Confusion and XP/Time, Teh Maths.

Enantiodromos · 12-27-2005 01:15 PM

CONFUSION AND XP/Time

I've returned from a hiatus, and was shocked to discover that everybody's STILL beating this dead horse. Now, C-force has a nice FAQ on the boards about this, a section of which goes over the below. I've decided to reproduce that section here, so that I can link people directly to my views, which is not to say that you shouldn't go read Cforce's FAQ. (Tried to post this a few minutes ago, and it didn't go. ::shrug:

HOW EXPERIENCE WORKS GENERALLY

Where:
X = Experience value of (average) spawn
D = fraction of the spawn's damage done by you, where 1 = 100%.

Under normal circumstances, everybody who damages a mob "takes" a share of that mob's experience yeild (X), proportional to the damage they do (D). That means if you and an unteamed stranger each do half the damage to a mob, and it's defeated, you each get half the experience value. Earned experience (Xp) is equal to the mobs's experience value times the fraction of damage you do to it.

Xp = DX

Ordinarily, you do all the damage to a mob, so D=1, in which case:

Xp= X (Duh!)

HOW EXPERIENCE OVER TIME WORKS GENERALLY

Where:
F = ("Fight") time each spawn takes to fully defeat
S = ("Search") time it takes after each fight to find the next fight
T = ("Time") fight plus search time = F+S

Experience per time (Xppt) is equal to experience value of the spawn (X) dividied by total time (T). Total time is a function of how long it takes to defeat a spawn (F) plus time between fights (S):

Xppt = X/T = X/(F+S)

HOW CONFUSION EXPERIENCE WORKS

Where:
Cmd = fraction of spawn's damage done by confused mobs (where 1=100%) = 1-D

When mobs are partly damaged by other confused mobs, thier experience value (Cx) is equal to the mob's base experience value times the fraction of the mob's damage once you EXCLUDE three quarters of the damage confused mobs did (Cmd) from the mob's base damage.

Cx = DX / (D + (Cmd/4)) = 4DX / (3D + 1)

HOW CONFUSION FIGHT DURATION WORKS

Fight durations depend directly on how much damage has to be dealt to finish the enemy. When they've been damaged by other, confused mobs, the amount of time fights last (Cf) is the normal fight time (F) times the fraction of the damage you yourself have to do (D).

Cf = time a spawn takes to defeat, if it's been damaged by confused mobs = FD.

HOW CONFUSION EXPERIENCE OVER TIME WORKS

Total time with confusions in play (Ct) is a function of how long it takes to defeat a spawn with confusions in play (Cf), plus downtime between fights (S).

Ct = confused fight plus search time Cf+S = FD+S

Experience per time with confused mobs doing some damage (Cxppt) is equal to experience value of the spawn damaged by confused mobs (Cx) dividied by total time with confusions in play (Ct).

Just like ...Xppt = X/T... similarly:

Cxppt = Cx/Ct = 4DX / ((FD+S)*(3D + 1))

DOING AT LEAST AS WELL

What we really want to do is compare normal experience per time (Xppt) to experience per time when confusions are in play (Cxppt). We can find a "break even" point by setting the two figures equal to each other. The break even point is should be a statement about when your experience over time WITH confusions (Cxppt) is the SAME as your experience per time WITHOUT them (Xppt).

Break-even point rule: Xppt = Cxppt

<font class="small">Code:<hr /><pre>
Xppt = Cxppt
X/(F + S) = 4DX / ((DF+S)*(3D + 1)) divide by X
1/(F + S) = 4D / ((DF+S)*(3D + 1)) invert
(F + S) = ((DF+S)*(3D + 1)) / 4D multiply out
(F + S) = (3DDF+3DS+DF+S) / 4D multiply both sides by 4D
4DF+4DS = 3DDF+3DS+DF+S subtract (DF +4DS +3DDF) both sides
3DF-3DDF = S-DS divide both sides by (1-D)
3DF = S
</pre><hr />[/color]

THE TRUTH

So, here's our statement about when your experience over time (Cxppt) WITH confusions is the SAME as your experience per time WITHOUT them (Xppt):

S = 3DF

In english:

Time each spawn takes to fully defeat is equal to three times the fraction of the spawn's damage done by you, times the time each spawn takes to fully defeat.

