The solo leveling limit conjecture

I've been hearing crazy leveling claims for almost as long as I've been playing the game. Sometimes, the claim is true, and sometimes it points to an exploit. Most of the times I think they are exaggerations, comparable to the ones made about endurance limits or one-shotting bosses.

It got me thinking about whether there was an actual mathematical limit on leveling; something that would prevent a solo player from being able to level any faster. And there sort of is: there is an endurance limit.

Fundamentally, we all convert ticks of the blue bar into damage, damage into kills, and kills into XP. Most characters have a limited amount of endurance (certain powers in certain sets can increase this to extremely high levels in theory, but most powerset combinations don't have access to this).

Now, kills are not the only way to get XP: you can get XP from mission bonuses (that intrinsicly do not require endurance, although they may require mission objectives that do ultimately require endurance) and you can get them from miscellaneous activities (such as finding exploration badges). But assuming that those are relatively minor, and assuming that things like CaB drops are relatively minor, I've calculated what I believe is the endurance limit on leveling from level one to level 50: its 35.6 hours.

This number is based on the following assumptions:

1. Throughout the character's leveling, they had the best damage modifier (the blaster ranged modifier, 1.125).

2. They were always operating at a DPE efficiency of 1.95*1.33 = 2.59 of base (which is scale 1.0 damage per 5.2 endurance), which is the efficiency of being slotted to the ED soft cap for damage and one SO worth of endurance reduction, from level 1 to level 50 (really from level 2 to 50, I'm not counting the time to level from 1 to 2).

3. You are always killing the most optimal targets in terms of endurance per XP point. And that is +2 bosses.

4. I do not assume you can farm targets with higher than normal XP, aside from the bonus for killing +2s.

5. I assume targets never regenerate.

6. I assume single target damage efficiency.

7. I assume fully slotted stamina from level 2 through level 50.

Given those assumptions, it takes about 35.6 hours to produce enough endurance to generate enough damage to earn enough XP to reach level 50. And while there are some assumptions that are conservative (I never assume AoEs will do better than single target attacks in terms of DPE), and some are not strictly always accurate (Brutes can be more efficient with fury than the list above assumes) most are highly aggressive (for example, it assumes targets are on an infinite conveyor belt and line up to be killed one after the other without pauses, and don't ever shoot back).

I'm not saying its impossible to level to 50 faster than in 35 hours. I'm saying it seems unlikely to be able to do so without help. But this is a very loose calculation. Its possible it contains some unreasonably conservative assumptions. So my question is: does anyone think they can level from level 1 to level 50 in less that 35.6 hours, under the following restrictions:

1. No teaming
2. No direct combat assistance
3. No exploiting bugs in the reward system

That's it. Beyond that, anything else would be fair game, twinking with inventions, any archetype, any powersets, even ones that break the assumptions about endurance limits (i.e. electric armor). Is it actually possible to solo level to 50 in less than 35.6 hours, and if so, how?

I was thinking of adding a fourth rule that said:

4. No leveling by dropping missions

Because I thought of the possible exploit of waiting three days and then logging in just to drop a mission, but actually I don't think that will work anyway.

I'm not interested in vague anecdotes about sorta fast leveling. I'm interested to know if it would be possible to do now, and what specifically would allow a player to exceed the apparent limits of this calculation. Is it that mission complete rewards are higher than I am assuming, or that combat is really far more efficient than I am predicting, or that AoEs are much more efficient than I think can be leveraged consistently? Or something else I just haven't thought of or thought was unimportant?

I don't necessarily expect someone to try to level from one to 50 all at once just to test this conjecture, so here's an extra bit of data for anyone that wants to experiment with this conjecture of mine. Here's my raw calculated numbers for the estimate for the minimum time to reach each level:

2	0
3	0.01
4	0.02
5	0.04
6	0.06
7	0.09
8	0.12
9	0.16
10	0.21
11	0.26
12	0.31
13	0.37
14	0.44
15	0.5
16	0.59
17	0.68
18	0.8
19	0.93
20	1.1
21	1.29
22	1.54
23	1.83
24	2.14
25	2.5
26	2.88
27	3.32
28	3.82
29	4.36
30	4.9
31	5.52
32	6.2
33	6.95
34	7.78
35	8.63
36	9.57
37	10.61
38	11.67
39	12.88
40	14.27
41	15.82
42	17.56
43	19.45
44	21.51
45	23.78
46	26.08
47	28.41
48	30.77
49	33.16
50	35.59

I'm not a good enough player to do this in practice, so I'm just going to talk theory.

1) Are you assuming that you're always running through Patrol Experience? I didn't see it mentioned either way, but that's a potential 50% bonus if you're not in AE. AE is most likely to give the easy-kill enemies we covet, though.

