Requesting math help

[Steamboat]

This is probably simple math, but I'm horrible at math so I'm asking:

I'm trying to figure what my average shadowbolt will hit for with different builds. I have a damage calculator that shows my min and max shadowbolts based on my gear, both crit and non-crit. I'm trying to figure what my overall average shadowbolt will hit for, including crits and with different crit rates.

Example:
With SM/Ruin, my min non-crit is 834, my max non-crit is 902. My min crit is 1669, and my max crit is 1803. With a 15% crit rate, what does my average shadowbolt hit for?

With SL and a sacrificed/rezzed pet, my min non-crit is 960, my max non-crit is 1037. My min crit is 1439, and my max crit is 1555. My crit rate is 10%. What does my average shadowbolt hit for?

With SL and just a sacrificed pet, my min non-crit is 890, my max non-crit is 962. My min crit is 1335, and my max crit is 1443. My crit rate is 10%. What does my average shadowbolt hit for?

Thank you

[Ebgreen]

minNCrit = Min Non-Crit
maxNCrit = Max Non-Crit
minCrit = Min Crit
maxCrit = Max Crit
cr = Crit Rate as a decimal. So 15% crit = .15

Average damage = (1-cr)(maxNCrit + minNCrit)/2 + cr(maxCrit + minCrit)/2


That should be right. Just an Expected Value calculation.

[Steamboat]

Thank you very much! Now I'm making headway in my build comparisons.

Here is a much harder math question:

Corruption is a DoT with 6 ticks. Each tick has a 4% chance to proc nightfall. What is the % chance that you will get 1 nightfall proc on a single cast of corruption?

[Ebgreen]

Do you want the % chance of just one proc? Or the chance of one proc or more? The probabilities are not the same.

[Steamboat]

The % chance of 1 proc or more.

[Ebgreen]

The probability of 1 proc or more is simply 1 minus the probability of no procs. The probability of no procs is (1-.04)^6 = 0.782757789696. So the probability of one or more procs is:

1-0.782757789696 = 0.217242210304 Or approximately 22%

[Steamboat]

You are awesome Ebgreen. I'm going to keep pushing my luck until you get tired of me and tell me to shut up.

Corruption lasts 18 seconds (1 tick every 3 seconds for 18 seconds.) Let's say that you cast it twice per minute. Would it be correct to say that your chance per minute of getting a proc would be additive, therefore 44%? And if you cast it 3 times per minute, 66%? And at 3.3 (repeating of course ) times per minute, 72.6%?

Thanks again.

[Ebgreen]

The probability is not additive. If it were then you could say with certainty that I will always get a proc if I cast it 5 times. That is not the case. To calculate the probability of one or more procs in 3 consecutive casts, it would work pretty much the same way as the previous calculation. The chance of getting no procs in three casts is (.78)^3 which is 0.474552. So the probability of one or more proc in three consecutive casts is 1-0.474552 = 0.525448 or about 53%.

Here is a table showing the probability of a given number of procs for one cast of the spell:

Number of trials 6
P(S) 0.04
# of Procs:_____Prob
0_____________0.78275779
1_____________0.195689447
2_____________0.020384317
3_____________0.001132462
4_____________3.53894E-05
5_____________5.89824E-07
6_____________4.096E-09

[Steamboat]

Ebgreen, you're pretty much my hero. Thanks for all the help.

Also, what does ^ mean mathematically?

[Flixified]

It means 'to the power of'.

So like 2^2 = 4, or 5^2 = 25 etc