Sith Assassin Deception analysis

[Alratan]

I'll admit, I have not the time, inclination or expertise to check your maths in detail, so I'll have to restrict myself to more general commentary. Therefore: how does the required damage change as our Surge value increases? If you're not aware, Surge increases the damage of all criticals, and let's assume for the sake of argument that we can get gain up to an extra +100% damage on all criticals (for a total of +200% for melee crits and +150% for force crits) from top-level gear.

[Kaedis]

Does Surge not stack with Crackling Blasts? I would assume that with 100% surge, both melee and force attacks (well, at least Shock and Discharge) with do 300% of base damage.

I'll run some calcs assuming both.

Edit: Ran the calcs. Assuming Surge is an additive increase in crit damage (so it doesn't do funky stuff like the crit damage metas do in WoW), we get the following graphs of threshold damage vs. effective crit damage, for Surge stacking with Crackling Blasts and not, respectively. For the non-stacking, all I did was assume that any Surge below 50% would not apply to a force attack. In other words, that Crackling Blasts gave Shock and Discharge a free 50% surge that didn't stack with regular Surge, just taking the higher of the two bonuses.





The take-away from this is that it really doesn't change much. Even at 500% effective crit damage (something that should be WAY WAY out of reach), it only drops the threshold to 136.1% of Thrash's damage. Honestly the only reason it changes anything at all is because melee and force attacks have a different effective crit chance (26.57% vs. 20%). The higher melee crit chance is compared to force crit chance, the lower the threshold. Theoretically with zero difference between physical and force crit chance, base crit damage, and Surge calculations, Surge wouldn't change a thing.

There's a slight possibility that Crackling Strike will be additive after Surge is applied, and that Surge will be multiplicative with the base crit damage. This could manifest in one of two ways. For these examples, I'll assuming a 20% Surge bonus.

Surge could apply as a multiplicative bonus to the crit damage bonus (this is more likely than the second option). In this case, you'd see the following:

200% base crit: 100% additional crit damage * 1.2 (surge) = 120% crit bonus = 220% total crit damage
-> 1.0% Surge = +0.5% total crit damage, +1.0% of base damage to crits

150% base crit: 50% additional crit damage * 1.2 (surge) = 60% crit bonus = 160% total crit damage + 50% (CB) = 210% total crit damage
-> 1.0% Surge = +0.25% total crit damage, +0.5% of base damage to crits.


The second possibility is that Surge acts as a flat multiplier on total crit damage:

200% base crit: 200% crit damage * 1.2 (surge) = 240% total crit damage
-> 1.0% Surge = +1.0% total crit damage, +2.0% of base damage to crits.

150% base crit: 150% crit damage * 1.2 (surge) = 180% total crit damage + 50% (CB) = 230% total crit damage
-> 1.0% Surge = +0.75% total crit damage, +1.5% of base damage to crits.


In either case, this would drastically affect the threshold calculations, as crit damage would scale differently with Surge for physical and force attacks. This would ONLY be true if Surge is multiplicative in one of these two ways with crit damage, rather than additive, and if that multiplicative equation did not take into account Crackling Blasts before the surge damage calculation.

Edit 2: In other words, the crit damage formula could easily be any one of the following patterns. The examples assuming 50% CB, 150% base multiplier, 20% surge.


BaseDamage * (BaseBonus * (1 + SurgeBonus) + StaticBonus + 1)
X * (0.5*1.2 + 0.5 + 1) = 210%

BaseDamage * (BaseBonus + StaticBonus + SurgeBonus + 1)
X * (0.5 + 0.5 + 0.2 + 1) = 220%

BaseDamage * ((1 + BaseBonus) * (1 + SurgeBonus) + StaticBonus)
X * (1.5*1.2 + 0.5) = 230%

BaseDamage * (BaseBonus + StaticBonus + 1) * (1 + Surge Bonus)
X * (0.5 + 0.5 + 1) * 1.2 = 240%

[Anubis Black]

Abilities have a base critical strike damage bonus of 50%, i.e. critical strikes deal 150% of the damage normal hits do. Crackling Blasts adds 50% to your critical strike bonus damage, making it a total of 100%, or 200% of normal hits. Surge rating is also additive with the above two, so if you have enough for 5% critical strike bonus damage, this will total 105% or 205% of normal hits. It is all very simple and additive, in your own notation

(09-21-2011 03:56 AM)Kore Wrote:  BaseDamage * (BaseBonus + StaticBonus + SurgeBonus + 1)
X * (0.5 + 0.5 + 0.2 + 1) = 220%

It is hard to get high values of crit bonus damage, due to Surge being relatively scarce on gear and possibly requiring a high amount of Surge rating for 1% bonus damage. The example of a lvl. 50 Smuggler shows a mere 3.53% crit bonus coming from Surge, even though we are talking about PvP gear and possibly not fully optimized. I highly doubt a value of 20% will be achievable with entry level raiding gear, let alone astronomical values like 100%. Hopefully the new build will have more high end items that we can base our numbers on. For now I would assume an optimal amount of 15% or less.

