself. The problem with using this model is that most people donít realize all of the effects of switching to it, and they rarely know all of the details of how the Exp system works, which you now do from section 1.2. Weíll get to all of that in time.
The Well model can be represented as a sum of all experience you have ever received. Since XP comes from limited sources, it is, then:
Total_XP = Quest_XP + Guild_War_XP + Guild_Dungeon_XP + Dungeon_XP
This model is most useful when analyzing the effects of differences in actual experience values. It generally ignores the watermarks of where a level is, but there are real effects of level on the model. Since xp/seg increases with level, and experience is what accumulates in the well, level does affect the Well. This model does not accurately indicate overall power, since we ignore levels, and it does not indicate how close someone is behind us in either power or time. 100 million experience is a hundred levels to a level 10 player, but 2/3 of L259. That doesn't make this model useless, since finding ways to manipulate the gap based on the hard numbers is a real advantage. Conversion of numbers to levels or time can hide ways they can be manipulated, so this model is necessary. In truht, manipulation of these hard numbers is what all these techniques do. We see the advantage of those manipulations in the other models.
2.1.3 The Day Model
This model is the least commonly used, because few have the patience and dedication to track people like I have. When you are attempting to catch another player, it is good to know what day that player was at your current level. That tells you how many days it took the other player to get where he is today, and if you follow the same Quest selection method, you will get there approximately the same number of days later (affected by Dungeons, Guild Dungeons, and the random number generator). But thatís not all. If you can see that last week, he was 30 days ahead of you, and this week he is only 28 days ahead, you really are catching up, because you should not gain on this model, unless your competitor is using a different quest selection method, misses a day, etc..
The Days model is vital for the competitive player, but only for helping determine if you really are catching up to your competition. You can catch up on the Level model and therefore in power, but be falling behind on the Days model when the level difference is significant. That won't become apparent until later in the game, but the mistake results in a permanent disadvantage. Three levels for those above L250 is 18 days, but the power gap between L247 and L250 is insignificant, since a L247 can beat a L250 45% of the time. 18 days at L100 is more than 18 levels, and that is too much for the lower level player to beat, so long as potions are equivalent.
The Days model is often significantly impacted by Playa's new content, especially something that changes the rate of xp/seg like the Sticker Book. Before it's release, I was 3 levels and 18 days behind Glykon, but with one Dungeon in hand that represented about 5 days. With the Album, those three levels turned into 14 days when I had completed it, catching me up to Glykon by four days in a few days, even if had he filled it as fast as I did, which he did not. In the long term, everyone will take the time to fill the album if they want to stay on the top of the HoF.
2.1.4 Other Models
Others may feel that there is another method of modeling the system, but this is all I have identified as useful and distinct. Other proposed models will usually just be one of these three with different terms that mean the same thing, or have a slight twist that when untwisted turns them into one of these..
2.2 The Regions
You will note from Part 1 that some effects take place in different level ranges. I identify these level ranges as Regions. Conclusions in one Region may not be correct for another Region. We may come to the same conclusions for each region, but if we don't separate the Regions and analyze each in turn, we can't assure ourselves that our conclusions are always accurate.
2.2.1 The Starter Region Ė Level 1-20
You pass through these levels so fast that there is no good reason to try to optimize it. Iíd save you less time than Iíd spend figuring any tricks out. Just burn through it as fast as possible.
2.2.2 The Logarithmic Region Ė Level 20-149
In this region, if you plot your level vs. time, you will get a curve that approximates a logarithm. (It might also be an arctan, arcsec, square root, or some other similar curve. There are more choices, but logarithm is close enough, and more people are familiar with that than the others.) You gain levels quickly at the start, and the rate of level gain decreases, so you get a curver that rises very fast at low levels, but that rise decreases and flattens as level increases. I have included one noticeable Threshold at L100, and the lesser one at L125, and those are not insignificant, but it is difficult to use them, like we can the ones at L150 and beyond.
2.2.3 The Linear Region Ė Level 150-?
In this region, the ďdiminishing levels per dayĒ effect almost disappears as the change in xp/level and xp/seg approach equality, but every 25 levels you hit a Threshold. Plotting this region will make your level vs. time look like a series of lines instead of a curve.
2.3 Optimizing Experience Rewards
Now that we have the experience system defined, the models we will use to analyze it, and the regions we need to analyze in, we can move on and begin to abuse the system and beat our enemies. Or our friends. Heh, okay, morality isn't my strong point.
