Experience from raids

[anita]

--------------------------------------------------------------------------------------------
Average experience from raids:
--------------------------------------------------------------------------------------------

Attack - Attack button (1, 5 or 20)
Buffs - tactics applied
Min.E - minimum amount of exp if all tactics will trigger
Min.E - maximum amount of exp if all tactics will trigger
AV.E/hit - Average experience per hit
AV.E/SP - Average experience per skill point (1 stam = 2 SP, 1 Hon = 1 SP)

STAMINA RAIDS

Attack_ Buffs________ Min.E_Max.E___AV.E/hit___AV.E/SP
-------------------------------------------------------------------------------------------------
|_1|___None____________1_____4______2,50_____1,25
|_5|___None____________5____24_____14,50_____1,45
|20|___None___________21___100_____60,50_____1,51

|_1|___PoE_____________2_____8______2,59_____1,29
|_5|___PoE____________10____48_____15,01_____1,50
|20|___PoE____________42___200_____62,62_____1,57

|_1|___LA______________2_____8______2,61_____1,30
|_5|___LA_____________10____48_____15,11_____1,51
|20|___LA_____________42___200_____63,04_____1,58

|_1|___TaC_____________2_____8______2,55_____1,27
|_5|___TaC____________10____48_____14,78_____1,48
|20|___TaC____________42___200_____61,65_____1,54

|_1|___PoE & LA________ 3____16______2,69_____1,35
|_5|___PoE & LA_______ 15____96_____15,62_____1,56
|20|___PoE & LA_______ 63___400_____65,16_____1,63

|_1|___PoE & TaC_______ 3____12______2,64_____1,32
|_5|___PoE & TaC______ 15____72_____15,30_____1,53
|20|___PoE & TaC______ 63___300_____63,85_____1,60

|_1|___LA & TaC________ 3____16______2,65_____1,33
|_5|___LA & TaC_______ 15____96_____15,38_____1,54
|20|___LA & TaC_______ 63___400_____64,19_____1,60

|_1|___PoE & LA & TaC___4____24______2,74_____1,37
|_5|___PoE & LA & TaC__20___144_____15,90_____1,59
|20|___PoE & LA & TaC__84___600_____66,35_____1,66


HONOR RAIDS

Attack*_Buffs________ Min.E_Max.E____AV.E/SP
-------------------------------------------------------------------------------------------------
|_1|___None____________1_____2______1,50
|_1|___PoE_____________2_____4______1,55
|_1|___LA______________2_____4______1,56
|_1|___TaC_____________2_____4______1,53
|_1|___PoE & LA________ 3_____8______1,62
|_1|___PoE & TaC_______ 3_____6______1,58
|_1|___LA & TaC________ 3_____8______1,59
|_1|___PoE & LA & TaC___4____12______1,64

* In honor raids it doesn't matter which type of attack you're using (1, 5, 20), they yeld the same amount of AV.E. But in stamina raids the difference is clear - 20-stam attacks gives you the most exp.

--------------------------------------------------------------------------------------------
Calculations:
--------------------------------------------------------------------------------------------

This is the amount of experience you get from raids:

Regular Raids
1x Attack = 1-4 exp
5x Attack = 5-24 exp
20x Attack = 21-100 exp

Alliance Raids
1x Attack = 1-2 exp
5x Attack = 5-10 exp
20x Attack = 20-40 exp

Currently we have three buffs (tactics) that could affect the amount of experience we receive:
Pursuit of Excellence (PoE) - doubles the amount of exp
Lightning Assault (LA) - gives a chance to trigger another attack without additional stamina cost.
Take a Chance (TaC) - doubles the amount of exp (or gives extra damage bonus, credits)

According to Rafael's tactics theorycraft, the proc rates (for exp only) of those tactics are:

1. Lightning Assault: +4.2%
2. Pursuit of Excellence: +3.5%
3. Take a Chance:+1.9%
Note: PoE + TaC together multiply the XP by 3 (not 4).