[Kaedis]

Good to know, though as I noted it really doesn't affect the balance point for delaying Discharge. Anubis, do you have any ideas as to the damage formulae in that workshop you have behind the curtains? I've pulled coefficients for all of the deception abilities out of the XML dump, but I can't seem to find a solid 'standard health' that works for them like in the healing thread. Then again, I may be using the wrong damage numbers. Do you know of a source that gives the tooltip damage values for at least two of the Deception abilities, relevant stats, and character level all for the same character? That would go a long ways towards figuring out the formulae.

[Anubis Black]

My first recommendation is to work with this video: http://www.multiupload.com/L04EY8PUAU It is a ~90min. Assassin gameplay video, where you can see what damage each ability does, its tooltip and possibly the character screen. I thought I had made a table with all the information, but when I searched my files, I couldn't find it. It was when I was working on tooltip damage discrepancy, but I was also checking how WP affects abilities' damage. I hope it helps. The second video I thought of, was http://www.youtube.com/watch?v=5ouv8_XE-go where you can see the stats at ~55sec. in and most of the abilities' tooltips if you can pause really fast : )

[Gorodetski]

• Assassinate, a high-damage attack usable on enemies with low health, has been added.

from the latest Patch Notes.... Sithstep anyone? *crosses fingers*

[Pred]

Biggest thing for me is we basically just received WoW Rogue's Vanish! Bring on the pvp!

[Gorodetski]

(09-24-2011 11:35 PM)Pred Wrote:  Biggest thing for me is we basically just received WoW Rogue's Vanish! Bring on the pvp!

frak yeah I'll SSOO be using that to get annoying Dps killed like I used to do with Pally Bubble.

question is, will Sithstep be usable for Tanks?

[Anubis Black]

To get back on track with proper theorycrafting, I just went over some of your numbers, Kore, and I would like to ask you some questions.

Just to make it clear to people who might not have been following you, in this post and in this post you have been concentrating on calculating the probability that X charges will be up at the end of a 12sec. cycle that includes 4 x VS, 2 x Shock and 1 x Maul. The charges you refer to are based on the talent Static Charges that grants you a 100% chance to increase the damage dealt by Discharge, every time a Surging Charge deals damage. All successful attacks have a 25% chance to proc Surging Charge.

Firstly, you assume that VS has a single chance to proc Surging Charge and respectively build a Static Charge. Thus, since it deals two attacks, from your assumption it follows that



is the chance you will get one proc from a VS. I am not sure how you get 37.5%, but for the following I assumed you were right and the chance was indeed 0.375.

Your second assumption is that Poisson binomial is the correct distribution that represents the amount of charges up at the end of the cycle. It seems like a solid assumption, considering we have a different chance of success and we are dealing with a form of a Bernoulli trial. But could you provide some further arguments? Is this really the best way to model this case? Regardless, for the following I assumed a Poisson binomial.

Here is where my actual questions lie. Do you assume VS has a 37.5%, and Shock and Maul- a 25% chance each to proc a charge? Then, using the recursive formula for Poisson binomial



Where



I get

0 charges: 6.44%
1 charge : 21.89%
2 charges: 31.51%
3 charges: 24.89%
4 charges: 11.65%
5 charges: 3.62%

I haven't run the calculations using 43.75% chance for VS, since I initially considered 37.5% to be correct. So am I missing something? I get a completely different set of outcomes. In addition, could you please explain your second and third tables?

P.S. As for the Sith Assassin video, I will post a spreadsheet in a new thread with a formula Beliel suggested that matches the data really well.

[Kaedis]

Quote:Firstly, you assume that VS has a single chance to proc Surging Charge and respectively build a Static Charge.