The easiest parts of this are the most obvious. Maximize your Guildís Instructor bonus (ie. buy Instructor instead of Treasure). Fill your Sticker Book. Help your Guild get higher Dungeon bonus. (Stickers give less reward than a boost to Instructor (0.06% vs. 2%), so if that means jumping out of the guild so a ringer can come and help, then do it, and fore-go the sticker.)
2.3.1 Maximizing your Quest Experience
The toughest question to answer is, "How do I raise my xp/seg?"
"Oh, no it isn't," you reply. "Maximizing exp is easy. Just take the quest with the most exp/minute!"
Do you think I'd be writing this, if that was the correct answer? More accurately...
Do you think I'd be 4 levels behind Glykon with 2 dungeons in hand if that was the right answer?
Choose the best quest from the following.
Quest 1: 1 segment, 100000XP Quest 2: 2 Segments, 150000XP Quest 3: 4 segments: 450000XP
Those that do know the answer would ask, "I can't answer that question, because I'm missing information. What is my current daily average xp/seg (ave_xp/seg)?"
We can determine our ave_xp/seg by spending one day questing on our best guess, and subtracting XP at the start of the first quest from XP at the end of the last (subtract Guild War reward if necessary), and then dividing by the number of quest segments used. For 50 mount, that's 40 segments per 100 thirst or 120 segments per day for 300 thirst.
So, we're going to use an ave_xp/seg of 150000 for the rest of this section. Now which quest do you select, since you know your ave_xp/seg?
"I don't know why I need that information, so how can my answer change?" Got ahead of myself.
We are dealing partly with the unknown here. When we select a short quest like quest 1, we are also not choosing a longer quest, like Quest 3. You're trying to compare two quests of different durations. The average xp/seg method tries to eliminate that time difference by reducing long quests to a series of short, equivalent ones. That is not the right way to approach the problem, though it is the easiest. What we are really doing when we select a short 1 segment quest is selecting three unknown segments to make up the difference in time. So if we add that information into the three options, we get:
Quest 1: 1 segment + 3 unknown segments, 100000XP + the unknown reward for 3 segments Quest 2: 2 Segments + 2 unknown segments, 150000XP + the unknown reward for 2 segments Quest 3: 4 segments: 450000XP
So, what is "the unknown reward for 1 segment"? Well, that answer comes from the statistical analysis of our previous quests. The reward we assign for an unknown is a prediction based on previous known quests. In order to predict the future, we look to the average of our recent questing, or ave_xp/seg. We want the average of what we selected, not what we didn't. This will ensure that when we make our decision, we are selecting at or above our achieved average, not the average of what the random number generator gave us. So, let's substitute that into our list above.
Quest 1: 1 segment + 3 unknown segments, 100000XP + 3 x ave_xp/seg Quest 2: 2 Segments + 2 unknown segments, 150000XP + 2 x ave_xp/seg Quest 3: 4 segments: 450000XP
Since ave_xp/seg = 150000, because I said so...
Quest 1: 1 segment + 3 unknown segments, 100000XP + 3 x 150000 = 550000 Quest 2: 2 Segments + 2 unknown segments, 150000XP + 2 x 150000 = 450000 Quest 3: 4 segments: 450000XP
Now, let's replace Quest 2, and try again:
Quest 1: 1 segment, 100000XP Quest 2: 3 segments, 425000XP Quest 3: 4 segments: 450000XP
Quest 1: 1 segment, 100000XP + 3 x 150000 = 550000 Quest 2: 3 segments, 425000XP + 1 x 150000 = 575000XP Quest 3: 4 segments: 450000XP
Things can get a little more complex.
Quest 1: 1 seg, 200000 Quest 2: 3 seg, 610000 Quest 3: 4 seg, 790000
Quest 1: 1 seg, 200000+3x150000 = 650000 Quest 2: 3 seg, 610000+1x150000 = 760000 Quest 3: 4 seg, 790000
And that's it.
BTW, do you know which model we've been using this whole section? The Well. There was no switching between models, so i did not need to identify it. We were dealing in real XP values, no level comparisons, and real time was irrelevant.
18.104.22.168 Calculating average Experience per Segment
You don't need to take your average every day, or even every level. Once every few levels is good enough after L150, since it changes very slowly. Before L150, you level faster so your ave_xp/seg changes rapidly; thus, you want to take it more often, and given that it takes less time to level up, that means taking the average much more frequently than at L250 when you only need to sample it every three weeks.
Part of why I wonít help in the Starter region is that I have found it difficult to keep track of ave_xp/seg in that region. It changes so fast and in so many ways that you canít get a good sample to figure out what it should be. Just use the normal method and get through as fast as possible, because you can't get the information you need to use my method.
