Defining the Problem
Grasp + Claws
We have a 50% chance of hitting a person for 3 damage. Upon hitting the person, we grasp the person. Further claw hits will land at 60% probability, with a 20% chance of missing and losing the grip, and a 20% of missing and retaining the grip. We need to find the average damage inflicted on the person on a long run.
Grasp + Bite
We have a 50% chance of hitting a person for 3 damage. Upon hitting the person, we grasp the person. Further bites will land at 40% probability, infilicting 4 damage. We also have a 30% chance of missing and losing the grip, and a 30% of missing and retaining the grip. We need to find the average damage inflicted on the person on a long run.
Solving the Problem
We have two states, State 1 being the lack of tangling grasp and State 2 having tangling grasp active. We calculate the probability of staying in a state for n number of hits, and find the value to which it tends to.
Grasp + Claws
| A
|
B
|
C
|
D
|
E
|
F
|
| Attack #
|
Probability of staying in State 1
|
Probability of staying in State 2
|
Chance of a hit from State 1
|
Chance of a hit from State 2
|
Total Damage inflicted on hit
|
| A = A n-1 + 1
|
B = (B n-1 * 0.5) + (C n-1 * 0.2)
|
C = (B n-1 * 0.5) + (C n-1 * 0.8)
|
D = (B n * 0.5)
|
E = (C n * 0.6)
|
F = 3 * (D n + E n)
|
| 1
|
1
|
0
|
0.5
|
0
|
1.5
|
| 2
|
0.5
|
0.5
|
0.25
|
0.3
|
1.65
|
| 3
|
0.35
|
0.65
|
0.175
|
0.39
|
1.695
|
| 4
|
0.305
|
0.695
|
0.1525
|
0.417
|
1.7085
|
| 5
|
0.2915
|
0.7085
|
0.14575
|
0.4251
|
1.71255
|
| 6
|
0.28745
|
0.71255
|
0.143725
|
0.42753
|
1.713765
|
| 7
|
0.286235
|
0.713765
|
0.1431175
|
0.428259
|
1.7141295
|
| 8
|
0.2858705
|
0.7141295
|
0.14293525
|
0.4284777
|
1.71423885
|
| 9
|
0.28576115
|
0.71423885
|
0.142880575
|
0.42854331
|
1.714271655
|
| 10
|
0.285728345
|
0.714271655
|
0.142864173
|
0.428562993
|
1.714281497
|
| 11
|
0.285718504
|
0.714281497
|
0.142859252
|
0.428568898
|
1.714284449
|
| 12
|
0.285715551
|
0.714284449
|
0.142857776
|
0.428570669
|
1.714285335
|
| 13
|
0.285714665
|
0.714285335
|
0.142857333
|
0.428571201
|
1.7142856
|
| 14
|
0.2857144
|
0.7142856
|
0.1428572
|
0.42857136
|
1.71428568
|
| 15
|
0.28571432
|
0.71428568
|
0.14285716
|
0.428571408
|
1.714285704
|
Grasp + Bite
| A
|
B
|
C
|
D
|
E
|
F
|
| Attack #
|
Probability of staying in State 1
|
Probability of staying in State 2
|
Chance of a hit from State 1
|
Chance of a hit from State 2
|
Total Damage inflicted on hit
|
| A = A n-1 + 1
|
B = (B n-1 * 0.5) + (C n-1 * 0.3)
|
C = (B n-1 * 0.5) + (C n-1 * 0.7)
|
D = (B n * 0.5)
|
E = (C n * 0.4)
|
F = (3 * D n) + (4 * E n)
|
| 1
|
1
|
0
|
0.5
|
0
|
1.5
|
| 2
|
0.5
|
0.5
|
0.25
|
0.2
|
1.55
|
| 3
|
0.4
|
0.6
|
0.2
|
0.24
|
1.56
|
| 4
|
0.38
|
0.62
|
0.19
|
0.248
|
1.562
|
| 5
|
0.376
|
0.624
|
0.188
|
0.2496
|
1.5624
|
| 6
|
0.3752
|
0.6248
|
0.1876
|
0.24992
|
1.56248
|
| 7
|
0.37504
|
0.62496
|
0.18752
|
0.249984
|
1.562496
|
| 8
|
0.375008
|
0.624992
|
0.187504
|
0.2499968
|
1.5624992
|
| 9
|
0.3750016
|
0.6249984
|
0.1875008
|
0.24999936
|
1.56249984
|
| 10
|
0.37500032
|
0.62499968
|
0.18750016
|
0.249999872
|
1.562499968
|
Emperic Testing
This simple C# program was run multiple times to verify the above calculated values. The results were as expected.
Random r = new Random();
int hits = 0;
for (int i=0; i<Convert.ToInt32(textBox1.Text); i++)
{
int nextRnd = r.Next(0,100);
if (state == 1)
{
if (nextRnd < 50)
{
state = 2;
hits += 3;
}
}
else if (state == 2)
{
if (nextRnd < 60)
{
state = 2;
hits += 3;
}
else if (nextRnd >= 60 && nextRnd < 80)
{
state = 2;
}
else if (nextRnd >= 80)
{
state = 1;
}
}
}
textBox2.Text = hits.ToString();
Conclusion
As we can see, the probability of Grasp + Claws tends an average DPS of 1.71429.
On the other hand, the probability of Grasp + Bite tends to an average DPS of 1.5625.
Thus, it's better to use claws to grasp and keep clawing.
Result for all Combinations
Well, I decided to go the full monty and finish all the possible combinations of Tangling Grasp and n skills. They are compiled here. The xls on which I did all the calculations will be put up on my site soon.
| Skills
|
Method of Attack
|
Damage / AP
|
| Vigour Mortis + Tangling Grasp
|
Bite
|
0.95
|
| Vigour Mortis + Tangling Grasp
|
Claw
|
0.824857
|
| Vigour Mortis + Neck Lurch + Tangling Grasp
|
Bite
|
1.184615
|
| Vigour Mortis + Rend Flesh + Tangling Grasp
|
Claw
|
1.218
|
| Vigour Mortis + Death Grip + Tangling Grasp
|
Claw
|
1.142857
|
| Vigour Mortis + Rend Flesh + Neck Lurch + Tangling Grasp
|
Bite
|
1.346154
|
| Vigour Mortis + Death Grip + Neck Lurch + Tangling Grasp
|
Bite
|
1.375
|
| Vigour Mortis + Rend Flesh + Death Grip + Tangling Grasp
|
Claw
|
1.714286
|
| Vigour Mortis + Rend Flesh + Death Grip + Neck Lurch + Tangling Grasp
|
Bite
|
1.5625
|
| 