If you start the next fight faster than that, your XPS is better with confuse than without. If you find them slower, experience over time gets worse.

WHAT DOES THAT PROVE?

Nothing, directly, since we have to be able to judge for ourselves whether we can meet the rule above. But we CAN safely say that if our downtime between fights is short enough, confusion is really helping with XP, to say nothing of being a hold with lots of fringe benefits.

In my experience, groups with any real interest in decent XP over time will EASILY be doing better than the S=3DF rule above. If the group can't manage S=3DF on the average, it's probably because they're doing something IN PREFERENCE to decent XP/time.

And as anyone can see, such a group has no business complaining: "Confusion is hurting our XP!" Because of course, if the group wasn't doing other things that hurt XP/time more, the confusion itself would be *helping* XP/time. If you're not trying to get decent XP, you ought to have no complaints about not getting the best possible XP.

DrLetharga · 12-27-2005 01:34 PM

Thanks for the time you took to post this Enan. I will make sure to use it in my forum-foo whenever the confusion topic comes up again.

Enantiodromos · 12-27-2005 09:00 PM

Oh goldangit. The crucial summation is hosed! ::cry:: it should read:

[ QUOTE ]

In english:

Time it takes after each fight to find the next fight is equal to three times the fraction of the spawn's damage done by you, times the time each spawn takes to fully defeat.

[/ QUOTE ]

MagicalAct · 12-28-2005 04:52 PM

Thank you....To all the groups who dont want me using confuse because of the "Our xp goes down". Once again Thank you lol

Ninja_NA · 12-29-2005 10:45 AM

I spent a lot of time trying to do math and figure out useful stuff to make a contribution, but my algebra skills are rusty and failed me. There are two comments that I'd be interested in hearing your response on.

First comment - you handle reduction in combat time (F) very efficiently, but you don't mention anywhere the reduction in downtime that confuse would contribute (since it both reduces damage from enemies and endurance expenditure, by killing them faster, and also reduces damage from enemies by preventing the confused enemy from attacking you.) That speaks positively for confuse, since it can only improve the ratio, but it seems like it's something that would contribute to the equations. I tried to factor in a variable y that was the ratio by which downtime (S) was reduced. My goal was to calculate the point at which reduction in time exceeded reduction of exp, in terms of y and D.

Secondly, I'm not really clear on how to interpret your final formula, with respect to determining personal effectiveness. It's easy to see how it equals out, but it is difficult to make a statement like "As long as my damage output times 3 = my downtime, I'm ok" or "decreasing my downtime would increase my xpps faster than decreasing my fighting time." Basically, the final equation is hard to put into practical use.

For example:

S = 3DF

If I do 50% of the damage in a fight, that lasts 120 seconds, I get S = 180. So that means if I have 3 minutes of downtime after a 2 minute fight, confuse exp will = normal exp? So if I have a 2 minute fight in which I do 50% of the damage, as long as I don't need more than 3 minutes down time, I'm coming out ahead.

Let's say I fight for 2 minutes and only have 10 second downtime. 10 = 3D(120). That means D = 0.0278. Does this mean that if fights are finishing in 2 minutes, with only 10 seconds of down time, that I only have to do 2.78% of the damage in order to get better xpps than if I were fighting normally? I'm assuming that the formula indicates "If you finish the fight in 2 minutes and only do 2.78% of the damage, that this fight would take 72 minutes normally."

So, it seems like in a 2 minute fight, as long as I do more than 2.78% damage, I'm coming out ahead, and if I do say, 70% of the damage, I'm coming out way ahead.

Let me know if this is an accurate interpretation. Nice work!

Paraflex · 12-29-2005 11:15 AM

[ QUOTE ]
...So, it seems like in a 2 minute fight, as long as I do more than 2.78% damage, I'm coming out ahead, and if I do say, 70% of the damage, I'm coming out way ahead.

Let me know if this is an accurate interpretation. Nice work!