2.3.2 Maximizing your Player Dungeon Experience
If Dungeons are constant rewards, there's no way to maximize it, is there? The Well model tells us that when a number can't change, it's irrelevant, right? Well, just because one model says there's no effect doesn't mean the number has no effect. Other models may disagree. Or we may not be connsidering every aspect of that model.
Under the Level model, Dungeon experience decreases as you level up. When we normalize an XP value, we divide it by the appropriate xp/level, which increases as level increases.
Normalized_reward_in the Level_Model = Experience/(total_Experience_required_to_level)
"Wait," says the concerned reader. "Isn't there a third model?"
Golly gee, you're right! The Days Model. I'd love to do that now, but we made a mistake. Let's go back to the Well for a moment. We oversimplified the Well model the first time. We're assuming that current Level doesn't affect the Well model, because the Well is:
Total Exp = Quest XP + Dungeon XP
You probably keep track of the highest xp reward you got for a 4 segment quest, and know that it increases without me telling you, and you realize unconsciously that minimum xp/seg also rises at the same rate, because you're not getting 50 xp quests like you did back at level 3. Since those both increase, ave_xp/seg must as well, so we want to be as high a level as possible to fill the Well faster. Lower level player falls behind when making lower ave_xp/seg, even while gaining on the Level Model and staying steady on the Days model, becuase the XP difference represents fewer levels and the same number of days. (Note that this is true only in the Logarithmic region, or between Thresholds, because a player above a Threshold can make lower ave_xp/seg than a player below, but we'll get into that next section which is all about Threshold effects.)
A L128 player makes less ave_xp/seg than a L129 player. Like the Level model, the Well model now tells us that we want to raise our level as quickly as possible, and killing Dungeons achieves that goal by jumping us up the Well. So the well model is in agreement with the Level model.
Under the days model, we need to know how long we're taking to quest, how much XP represents how long it takes to level. Do we need the specifics, no, not really. It takes longer to gain level 129 than level 128. Since the dungeon reward is constant, it represents more of a percentage of L128's experince than L129's. Since L128 takes less time, a dungeon burned at L128 represents more time than the dungeon burned at L129. It's not a huge difference in this case, so no big deal, but it does mean that those that wait to burn quests until they are equal to the monster's level are taking longer to reach L350 than someone that burns them earlier.
Goodness, all three models agree on something! So, always burn your dungeons ASAP!
Heh, whoops, no. We only considered the "Diminishing Experience per level" effect. There was this really nasty business I called Threshold. All we did was analyze in the Logarithmic Region.
As a final consideration, try this example to consider how the Logarithmic region works:
Clone your character. Your clone does not burn his next few dungeons while you do, so youíre higher level. You both quest for a few days, then your clone burns the same dungeons you already beat. So, who is now ahead in levels? Many would say, ďThe Clone,Ē because the clone gained on the level model during that period, but this simply is not true, partially due to the level reward from dungeons diminishing, but not entirely. During those days when you were higher level, you gained more exp/segment, but dungeon experience is constant, so you must be ahead of your clone at the end. If people need a mathematical demonstration, I can do it, but it shouldnít be necessary. That makes the Level model unwieldy and inappropriate to use. The Well model is a more accurate model, since this problem is one of pure experience values. Knowing when to use which model is vital, since this should demonstrate that the Level model doesnít always work.
22.214.171.124 Dungeons in the Linear Region
The Linear region excludes fast changing level/day, but in this region, we have a different effect, called the Thresholds. These Threshold greatly change our ave_xp/seg and levels/day, and by that you can tell the Days model is going to be vital to our analysis.
Under the Day model, L249 takes 4 days to complete, but L250 takes 6-7 days. that is a huge difference. So how does that affect our dungeon reward, which is constant and unaffected by the Threshold effect?
Well, let's arbitrarily choose a value for a dungeon, such as D12-3, and state that it provides 50% of a level from the Level model. Okay, that wasn't arbitrary. That's how much I really got when i burned it at L250. Since xp/level at L249 is not significantly different from L250, it would provide 50% of L249, too.
Under the Day model, 50% of L249 represents 2 days of questing, but at L250, it represents 3 days! We literally gain a full day on our competition if we do not burn the dungeon until after we pass the Threshold. That's not insignificant.We are quite literally gaining a day on our competition, if they burned the dungeon before the Threshold.
