Protection Theory from the Protection leader (in General)

In case anyone was curious :)

I knew that if I tracked statistics on Protection long enough, a pattern would emerge. At high levels of the spell, a clear pattern has emerged whereby I can predict the next effect levels.

First, let's define our terms.

level = the big number. the one not in parentheses. (e.g. in "173,348 (27)", 173,348 is the level)
effect level = the little number. the one in parentheses (e.g. in "173,348 (27)", (27) is the effect level)

X = the "next" level of Protection (i.e. the one we are trying to predict)
A = the "current" level of protection (i.e. the one we are working with)
B = d/dx A (i.e., the difference between the current level of protection and the one prior to it)
C = d/dx B (i.e., the difference between the current difference and the one prior to it. the "acceleration" if you will)
D = the acceleration of the previous protection level.

Now the formula is:

X = A + B + C + D

This formula works for all current protection data that I have from effect level (22) through (28) within +/- 1%. It works for the lower levels but with more error. According to the formula, the next protection level should be 273,800 (29), again, give or take 1%. After that I probably won't reach (30) until level 361,000 or so.

I'll post a new Excel spreadsheet with my findings later on tonight ...

That sounds about right, considering what I've seen as I advance Protection levels. =)

I forgot to post a few other important items.

First, my current data table is available here:
http://poingenterprises.com/Chris/cb/cb2prot.htm

Second, I am always on the lookout for better level numbers. When I say "better" I mean the smallest possible level you can have and still have the effect level in parentheses.
(e.g. "173,348 (27)" and "174,664 (27)" are both true in terms of game play, but "173,348 (27)" is better because the level number is smaller)

I firmly believe that the majority of my error is due to having numbers which are too large, especially for (14) and probably for (16) through (20) as well. Any numbers that you can provide for these effect levels would be greatly appreciated. Remember this is purely in the name of science :)

With that in mind, here's my first data table using the formula. Enjoy :)

Protection Level	Effect	Difference	Diff of Diff	Formula (predicted value)	% Error
0	(4)	0	0	N/A	N/A
1,100	(5)	1,100	1,100	N/A	N/A
3,126	(6)	2,026	926	3,300	5.27%
4,943	(7)	1,817	-209	7,178	31.14%
7,081	(8)	2,138	321	7,477	5.30%
9,394	(9)	2,313	175	9,331	0.68%
11,919	(10)	2,525	212	12,203	2.33%
14,822	(11)	2,903	378	14,831	0.06%
17,682	(12)	2,860	-43	18,315	3.46%
21,133	(13)	3,451	591	20,877	1.23%
26,293	(14)	5,160	1,709	25,132	4.62%
28,761	(15)	2,468	-2,692	33,753	14.79%
33,118	(16)	4,357	1,889	30,246	9.50%
38,452	(17)	5,334	977	36,672	4.85%
43,856	(18)	5,404	70	46,652	5.99%
50,298	(19)	6,442	1,038	50,307	0.02%
57,830	(20)	7,532	1,090	57,848	0.03%
66,273	(21)	8,443	911	67,490	1.80%
76,293	(22)	10,020	1,577	76,717	0.55%
88,710	(23)	12,417	2,397	88,801	0.10%
103,130	(24)	14,420	2,003	105,101	1.88%
121,048	(25)	17,918	3,498	121,950	0.74%
143,659	(26)	22,611	4,693	144,467	0.56%
173,348	(27)	29,689	7,078	174,461	0.64%
214,369	(28)	41,021	11,332	214,808	0.20%
273,800	(29)	59,431	18,410	273,800	0.00%
362,973	(30)	89,173	29,742	362,973	0.00%
500,298	(31)	137,325	48,152	500,298	0.00%
715,517	(32)	215,219	77,894	715,517	0.00%
1,056,782	(33)	341,265	126,046	1,056,782	0.00%

(Bold/yellow cells indicate predicted values only!)

I put the new data up on the web page:

http://poingenterprises.com/Chris/cb/cb2prot.htm

The yellow numbers are predicted values. The graphs only graph the verified data. If my numbers are correct .... It's gonna be time to stop training Protection soon ;)

haha this data is sure helpful to show jon how ridiculously huge level needed for a mere 33 protection, so he can plan his next change month :)

No, I seriously doubt that Jon will change Protection. I have a feeling that, balance-wise, Protection operates exactly as it's meant to.

I'm highly inclined to believe the theory that in CB2, Protection's effect level is a straight percent-off of the damage your minions take, which makes it extremely powerful. He's said once before that incoming damage is taken off in a certain order, which if I remember correctly, is Protection, ToE, and then AC. But no matter what order it's taken off, Protection is a powerful spell as-is, and I Jon will probably see no reason to change it.

damage reduction changed to AC/Endurance/Protection, in that order

--Jonathan, May 3 2005 1:43 PM EDT

I've long been a fan of the straight-percent-reduction theory. It makes sense to have protection last in this case because AC & ToE have a fixed-reduction element to them.

That brings me to another point: why is AC listed in post-battle stats? The only reason I can think of is that it's a remnant from CB1. As comforting as it is to know that my AC is still the same as before battle, I'm not sure it's entirely necessary. ;)

AC is shown in battle stats because it is shown in home page/character info thing.

just like HP st dex are shown with stats.

HP, ST and DX can change during battle, and from one battle to the next. The PBS shows what has changed from before the battle starts. The only stat that can not and will not change is AC. I doubt anyone can give me a good reason it should be there.

To elaborate, the CB1 version of Protection was a direct increase of AC. That made it relevant in PBS. Obviously that doesn't hold in CB2.

it is there because it shows up as a stat when doing character view, the reason it does not change is because nothing can lower ac.

VB just makes dmg reduction reduced by .40% of w/e the dmg reduction is.

So there is no way for ac to change.

Just got a new number!! :)

Protection: 272,557 (29)

This only differs from the formula's predicted value by 0.46% :)

That's awesome, but it stinks as well, in a way. I had intended to stop at 33% reduction. Not a chance of that now. ;)

28% damage reduction for about 200k skill point investment isn't bad at all though....

But the corollary is that it is all useless xp if your fighting someone with a decent sized DM. So even if it gave 75% reduction it would still be useless vs a lot of characters. Unless you use a ROS, then it is quite a powerful investment.

Similarly, having decay is useless against a big AMF. Which is is why counterbalancing skills is pretty important. big AMF and big DM are mutually exclusive. So... if you have two skills trained on your team, each of which takes advantage of the lack of one of those skills from your opponent, you will always have something to bring to the table.

At 200k skill points, that's a pretty big fork to bring for a relatively modest investment.

I have enough new data to justify an update. Thanks to the hard work of jayuu and NightStrike, I have a lot of new data and better numbers. Thanks, guys!

Here's the new sheet. Enjoy.

Numbers in bold indicate exact numbers: the absolute lowest level you can have to get the desired effect. Getting these numbers is quite time-consuming, and so I thank both of you immensely.