[/ QUOTE ]

/em blinks rapidly and begins to shake.
<head explodes>

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Enantiodromos · 12-29-2005 01:27 PM

1. Right you are-- this was meant to address only the "effect of confusions, or not, on combat." That's based on the assumtions that either you don't have to play with confusion-spamming mind controllers at all, or if you do, the mind controllers can be well-built without doing much with confusions. (Either is true.) So this attempts only to show: does it get worse if somebody's using confusions instead of holds (and, also, discounting badguy buffs to your team, and the minor scatter or cluster you get using it, depending on your skill level and luck.)

Compared with a mind controller contributing with a Brawl/Levitate/AirSuperiority chain, confusions are WAAAAY better.

2.
[ QUOTE ]
If I do 50% of the damage in a fight, that lasts 120 seconds, I get S = 180.

[/ QUOTE ]

Yep. If the fight would last 2 min without confusion, and you do half damage, you've got 3 min to start the next fight. Faster, and your XP improves.

[ QUOTE ]
fight for 2 minutes and only have 10 second downtime. 10 = 3D(120)

I'm assuming that the formula indicates "If you finish the fight in 2 minutes and only do 2.78% of the damage, that this fight would take 72 minutes normally."

[/ QUOTE ]

Sorry, no, F was presented ambiguously, wasn't it? F is the time it would normally take to defeat the mob in a fight without confusion running.

If there were some fight that you could normally finish in 2 minutes, and you popped mass confusion and, say, Gale at Acc,Acc,Dmg,Dmg,Dmg, to get in your 2.7% damage on the group, and then could move on to the next group in 10 seconds and do the same thing with mass confusion, you'd be steadily making equivalent XP per time on what amounts to microdamage.

Mind you, I think we've crossed the bounds of realistic S over the course of normal, serial XP persuit, when we set it at 10 seconds. Also, you'd need to be weilding Mass Confusion to get scenarios like that, and I'm thinking it wouldn't always be back up in time.

[ QUOTE ]
if I do say, 70% of the damage, I'm coming out way ahead.

[/ QUOTE ]

Remember, none of this speaks to *how much* better the XP would be if you were getting in more than your 2.7%.

To generalize, Cxppt/Xppt -1 is the % bonus to XP you get (Cb).

Cb= Cxppt/CXppt = (4D(F+S) / ((FD+S)*(3D + 1)))-1

... anyhow. I can't see how to simplify that further ATM. Let's take a couple cases.

Ocb (optimum Cb) = highest value for Cb obtainable with a D between 0 and 1.

Od (optimum D) = D between 0 and 1 that obtains highest value for Cb.

Where
F=120
S=10

Cb ~= (26D / (18DD +7.5D+1)) -1
Ocb= +62.5%
Od = .25

Where
F=30
S=30

Cb= 8D/(3DD+4D+1) -1
Ocb ~= +7.2%
Od ~=.58

You're right. It's not easy to see the useful rule in this. Or at least, I'm not, yet.

Ninja_NA · 12-29-2005 01:37 PM

Hehe, thanks for clarifying. Nice post too. I do <3 math, even if I don't have any regular opportunities to practice it lately.

Local_Man · 12-29-2005 02:20 PM

Nice, nice work on the formulas (and I actually followed it, as many moons ago, I was a math major). However, this to me is almost more like economics, in that so many factors have to be "assumed," that these calculations are more like an educated guess than an absolute.

I love Deceive/Confuse. Even if it cost XP per minute, I would still use it because it is so much fun. However, I have to give one point to the naysayers. In a given mission, there is usually a certain amount of XP. Ignoring the time element, using Deceive/Confuse will in fact reduce the total XP available to the team, even if it may help the team complete the mission faster. Personally, I believe it is a very small reduction, as confused bad guys cause a very small percentage of the overall damage.

On the other hand, Deceive/Confuse can be a big part in avoiding debt. If you assume (there is that word again!) that the team has avoided one or more deaths thanks to the use of Deceive/Confuse, then you have to add that damage back in. It is also very hard to quantify the other benefits of Confuse/Deceive, in terms of changing enemy debuffs into your team's buffs, etc. How do you calculate the benefit of changing a Sky Raider's Force Field from the bad guys to your team? It increases the damage you are able to do to the enemy, while decreasing the damage done to your team, but on a nearly random basis.