Since the days/level from 250-274 is unlikely to decrease significantly, but XP/level will increase significantly, saving D12-3 until L274 diminishes the days of questing it represents. You do gets ome of that back waiting to cross the next Threshold at L275, but it does not all come back, because ave_xp/seg does not fall back to where it was at L250, but somewhere near L263. (You can calculate the number of days a dungeon represents by dividing the dungeon reward by the ave_xp/seg, and then dividing that result by number of segments you play per day.) This is where those that burn dungeons at their "proper" Level (ie. at the level of the monster) are hurting themselves severely. There is enough decrease that waiting too long will significantly diminish days/dungeon. (Where I got 6 days out of killing D12-11 at L254, you may only get 3 days at L345 in three years.) If you hold off D 1-1 until L250, youíre not even going to save 1 segment of quest time, but at Level 15, it may account for many segments.
But we are not done with this trick. Using our dungeons this way affects other sources of XP.
Remember that the Threshold diminishes ave_xp/seg, so that a player at L250 makes less ave_xp/seg than a player at L249, so when you are below a Threshold and another player is above, you are actually gaining on the Well model! Remember the old argument that you canít catch someone because their Exp per day will always be higher than yours? That is completely false, because of the Thresholds. At L250, I may only get 250000/segment, where at L249, I could get 350000/segment, so that player behind me makes 12 million experience on me per day! As a direct example, when Darstard hit L200, and I was a few levels lower, I gained 10% of a level per day on him, going from 5.9 levels lower to 4.9 levels when I crossed the L200 Threshold. (All of that is in my tracking, but I'm not asking D's permission to reveal his level advancement, and I won't even if he gives permission.) Before then, when we were both below the Threshold, I gained 1/10th of a level per week. Quite literally, those maximizing XP gain want to stay below the Threshold (meaning staying lower level) as long as possible, while making as much xp/seg as possible, so that we catch others on the Well and Level models.
That brings us to the third effect, and this comes from burning those dungeons after crossing the Threshold.
The levels immediately after a Threshold have the worst xp/seg you're going to see, but it rises fairly quickly, so getting back to where you are gaining on the Well model requires passing through that region as quickly as possible and getting to the region where your xp/seg is higher than the level below the Threshold. (It takes about 12 levels to get back to pre-Threshold ave_xp/day.) Remember that while we are above the Threshold, we too are being caught on the Well model by those below, so to hold off the competition, we want to get back to where we are filling the Well faster than them. Killing dungeons achieves that goal, by using the constant reward from dungeons to achieve higher ave_xp/seg rewards. The Days model likes burning them at lower level, because rising xp/level still reduces the number of days that reward equates to. The Level model still likes burning dungeons right after the Threshold, for exactly the same reason as the Logarithmic Region.
So, in a nutshell, in the Linear Region, save your dungeons for the levels immediately after a Threshold because:
a) it reduces the amount of time you spend in a lower ave_xp/seg region,
b) it keeps you below the threshold as long as possible in a region with high ave_xp/seg,
c) it maximizes the number of days of questing the dungeon saves you.
So, burn dungeons right after crossing a Threshold until your ave_xp/seg is equal to what it was before crossing that Threshold. Save the remaining dungeons until you cross the next Threshold.
It's that simple. And it works. I only wish I figured that out for level 150, instead of L200. I am, of course, pleased with the release of Dungeon 13, since that will permit me to use this trick two more times.
2.4 The Sticker Album
This hangs out like a sore thumb, I know. It is released after I had originally finished this document, so it was going to have to shoehorn into a completed work.
The bonus from the Album is significant. I have increased from 6 days per level to a little more than 4, which was what I was getting from L225-L249 (L259 at the time of this writing). You should be aware of that from other threads.
Maximize the number of Stickers you have in your album. Simple. There's no need for significant analysis, since this effect is constant, and the bonus it provides can only increase. The only concern is for those that are in guilds that bring in ringers to complete dungeons. If asked, get out of the way so the dungeon can be completed, because the 2% increase from the dungeon is more than the 0.06% bonus from a single sticker.
Anyone blowing shrooms on the Stickers is looking to save time/sticker, not stickers/attack, so just do whatever you need to achieve that. All I can suggest is hunt mainly in the Level 20-35 region, since it has the widest variety of equipment.
For those that are not using shrooms, and are stuck at one attak per 10 minutes, like me (!!! yes, I don't use shrooms to attack!) I cna help you out. You have time you can use to prepare for the attack, so you can hunt for better targets.