2) There are arc completions that award large amounts of XP. Of course, those arcs are not conveyor belts of +2 bosses, but I remember getting close to a bubble of XP for finishing one of the Croatoa arcs. I don't think it's likely to be exploitable (I think it's either Skipper or Buck, so best case it's six missions and two are Defeat All) but with Ouro, it's one loophole I'd look at. (They closed the "Welcome to Vanguard" version of this but there may be more subtle ones.)

3) I think that AOE's are potentially huge, but I don't know the +2 boss to +1 minion XP ratio. Given a conveyor belt of pacifist minions, and perfect placement, a Fire/Mental blaster could beat ten +1 minions per cycle of AOE's (maybe +2, but I don't think so), and given 100% recharge in Fire Breath could do so every 10.67 seconds. (Given infinite recharge and a pretty fast conveyor, they could do so every 5.5 seconds or so.) Drain Psyche virtually eliminates endurance as a consideration, so we're damage-limited.

4) I don't know if CaB's can be discounted. You can start with a full tray of CaBs. (How do those compare to carrying damage enhancements?) You can combine to create CaBs. If you're beating bosses you will not generate as many inspirations but they will tend to be larger; I don't have useful numbers on that. If you remember the old Nethergoat Dark Astoria runs, if you beat enough minions fast enough you can keep yourself in perma-inspiration. I don't know if they tweaked the inspiration drop rates after that was discovered.
5) I'd be interested in the "damage chain" measurement- assuming enough damage to exactly match an AV's regen rate, how does that convert to +2 Bosses Per Second and how long would it take to hit level 50 at that damage rate? (I picked that as a level of damage that some sub-50 characters can reach, but few can significantly exceed. If you have a better standard, feel free. )

one thing i didnt read in your text is that each lvl up grants you 100 end and the 60 sec 50% damageboost
i am not sure if you got that in your calc or simply forgot it

As always its very hard to comment on a calculation without seeing the work

But that said

1. Recovery IO availability
2. Recovery powers (quick recovery, drain psyche, etc)
3. Insp drop rate and the ability to combine them
4. Effectiveness of AOE powers to leverage end
5. The ability to buy insps
6. The effect of red insps on the dpe

Of these the insp drop rate is the only one mentioned and that is to discount it.

It would seem to be more effective to calculate the time it takes to kill a spawn on average using aoe/st attacks then plug that in to the calcualtion of kills/level.

Just as example an archery or assault rifle blaster can kill entire spawns as fast as full auto, rain of arrows and aim and buildup are up. I cant see how or if this is accounted for in your estimation

I wonder if a MM or controller might do better by use of pets, which sidestep the individual character End limit?

Alternatively, one might be able to leverage "pets on the fly", e.g. confuses. One of the quickest Posis I was on had a Plant controller along, those Vahz spawns can really take each other out fast when they are confused. . .

1. I'm a huge fan of your work. (that said...)
2. I'm not convinced that anyone would, solo, ever beat that curve because your conditions (fully slotted stam at lvl2?) are simply impossible to set-up.
3. The only possible way to do this would be to test this in AE.
4. If you could set up these conditions in AE, run the mission over and over (to simulate the conveyor belt), and I got such rates, the miss arc would likely be terminated.
5. The likelihood that lvl2's could sustain damage/end to kill +2 bosses long-term is too low and them NOT attacking is absurd.
6. This yields a hypothesis that cannot be tested (there exists no lvl2 that has stamina, so based on this model we cant prove you wrong).
7. Endurance much more sharply bottle-necks performance, and I doubt devs would ever allow for this level of performance.
8. MM's = self-help?
9. I'm sorry if this post comes off as snarky. It's not ment to be. I just find the whole thing entirely unlikely, or at least inconsistant enough that any player base wont be effected anyway. I think I see what you are trying to express: Given maxium damge/end attack chains, how fast could a toon lvl. Maybe when I get my stone/wp scrapper completly IO'ed at lvl2 with lvl50 slotting with stamina and purples, I could tell you.
10. I agree with the points others raised.

Fulmens:

I'm not assuming patrol XP. Thanks for reminding me of that. I'm going to assume that for someone attempting to level quickly patrol XP is going to have only a small effect. Its theoretically possible, of course, to take ten days off per level to gain maximum patrol XP and level in half the time in terms of play time, but that would take over a year of calendar time to pull off.