I've calculated the average experience from raids by using the following formulas:

Exp without buffs:
Basic AV exp = (Max exp - Min exp)/2 + Min exp

Exp with PoE applied:
AV PoE exp = Basic AV exp * 0,965 + Basic AV exp * 0,035 * 2

Exp with LA applied:
AV LA exp = Basic AV exp + Basic AV exp * 0,042

Exp with TaC applied:
AV TaC exp = Basic AV exp * 0,981 + Basic AV exp * 0,019 * 2

Exp with PoE & LA applied:
AV PoE & LA exp = AV LA exp + AV PoE exp - Basic AV exp

Exp with LA & TaC applied:
AV LA & TaC exp = AV LA exp + AV TaC exp - Basic AV exp

Exp with PoE & TaC applied:
(This one's a little bit more complicated - there is less than 1% chance they'll trigger at once (exp x 3) and more than 99% chance for seperate effect)
AV PoE & TaC exp = (AV PoE exp + AV TaC exp - Basic AV exp) * 0,999335) + Basic AV exp * 0,000665 * 3

Exp with PoE, LA & TaC applied:
(I'm assuming there's 50% chance PoE & TaC will trigger at the same strike and 50% chance they'll trigger at different LA strikes)
AV PoE & LA & TaC exp = 0,5 * (AV LA exp + AV PoE & TaC - Basic AV exp) + 0,5 * (AV LA exp + AV PoE exp + AV TaC exp - 2 * Basic AV exp)

When we finally have AV exp for different tactics applied, we have to divide it by the number of skill points (SP) used in the attack.
1 stamina attack = 2 skill points
5 stamina attack = 20 skill points
20 stamina attack = 40 skill points
1 honor attack = 1 skill point
5 honor attack = 5 skill points
20 honor attack = 20 skill points

This way we get AV.E/SP - experience per skill points

--------------------------------------------------------------------------------------------
Conclusions:
--------------------------------------------------------------------------------------------

Conclusion 1: The best tactic for experience is LA, PoE takes the second place and TaC is the third.
Conclusion 2: Stamina is best for experience, but only it you're using LA, PoE and Tac together. Otherwise energy is comperable.

--------------------------------------------------------------------------------------------
You can see also my average experience from missions charts for comparison.
--------------------------------------------------------------------------------------------
Update log:
13.07.2011 Added TaC

[Rafael]

Nice work

[anita]

Update
I've finally added TaC & changed the display a bit.

[anita]

Nice, back then when I was a newbie I thought that a higher attack equals a higher amount of experience gain, well anyway, how long did it take you to do all the research for these facts? Lol

I took the proc data from Rafael's tactics theorycraft, so my contribution is relatively small - just some calculations. It took me an hour or two hours to prepare it, I was never a math genius.

[Lycano]

Great work and nicely explained - Thanks Anita

[Rafael]

Heh, thanks I'm glad that info has been useful then

Exp with PoE & LA applied:
AV PoE & LA exp = AV LA exp + AV PoE exp - Basic AV exp

Exp with LA & TaC applied:
AV LA & TaC exp = AV LA exp + AV TaC exp - Basic AV exp

Exp with PoE & TaC applied:
(This one's a little bit more complicated - there is less than 1% chance they'll trigger at once (exp x 3) and more than 99% chance for seperate effect)
AV PoE & TaC exp = (AV PoE exp + AV TaC exp - Basic AV exp) * 0,999335) + Basic AV exp * 0,000665 * 3

Exp with PoE, LA & TaC applied:
(I'm assuming there's 50% chance PoE & TaC will trigger at the same strike and 50% chance they'll trigger at different LA strikes)
AV PoE & LA & TaC exp = 0,5 * (AV LA exp + AV PoE & TaC - Basic AV exp) + 0,5 * (AV LA exp + AV PoE exp + AV TaC exp - 2 * Basic AV exp)

There are some (very small) inaccuracies in the way you combined the tactics, but the difference between what you obtained and the actual increase is so small that it probably wouldn't even change the numbers. Below is some mathematical explanation of how these can be accurately calculated - but for those who don't like math it might be boring, so I put it in a spoiler tag.

First when you do this:

Exp with PoE & LA applied:
AV PoE & LA exp = AV LA exp + AV PoE exp - Basic AV exp

You are assuming PoE can't proc on both LA hits. The probability of that happening is so small that there is no problem in ignoring it, but if you want to consider it, a simple way to calculate it is to say the basic AV is multiplied by 1.035*1.042 (what you did adds them, instead). Using your own notation, that would be:

AV PoE & LA exp = Basic AV exp * 1.035 * 1.042 (or if you prefer: AV LA exp * AV PoE exp / Basic AV exp)

Same with LA + TaC, the way you did it you're considering TaC can't happen on both hits. The actual increase would be 1.019 * 1.042.

The TaC + PoE procs are actually independent, which means that using only 1.019 + 1.035 = 1.054 as the XP multiplier should already work. This is the same as:

AV PoE exp + AV TaC exp - Basic AV exp

That already gives the correct result. There is no need to use that 0.999335 value - because triple XP when both procs is already the normal behavior of this kind of reasoning.