1) Normal equipment is broken into four types -- Starter, Beginner, Intermediate, and Expert. For Tabs 3, 4, and 5, except for Warrior weapons, there is one type of starter item for each slot, three types of Beginner, three types of Intermediate, and three types of Expert. Warriors have 3x as many weapons, but still only one type of starter weapon. The items are displayed in order of level, with Starter gear on lower page numbers through Expert on the highest numbered page. Starter gear stops spawning around Level 5, Intermediate spawns level 3-20, Intermediate 15-35, and Expert can spawn from L25 and up.
2) Do not hunt Starter gear until last. Starter players often have very few items, so you won't get many stickers/attack. Epics, also, are not really rare, so don't hunt those right off, either. Further, Jewelry is common to all players, so you'll pick most of it up by accident, so don't hunt it early on.
3) The L20-35 region can carry everything including rare Starter gear that hasn't been replaced. Start there. Until you've got a 40% bonus, don't waste time trying to optimize, except to find targets that have equipment in every slot. Warriors do carry one extra piece of equipment and therefore give one more sticker, but concentrating on them more quickly causes duplication, so don't... yet. You'll get 6-9 items per attack, so you'll gain bonus quickly.
4) Once you're up to 40%, start paying attention to the weapon of your targets. Choose only enemies that carry a weapon that you don't have. Switch between the four groupings (Starter, Beginner, etc), and different classes, and don't concentrate on finishing any weapon types at this point. This will minimize the chance of duplication, and prevent you from having to spend lots of time picking the perfect target. If you have the patience to do that, go ahead, but I don't. Willpower is a consumable quality, so the less you need to use, the more you'll have later. Optimization isn't just about managing the numbers, but also of managing yourself. You can do something against your nature for only so long, so try to limit when you do so
5) When you get to 60%, you'll start having problems finding targets quickly, so you'll want to start preparing a list ahead. I used alt-Printscreen and paste into Paint to have a visible image of the weapons I was hunting. Also note that Right-click will give you a Zoom-in feature that let's you see the colours better. Some Scout weapons are only identifiable by the fletching on their arrows, which aren't in the book, unless you zoom in.
6) The Warrior page can be almost entirely completed by looking only for weapons. I built up a list of 10 targets with a weapon I needed, then used the time to hunt down new targets for the ones already found that also carried one or more items I needed from Shields, Chest, Jewelry, etc.. I was able to complete the Normal Warrior Tab with 152 attacks, because I could not double up two starter Shields. And I had only 9 Epics to find, which I got in 6 attacks.
7) After completing normal equipment, focus on Epics for the classes. The last three Epics of each type only drop for L105 and higher characters, so you can't get those at lower level with out people dropping their weapons to let you win. After Epics, do Tab 2. After Tab 2, finish the class Starter equipment.
8) If you're colourblind... oh, man, good luck.
Good luck to everyone filling their albums! Trust me, it's worth it.
Last edited by Charista; 05-27-2011 at 08:37 PM.
Confessions of an XP Addict: Part 3
Confessions of an XP Addict: Part 3, Choking on Regurgitated Arguments
by Chris "Charista" Wilde
Part 3 The Big Lie
3.1 What was the Big Lie?
Simple. “Stats and gold are better than levels.”
Lots of newer players (ie. people starting after Sept 2010) will be shaking their heads at that. Why did they claim that? Heh, you know, I get to try to explain an argument that I never agreed with.
You can quickly gain a lot of stats by maximizing your gold reward, and that would give you a temporary boost to defeat an annoying enemy, like a dungeon or an Arena competitor. And there was a lot of jealousy on the Arena in those early days, with people trying to be the highest rank of their level, or wanting to get revenge on anyone that beat them. It is a lot quieter south of the top page now.
The low level players that were doing this could see massive stat gains, since in the Starter Region, and low Logarithmic Region (see Part 2 for definitions), stats were very cheap, so you could get a massive power boost quickly. And given that 20 stats for someone with 200 is +10% power, but for 2000 is only +1%, farming for stats was a lot more effective at L50 than L250. These players claimed that stats were always better, because this could be demonstrated over and over.
This lead to a few individuals farming gold all the time, foregoing all leveling. These players became monsters for people of their own level, nearly impossible to beat. They would have the best equipment for that level, because they stayed in that level for much longer collecting equipment over days, as well as buying insane Base Stats. I called these people, "Speed bumps." They called me, "High level jerk."