As to the other assumptions, well, that's why I'm posting this. I'd like to see someone demonstrate either by example (actually testing leveling) or by very strong argument (something fairly mathematically rigorous) that assuming those are relatively minor leads to an incorrect guestimate for the leveling limit.


vernichterhelge:

I didn't forget about leveling inspirations, but I did forget to mention them. I'm assuming that inspirations in general, including the leveling ones, are not material. This includes damage insps (which increase DPE), CaBs (which give E) and the lifesaver roll you get on dinging a level.

To give you an idea why I didn't consider them significant, my estimate for the amount of endurance necessary to reach level 50 is about 213509. 50 dings of full endurance is about 5000 endurance.


Another_Fan:

I'm not so much interested in comments on the raw calculations themselves as I'm interested in knowing if there are empirical tests that can contradict them. I posted the per-level table so that theoretically speaking anyone could take a character of any level and test leveling strategies to see if its possible to beat the curve I specified. You could take anything and see how high you can get XP/min to go at a particular level, and see if its faster than the curve implies.

The other way to look at this is the way you mention: try to calculate how *fast* someone can generate damage. But the problem with that is that sustainable damage is actually very tricky to calculate boundaries for. When I attempt such calculations, I end up with limits higher (faster) than the endurance one. So the endurance one is, at least for me at the moment, the stronger constraint, so its the more interesting one.


gec72:

Personally, in terms of *normal* play, I've never reached 50 in anything remotely close to this limit. My fastest leveler to 50 is probably around 200-250 hours myself, and usually I take even longer than that, because I am almost never focused on leveling speed.


Scientist:

I wonder about controllers and masterminds myself, because they aren't bound to this limit directly (as are some powerset combinations). But I'm curious if their ability to side-step this limit comes with other disadvantages that prevent them from exceeding it anyway, which is the purpose of my post.


Kractis_Sky:

The assumptions are very extreme because I'm looking for the boundaries of solo play. However, as extreme as they might appear, its still actually possible that someone could beat them, or at least come close to them, if just one of my assumptions turns out to be too conservative. For example, if you could be dinging arc completions all the time, those bonuses could be huge. But I don't think there are enough of them, or that you could do enough of them quickly enough. If I'm wrong, there might be a strategy that doesn't have to do the extreme levels of work the calculation assumes and can sidestep them. And actually Warburg missions with the old bonus reward came surprisingly close to doing so.

If absolutely no one jumps in and tells me that this is possible, I will probably go back and refine and loosen the calculation to come up with a lower (slower) limit, and see if someone challenges *that*, until I'm satisfied I have a reasonable guestimate for the limit, or until I get distracted by something shiny and go do something else.

Interesting conjecture here; I do know of a couple of early (now plugged) AE missions that could easily break your averages; I assume no exploit or "under the radar" AE missions of which there still are a few in the list.

The fastest I've yet managed to take a character 1-50 mostly solo is in the 100 hour range, and that included considerable time in the auction house and other, non-XP gathering, activities. From that I'd estimate that at least 50% of the time was wasted as far as pure XP goes... traveling from A to B, hitting contacts, looking for lost mobs in kill-all missions etc. This was an AOE heavy Fire/WP brute and I did focus mostly on large swarms of +1 mobs (old 2nd difficulty level, later the +1/8 setting).

I've leveled a solo Night Widow to 28 using AE in about 6 hours, although it's admittedly using one of those exploitable missions; I don't see getting him to 50 in 50 hours though; one once a character gets to a decent level I prefer to actually play it rather than grind it through a PL mission. I'd imagine you'd get better results with something hugely AOE heavy running at -1 to +0 set for 8 than single target heavy running +2 bosses; the hordes of minions/LT's are much faster to kill than the bosses. Maybe they're not worth as much individually, but killing 10+ of those in the time it takes to kill 1 boss?

You are always killing the most optimal targets in terms of endurance per XP point. And that is +2 bosses


Not every toon can run mishes at this level.

I understand you are running entirely hypothetically, Arcana, and I'm trying to imagine a way in which someone could either make or beat this time, and I come to two conclusions

1. it would have to be a MM with damage enhancing powers, /dark has an early start, but I think Storm, TA, or possibly Therm might take the advantage in the higher game. Picking the highest damaging primary would be the only possibility (not sure which one that is)

2. It is not possible to reach your +2 boss condition, simply because AE would be the only way to fight an almost constant stream of such enemies, but if that was all you fought, you would lose XP because of the anti-farming measures that were implimented.

As always, Arcanaville, your posts are interesting and thought provoking.

A couple nuances I'll toss into the mix.

A> With regard to your point #3 and killing the most efficient enemy, I would
also consider that to be: only the enemies that directly complete the mission ... ie. stealthing missions.

To me, this maximizes endurance usage, and it also weights the XP (especially early)
towards completion bonus > killing bonus.