Another aspect that is impossible to quantify is the effect of the power being used by an experienced, skilled player or a novice. Add to all this the key point that you are making, that Confuse/Deceive lets you do more damage faster, allowing you do complete more missions (or more hunting) faster, and it is easy to see that teams are going to be better using Confuse/Deceive than not using it.

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Dwimble · 12-30-2005 09:51 AM

Nice work, Enantiodromos, and thanks for all the effort you put into that.

And for those who would like a simple illustration of the actual percentage of XPs you get when you and your team "share" the damage with confused mobs, here's the chart I posted in cforce's guide (note this only shows the actual percentage given per mob...it doesn't take into account any of the time factors outlined by Enantiodromos):

Experience Rewards for Confuse

Controller___Confused__"Bonus"____"Lost"______Controller
Damage____Damage____XPs________XPs_______XPs
1%..............99%............2.88%..........96.12% ............3.88%
5%..............95%...........12.39%..........82.61% ..........17.39%
10%............90%...........20.77%..........69.23%.. ........30.77%
15%............85%...........26.38%..........58.62%.. ........41.38%
20%............80%...........30.00%..........50.00%.. ........50.00%
25%............75%...........32.14%..........42.86%.. ........57.14%
30%............70%...........33.16%..........36.84%.. ........63.16%
33.33%.......66.67%......33.33%........33.34%........66.66%
35%............65%...........33.29%..........31.71%.. ........68.29%
40%............60%...........32.73%..........27.27%.. ........72.73%
45%............55%...........31.60%..........23.40%.. ........76.60%
50%............50%...........30.00%..........20.00%.. ........80.00%
55%............45%...........28.02%..........16.98%.. ........83.02%
60%............40%...........25.71%..........14.29%.. ........85.71%
65%............35%...........23.14%..........11.86%.. ........88.14%
70%............30%...........20.32%............9.68%. .........90.32%
75%............25%...........17.31%............7.69%. .........92.31%
80%............20%...........14.12%............5.88%. .........94.12%
85%............15%...........10.77%............4.23%. .........95.77%
90%............10%............7.30%............2.70%. .........97.30%
95%.............5%.............3.70%............1.30% ..........98.70%
99%.............1%.............0.75%............0.25% ..........99.75%

From the chart you can see that you get the most "work" out of the confused mobs when you do one third damage. That is when you get the highest "bonus" XPs (i.e. the most XPs credit for damage you didn't do). One third damage gets you two thirds of the XPs. That's when you're getting the best work-to-XPs ratio.

A personal note: Although I can understand the limitation forcing you to share damage in order to get XPs (to prevent exploits), I'd still like to see the percentages increased a little more, or them give a very small amount even if you do none of the damage at all. Leveling a mind controller can be a bit slow when compared to the other controllers, who get 100% of their pets' XPs. My gravity controller constantly gets XPs for mobs I never touch...or even see for that matter, but from the numbers Enantiodromos posted, they can still potentially level fast in spite of it, so maybe that invalidates my point. Still, in any case, Confuse has a definite "fun factor" that's hard to beat regardless of the XPs given.

Dwimble

Enantiodromos · 12-30-2005 01:04 PM

Now, for something wildly beyond even my attention span.

To find Od based on F and S, what you do is find the derivative of Cxppt/Xppt -1 , then set it equal to zero.

(derivative with respect to D)(Cxxpt/Xppt -1) =(4(F+S)(3FDD + 3SD - 5FD -F -3S -1))/((FFDD+SS+FSD)(9DD+6D+1) + FSD(9DD+6D))

I'm totally out of the habit of even simple calculus tricks like the quotient rule, so that was a lot of error prone work in the first place, and I might have made a mistake. Assuming I didn't, though, you set that baby equal to zero, and solve it for D, and you'll have the perfect rule for how much damage you want to do to optimize XP.

>.>

Dang. I still have to be on the clock another hour and a half.

Ninja_NA · 12-31-2005 01:36 PM

I wonder if I can make my TI-83 do this..