See, I would identify them when I was a lower level than them, since I was belligerent in the Arena from the start. I could tell that they were using shrooms, like me, by their consistent potion usage. I caught up to their level, passed them, and then beat them when I was 6 levels higher. They complained that I was attacking lower level players, but what they didn't realize was that I had played the game a much shorter time than they, and thereby proving without a doubt that they had made the wrong choice. You see, they were making these claims that level was useless at the same time as claiming that level was very important when they lost. Their assumption was that the higher level player that just beat them started before they did, when in fact, most had started well after. It was a completely inconsistent position. To properly complain, they needed to attack people that had played the same length of time, and ignore players' level. You can do that on the Adventure (quests) and Employment (guard duty) medals, which are strong indicators of time since character creation. Adventure actually balances you against players that don't use shrooms, if you do, since it takes the same number of quests (assuming the same Instructor bonus) to reach the same level, if you use the same selection strategy. If someone maximizes quests, they'll have lower quests per level, which indicates that the match-up isn't fair. People of the Stats First philosophy should be complaining about being attacked by people with higher Quest count, not high level count.
The argument was anecdotal, not mathematical, and there was far too little sampling done to demonstrate whether it held up long term. It is easy to see why it worked at low level in the short term. Someone that leveled gained access to higher level equipment, but that didn't turn into real equipment in every slot immediately. It would take time to see the level advantage turn into a real power advantage, so that quick boost gave you your revenge, but hid the fact that weeks later you wouldn't compete with that person anymore. Leveling up raised HP (a little), reduces enemy crtical chace (microscopically), but that was nowhere near the power you could get from a day's gold mining. Stat gain was real, immediate, and effective for achieving those specific goals.
So why did it break down? Well, it didn't... it was just inappropriately assumed to be effective over the long term as well as the short.
Because no one checked the numbers. Some argued that the numbers wouldn't work long term, but no one sampled data to prove it. The loud and vociferous proponents of the Stats theory simply shouted them down, and believed that winning an argument proves that you're right. And the Smart ones that realized the argument had serious holes, and didn't buy into the Stat argument just because they gave up trying to point out to idiots that they were wrong? They just laughed and ignored them. Why demonstrate the math to win an argument, when you can destroy them on the HoF, and leave them in the dust, and they wouldn't even realize what had happened? Why give up the Secret and let them get revenge?
So let's talk about the numbers.
Every level you gain, normal equipment increases by 2-2.5 stat points. You inevitably choose either Primary Attack Stat or Con, which are also the highest and therefore most expensive Base Stats. Equipment is the cheapest source of stats, and equipment usually accounts for 50-66% of your Primary stat, and 50% of your Con. While a +1 increase in a stat from a small equipment upgrade may be an equivalent cost to a Base stat point, a +10 stat increase on a piece of old equipment may cost 1/10th of a Base Stat point, giving you 10 points for the cost of one. Leveling faster therefore increases your stats from equipment and decreases your gold spent on the total stat, so even while your Base stats suffer, your equipment stats are better than the gold miner in the long term. But it's not just Equipment stats. There is also weapon base damage and Armor.
Both offense and defense are exponential. Your damage is proportional to your Primary Stat multiplied by Average weapon damage, and both of those are affected by equipment. Your defense (against anyone except Mages) is proportional to Armor, Con, and the attacker’s Primary stat (which is also multiplicative but has a smaller effect so can be effectively ignored for a First Order discussion like this). Basically, those increasing only Base Stats are advancing linearly, while those that are advancing in levels are advancing exponentially in power. And this was hidden from the Gold Miners by the time it took to gain the better equipment. A short term gain was assumed to not be recoverable by a long term gain, but with the equivalent of ten pieces of equipment at 2 stats each, one level equates to 20 very cheap stat points. 20 Base Stat points aren't cheap for anyone.
Let's talk about that exponential comment, since most people might not know what I'm talking about. Let's look at a simple equation:
Y = A x B
Now, let me give you a choice. You may increase A and B, but the total increase may not exceed 200%. So:
Y3 = ((1+ C)xA) x ((1+D)xB) where C+ D = 2
Y3a = ((1+ 2)xA) x ((1+0)xB) = 3xAxB = 3xY
So, how about C = 1, D=1?
Y3b = ((1+1)xA) x ((1+1) x B) = 2A x 2B = 4xAxB = 4xY
(average damage per round) = (number of attacks) x (chance to hit) x (average damage per hit)
Side note: On defense, you want to do the opposite. Choose one and crank it. I might insert the math for that at a later date, or discuss it in any debate if someone asks.
3.1.2 Gold per Segment vs. Level
Gold/segment also increases as you level up, just like xp/seg does. The real question is, "If I sacrifice xp/seg for higher gold/seg, will someone that does not make that sacrifice make more gold overall than me because he'll have higher gold/seg forever?"