For the last one you don't need to make the 50% hypothesis thing - in fact, that would be wrong.
The simpler way is to just use the multipliers as in the processes above, the multiplier in this case is 1.042*(1.019+1.035).

So as a summary, here are the multipliers for each tactic combination:

TaC: 1.019
PoE: 1.035
LA: 1.042
T/P: 1.019 + 1.035
T/L: 1.019 * 1.042
P/L: 1.035 * 1.042
T/P/L: (1.019 + 1.035) * 1.042

Anyway, again, the differences between the numbers above and the ones you got would be very small anyway - when rounded to only 2 decimals it might even not change anything. I wish I could have helped earlier though, because the way you did you actually had much more work

Keep up the good work

[anita]

Heh, thanks I'm glad that info has been useful then



There are some (very small) inaccuracies in the way you combined the tactics, but the difference between what you obtained and the actual increase is so small that it probably wouldn't even change the numbers. Below is some mathematical explanation of how these can be accurately calculated - but for those who don't like math it might be boring, so I put it in a spoiler tag.

First when you do this:



You are assuming PoE can't proc on both LA hits. The probability of that happening is so small that there is no problem in ignoring it, but if you want to consider it, a simple way to calculate it is to say the basic AV is multiplied by 1.035*1.042 (what you did adds them, instead). Using your own notation, that would be:

AV PoE & LA exp = Basic AV exp * 1.035 * 1.042 (or if you prefer: AV LA exp * AV PoE exp / Basic AV exp)

Same with LA + TaC, the way you did it you're considering TaC can't happen on both hits. The actual increase would be 1.019 * 1.042.

The TaC + PoE procs are actually independent, which means that using only 1.019 + 1.035 = 1.054 as the XP multiplier should already work. This is the same as:

AV PoE exp + AV TaC exp - Basic AV exp

That already gives the correct result. There is no need to use that 0.999335 value - because triple XP when both procs is already the normal behavior of this kind of reasoning.

For the last one you don't need to make the 50% hypothesis thing - in fact, that would be wrong.
The simpler way is to just use the multipliers as in the processes above, the multiplier in this case is 1.042*(1.019+1.035).

So as a summary, here are the multipliers for each tactic combination:

TaC: 1.019
PoE: 1.035
LA: 1.042
T/P: 1.019 + 1.035
T/L: 1.019 * 1.042
P/L: 1.035 * 1.042
T/P/L: (1.019 + 1.035) * 1.042

Anyway, again, the differences between the numbers above and the ones you got would be very small anyway - when rounded to only 2 decimals it might even not change anything. I wish I could have helped earlier though, because the way you did you actually had much more work

Keep up the good work

Thank you very much for this, I was hoping someone would point out the mistakes I might have made. I'll correct it as soon as I come back from vacation (September).

[Yez]

Doing 1,000 1 stams will post results with % of getting 1-4 experience and the average overall gain.

Ended up doing 777 1 stam hits.

Break Down:
777 Attacks
Gains:
1: 201
2: 162
3: 208
4: 206

Total Exp Gain: 1973
Average Exp Gain: 2.54 (rounded a thousandth up)
Average Exp Gain/SP: 1.27 (rounded a thousandth up)

And a nice pretty chart:

One Stam.jpg

edit: Both the one and twenty are allowed for having 7 LSI so no gains of PoE/LA are factored in. Nor is TaC added.

[Yez]

There will be more but this is off of 100 - 20 Stam hits.

Break Down:
100 Attacks
Gains:

Total Exp Gain: 6208
Average Exp Gain: 62.08
Standard Deviation: 20.68
Avg Exp Gain/Stam: 3.104
Avg Exp Gain/SP: 1.552

And a nice pretty chart!:

20 Stam.jpg

[squirrelbait]

The probablity of autolevel is approximately given by

Probability = .5 * (-1 + erf( (14-elsi*xpppt) / (0.5701 * sqrt(2) * sqrt(numattacks) ) ) )

This assumes that you are getting the vast majority of your xp from 20 stam attacks, although missions dont break the formula much. Large numbers of 5 stam attacks and 1 stam attacks will alter the results unfavorably. This formula also assumes that no xp enhancing tactics are used. XP enhancing tactics will improve the probablility

Variables and Notation

erf is the Error Function
elsi is effective lsi = (total stam) * 2 + (total energy) + 1 Notice this uses total stam/energy not base. The +1 assumes that you are in an alliance and burning honor on raids.
xpppt is xp per stat pt spent on stam. Approximately 1.5 as determined by Yez (1.552 may give more accurate results)
numattacks is the number of 20stam attacks you can make. = (total stamina)/20