B> CaB drops - this seems a low hitter to me as they can be purchased
in so many places these days that endurance needn't be too dependant
on drops.

C> Also on the limiting side: travel time might be an additional factor.

In any case, interesting conjecture - to me (an avid soloist) many of the
times have seemed overrated (sometimes grossly so), but having said that,
I've never been one to rush the levelling process. Consequently I'd be a
very poor candidate to test your idea.

Your limit of ~35 hrs does seem to be in the ballpark of folks that claimed
to get L50's over a weekend... I'm not sure whether those claims were
for soloists though - my sense of it was more in PL teams.


Regards,
4

PS> In terms of your limit, I've never levelled to 50 in anywhere near that
time - I'd have to check, but I doubt I've ever done it in under 100 hrs
(again, not that I've ever rushed levels either).

FWIW

I extended out your table for a variety of reasonable endurance regimes.

2    0                
3    0.01    0.01    0.01    0.01    
4    0.02    0.02    0.02    0.01    
5    0.04    0.03    0.03    0.02    
6    0.06    0.05    0.05    0.03    
7    0.09    0.07    0.07    0.05    
8    0.12    0.10    0.09    0.07    
9    0.16    0.13    0.12    0.09    
10    0.21    0.17    0.16    0.12    
11    0.26    0.22    0.20    0.15    
12    0.31    0.26    0.24    0.18    
13    0.37    0.31    0.29    0.21    
14    0.44    0.36    0.34    0.25    
15    0.5    0.41    0.39    0.29    
16    0.59    0.49    0.46    0.34    
17    0.68    0.56    0.53    0.39    
18    0.8    0.66    0.62    0.46    
19    0.93    0.77    0.72    0.53    
20    1.1    0.91    0.85    0.63    
21    1.29    1.07    1.00    0.74    1.18
22    1.54    1.27    1.19    0.88    1.30
23    1.83    1.51    1.42    1.04    1.42
24    2.14    1.77    1.66    1.22    1.56
25    2.5    2.07    1.94    1.43    1.72
26    2.88    2.38    2.23    1.64    1.89
27    3.32    2.75    2.57    1.89    2.09
28    3.82    3.16    2.96    2.18    2.31
29    4.36    3.61    3.38    2.49    2.55
30    4.9    4.06    3.79    2.80    2.79
31    5.52    4.57    4.27    3.15    3.06
32    6.2    5.13    4.80    3.54    3.37
33    6.95    5.75    5.38    3.97    3.70
34    7.78    6.44    6.02    4.44    4.07
35    8.63    7.14    6.68    4.93    4.45
36    9.57    7.92    7.41    5.46    4.86
37    10.61    8.78    8.21    6.06    5.33
38    11.67    9.66    9.03    6.66    5.80
39    12.88    10.66    9.97    7.35    6.34
40    14.27    11.81    11.05    8.14    6.95
41    15.82    13.09    12.25    9.03    7.64
42    17.56    14.53    13.59    10.02    8.42
43    19.45    16.10    15.06    11.10    9.26
44    21.51    17.80    16.65    12.28    10.17
45    23.78    19.68    18.41    13.57    11.18
46    26.08    21.58    20.19    14.89    12.20
47    28.41    23.51    21.99    16.21    13.24
48    30.77    25.46    23.82    17.56    14.29
49    33.16    27.44    25.67    18.93    15.35
50    35.59    29.45    27.55    20.31    16.43

I got the "arc complete" bonus for Piercing the Veil and... didn't write it down. It was approximately 16K for a level 30 character, doing 1 hunt, 2 talk-tos, 2 "regular" door missions and 3 kill-alls. Mission complete was approximately 2.2K just before that, so the arc bonus looks very roughly like "the same as all the mission bonuses" in this case alone.

The FASTEST I've ever heard of people doing an ouro mission [back when there was that level 9 or 14 timed in KR which gave juicy merits] was around 3 minutes. I've done them in under 5 (the loa bone) myself.

If all the missions were 4.5 minutes [I know, they're not, due to kill-all] and intermissions were 30 seconds that's, plus or minus fenceposts, 40 minutes. Mission and arc bonuses are something like 32,000 XP out of a 256,000 XP level. So in this case, which is memorably large, you get 1/8 of a level in arc bonuses in the time that, by your DPE calculation, you'd be getting about an entire level.

If you could somehow get 4000 XP per mission in mission/arc bonus at level 30, with a 3 minute mission, you'd be getting XP at almost 1/3 of a level per hour not counting any defeats along the way. That's roughly 6 times slower than your optimum rate. For me that's just on the "ignore" side of the line, but it's close.

I need to get better Loa bone measurements before I come back to this thread.