The answer is, "In the medium term, the gold focused player makes less money than the level focused player." This is because gold/segment can increase significantly faster than many think. It doesn't even take the long term to recover the gold.
Examine attachment "Levels.txt". This is me compared to a player that announced to me that he was running about 80% maximum Exp, trading off for more gold for Base stats. (The player has retired, but I won't tell you his name.) He was 10 levels below me at the time, and only initially kept up with my own minimal gold/day. As you can see, the player steadily fell behind in level and in gold/day, despite making a small Exp for gold trade-off. It is actually worse for Gold Miners that maximize gold and sacrifice even more Exp. (I tried to track one of those at the same time, but he didn't play every day.) They may be the toughest players at their level, but anyone maximizing exp will surpass them in a lot less time than the Gold Miner ever thought. I know I did. Over. And Over. Until I became one of the top 10 players on the server.
It is true that in the short run, by sacrificing exp for gold, you can surpass an enemy of near your level, but that effect is only temporary. That lost gold/segment due to lower level will add up over the long haul, and the enemy you surpassed will have that small gold/segment advantage forever, accumulating slowly even if you switch to Maximum XP later. Of course, by the time that happens, the Gold Miner has long since forgotten that player, so he won't associate the losses he takes from the higher level player with his own choice to sacrifice xp for gold.
But I remember, because I'm a competitive son of a...
3.1.3 Diminishing Returns
The higher your Base Stats, the more the next point costs. You get a diminishing reward for your cash. Staying at one level and buying stats costs you a larger percentage of your daily income.
Someone that does not stay at the same level, but instead reduces income to level higher receives an increased income at the next level, which reduces the cost of that next stat point as a percentage of income.
The gold miner can stay ahead on Base Stats for a long time, but the failure to raise base weapon damage and armor, and the stats from equipment mean that in terms of power, the Gold Miner slows down quickly, while the XP Addict maintains a steady increase. In the fullness of time, the XP Addict is Victorious, permanently. The Gold Miner that changes to XP Addict too late has fallen behind too much to ever fully recover.
3.2 Effects of Choosing Archtypical Quest Methods
There are as many methods of choosing quests as there are player in the game. Generally, though, they reduce to three archtypes -- Gold Miner, Optimizer, and XP Addict.
The Gold Miner ignores XP reward and takes the best gold/seg. He could use my tricks in Part 2 to optimize Quest reward, interestingly enough. We've dealt with him ad nauseum so there is little more to say.
3.2.1 Choosing to be an Optimizer
The Optimizer has noticed something. Quests are not created equal. Some day, record the XP and Gold rewards of all quests, including those that you do not select, but ignore any with equipment rewards because they reduce gold and XP rewards..
Calculate the average for gold/seg and xp/seg. Convert each quest to its equivalent for a 1 segment quest by dividing the rewards by the number of segments. Now, divide each reward by its average. Sum together the two numbers and you get a rating for the total reward of each quest, normalized to the average. Okay, that was probably confusing, so you're just going to trust me. Not all quests are created equally in terms of reward. From the average, the total reward can be better or worse by 20%. In other words, the best quests can have 50% better rewards than the worst. The Optimizer chooses the more exceptional quests.
This version of the Optimizer is rare. Unless you have one of these amazing math brains that instantly do divisions, you're going to be pumping numbers into a spreadsheer every time you select a quest. Gets old fast.
So, the person I'm lumping in with him is a Pseudo-Optimizer. He intentionally chooses not to maximize XP, but trades off some known portion by selecting XP quests X% of the time and gold quests 100-X% of the time. The player in "Levels.xls" was an Optimizer at 80% XP. I count them the same because the effects of the slightly higher gold reward of a true Optimizer can't overcome the effects I described above in gold/seg increases for the XP Addict. The only difference between the Pseudo-Optimizer and the Optimizer is a slightly higher gold reward for the true Optimizer.
126.96.36.199 Optimizers in the Logarithmic Region
In the Logarithmic region (L1-150), if you choose 80% of max exp gain, you will actually reach a point of steady state where you are constantly X levels behind a player with 100% of max exp gain. For some any level, there is a lower level where level/day = 80% of our level/day. What this means is that when the Optimizer falls behind by a certain number of levels, we will have the same levels/day and level up at an equal rate.