Yes, I assumed two chances at a proc, but an internal CD on Surging Charge of 1.5 seconds, and therefore no more than a single proc per VS. I originally noted 37.5% because I had misapplied the percentage chance (that, I believe, was 25% + 25/2%. Don't ask me where that came from, I ran the calcs for that post very late at night). The math in my later post uses the 43.75% chance rather than the 37.5% chance.

Quote:Your second assumption is that Poisson binomial is the correct distribution that represents the amount of charges up at the end of the cycle. It seems like a solid assumption, considering we have a different chance of success and we are dealing with a form of a Bernoulli trial. But could you provide some further arguments? Is this really the best way to model this case? Regardless, for the following I assumed a Poisson binomial.

Well, frankly, it was simply that. It's a Bernoulli trial system, which means by default it should be a binomial system (since it isn't a discrete count average, such that you would use a Poisson distribution), and a standard binomial requires a static proc chance among all events. A Poisson binomial distribution is the same for different proc chances, hence my use of it. I'm not sure what other distribution would potentially be more appropriate, to be honest.

Quote:Here is where my actual questions lie. Do you assume VS has a 37.5%, and Shock and Maul- a 25% chance each to proc a charge? Then, using the recursive formula for Poisson binomial

That's how I did it. I wrote a C++ program for it rather than manhandle it with Excel where I'd done most of the other calculations. I've attached the code for the program at the end of this post. I did however assume a 43.75% chance on VS, not 37.5%, and I assumed Shock, being a force ability rather than a physical ability, could not proc it.

The second and third tables were based on the supposition that it may be advantageous to delay Discharge for one or more additional GCDs to get in additional VS attacks for more charges to amplify Discharge's damage. Thus the second and third table are adding one and two additional GCDs (respectively) into the cycle. I did however assume that the additional GCDs would be filled at a 2:1 ratio with VS and Shock (and thus using a sliding rotation around discharges rather than an identical iteration each cycle), rather than pure VS's, to take advantage of the benefit VS gives to shock. Thus the additional GCDs were granted an averaged 29.2% proc chance (43.75% * 2/3) rather than the full 43.75%.

The Poisson binomial code is fixed below. The output prints chances of k procs, not k charges. If n > 5, you'll need to add the chance of all procs >= 5 to get the chance of 5 charges per discharge. I was too lazy at the time of writing to throw in a variable to collect and add them together. The PROBS array defines the chances of procs occurring, with optional GCDs listed last. The array, in order, refers to Maul, 4 VS's, then two extra GCDs.

I just re-ran the code to check it, and I'm still not getting the values you did, even when I ran it with n = 7 and changed the last two digits of the array to 0.25 to assume Shock procs. Perhaps you can check my code and see if I'm misinterpreting the equation or miscoding the calculations somehow.

Code:

const int DEFINED = 7;
const double PROBS[DEFINED] = {0.25, 0.375, 0.375, 0.375, 0.375, 0.292, 0.292};

double p(int k, int n);

// ============================================================================
int main()
{
    int n = 0;
    
    do
    {
        cout << "Enter n: "; // Number of GCDs per cycle, defined in PROBS
        cin >> n;
        if(n && n <= DEFINED)
            for (int k = 0; k <= n; k++) // chance of k procs
                cout << "k = " << k << ": " << p(k, n) << endl;
        else if(n)
            cout << "Invalid, n must be less than or equal to " << DEFINED << endl;
    }
    while(n);
    return 0;
}
// ============================================================================

// ----------------------------------------------------------------------------
double p(int k, int n)
{
    double result = 0.0;
    double jresult = 0.0;
    
    if(k) // k > 0 case
        for(int i = 1; i <= k; i++) // First summation
        {    
            jresult = pow((PROBS[0]/(1 - PROBS[0])),i); // j = 1
            for(int j = 2; j <= n; j++) // Second summation
                jresult += pow((PROBS[j - 1]/(1 - PROBS[j - 1])),i);
            result += pow(-1.0,i - 1) * jresult * p(k - i,n);
        }
    else // k = 0 case, executed on final recursive function call
    {
        result = 1 - PROBS[0]; // i = 1    
        for(int i = 2; i <= n; i++)
            result *= (1 - PROBS[i - 1]);
    }
    return k ? result/k : result;
}
// ----------------------------------------------------------------------------

Edit:

Quote:P.S. As for the Sith Assassin video, I will post a spreadsheet in a new thread with a formula Beliel suggested that matches the data really well.

This make me happy in the pants. I've got all of the coefficients and such from the XML, I just haven't had the time to try to dig out a formula to use them. Now I can start some serious applicable theorycrafting.