188.8.131.52 Optimizers in the Linear Region
Once you pass 150, you're into the linear region, where the level/day does not significantly diminish. In this region, Player.A makes 4 levels in the time it takes Player B to make 5 (so long as they are between the same Thresholds). The Optimizer now falls behind at a constant rate, until a Threshold is reached by the XP Addict. The Optimizer may catch up some once that point is passed, if his ave_xp/seg is not too low, but the moment he crosses that Threshold, he falls behind again, so he will never catch the XP Addict. He can reserve dungeons to help, but he cannot stay ahead of the XP Addict, if he began close enouhg to jump ahead after crossing the Threshold.Once all dungeons are used up, he falls behind and stays behind.
3.3 The Costs of being an XP Addict
Is the right answer, "There are none?"
Nope, there is one very big one that will startle you.
I lose quests once in a while. Been a while, though. I lost one in April, three in March. one in December, and one in Nov, though in my defense, all were when I had let my daily potions dissipate. I must have good daily potions, or I risk losing quests. If I ever give up my PoEL, I will have to gain a lot of stat points or lose much more often.
So, I should raise my stats, right?
Not a chance.
I lost one quest per month for the last 7 months. That represents a tiny amount of loss. On average, with 54 quests per day (300/ 5.5 minnutes for average quest length), I am losing less than 0.001% of my XP and gold to lost quests. Throwing away 20% of my XP in order to get back that tiny fraction of a percent is simply not good return on investment. The lost quest is insignificant compared to the effort required to prevent the loss. Further, we know that the sacrifice costs us XP and Gold on the long term that will be far greater than a single lost quest.
And I also have weak Base Stats, which I mentioned way back in the Preamble. I do not kill dungeons at the same level as higher Base Stat competitors, but as you've seen from Part 2, that can be a positive by times. I lag behind on dungeons by two or three levels, when my equipment catches up. So, yes, I'm not as powerful as someone else of my level, but we're only talking about a 10% difference at this point. I run about 40% win rate against the players above me in level... except for Bain. I haven't tested him, so I do not know how I would do. He is backed up by a complete set of +triple Epics, and that, not BAse Stats, are what will wreck me. Back in the 80's when I had Speed Bumps to deal with, I would get completely destroyed by similarly leveled Gold Miners, but no one is like that in the top 15 now. We left people of that philosophy behind long ago.
4.0 Detoxing on Conclusions
The most important problem with the tired old Gold for Stats argument is that it had no mathematical foundation. It relied on a lack of knowledge of the specifics of the S&F experience and gold system (specifically, the rate of increase in gold/seg and xp/seg are vital to any discussion of this sort in order to evaluate the long term cost of any method), and so long as no one did the work to demonstrate its assumptions were false, it made sense due to anecdotal evidence. But this is the most important lesson you need to ask when talking about systems of numbers is…
Show me the real numbers.
Don’t let anyone argue from a foundation that lacks numerical analysis and proper sampling. That was the falsehood in the Stats argument. It relied on no one ever being able to analyze the actual system, but all it really took was comparing the Medal of Commerce and Experience bar by logging on every night. The numbers are there to use to prove your case, but you have to be willing to go after them, and you have to know how to analyze them.
I hope that you enjoyed this. I hope that you learned something. I'm just glad that it's done. It's been haunting me for a long time. And yes, it's an indulgence.
Last edited by Charista; 05-28-2011 at 09:38 AM. Reason: First Order discussion, not First Principle.
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Last edited by Bullbound; 05-27-2011 at 10:58 PM. Reason: added sections found
Follow up thoughts
Here are a couple of follow up optimizations on what Charista has said:
1. The probability of receiving a mushroom does not change by quest length.
This should give an additional value boost to the shorter quests, especially if you are budget constrained.
(Actually, I haven't checked this in a while; but it was last time I checked).
2. There should be a probability assessment to quest selection.
Here is what I mean:
Let's say my avg xp gain is 5x the time (so on 10mins I make 500kxp on avg).
If my choices are: 4segments at ~3x, 4segments at ~3x, and 1 segment at ~2x my expected value is much better taking the 2x xp (ev 4.25x) than the guaranteed 3x.
Where ev is short for expected value, and is calculated in the example above as: (1*2+3*5)/4 > (4*3)/4
I wouldn't sacrifice known good XP for a possibility of a mushroom, though.
Excellent analysis Charista, thank you for proving what some of us have been unwilling to calculate. I hope you use your math and statistics skills in real life too..
Wonder how this strategy plays out for non-shroomers. I gather being unable to pot as much would lead to significantly higher loss rates. I'd expect this would shift the balance towards certain amounts of optimization so as to keep win/loss rates high.