Monday, June 25, 2012

Starcraft 2 4-Gate and DotA 2's Mortred Blur Statistics

I made a youtube video for people looking for a little help with their 4-gate rush build for Protoss players of Starcraft 2.  I've moved on to different games, but the video tutorial may still help some people and can be found below:

I've also been playing a lot of Valve's DotA 2 lately.  Mortred the Phantom Assassin is one of my favorite heroes, so I made a guide for on how my playstyle with her goes.  I also crunched some probability numbers in there, it can be found here (it has some really cool formatting that you can't copy with blogger), I have an excerpt from the guide listed below about the statistics of her Blur ability:
So why is Blur so good and why do we max it first?  The reason is because it scales so incredibly well per level.  Just how well?  Well, let's do some basic statistics to find out exactly how much staying power it offers you.

The probability of an event is the proportion of times it will occur if we repeated a random trial over and over again under the same conditions.  For evasion with Mortred, we see that with level 0 [[Blur]] you have 0% chance to dodge, level 1 provides a 20% chance to dodge, level 2 gives you 25%, level 3 offers 30%, and 4 gives you a 35% chance to dodge incoming attacks.

If we classify [Evading an Attack] as a success in this trial and [Not Evading an Attack] as a failure, we can deem that [Evading an Attack] is both mutually exclusive and independent of [Not Evading an Attack] as they cannot both occur simultaneously and the first does not change the probability that the second will occur. 

With that knowledge in mind we know the basic statistical formula to follow for our study:

Pr[A] and [B] = Pr[A] x Pr[B]
Pr[Evading an Attack AND Not Evading an Attack] would be Pr[Evading an Attack] x Pr[Not Evading an Attack]

This means that with level 1 Blur the probability of evading 1 attack in a trial of size 2 would be .2 x .8 or .16 or 16%

But Mortred doesn't die in two attacks.  For the sake of sanity I'll limit our trial size to a size of 5.  With this constant, 5 consecutive attacks against Mortred will provide 32 outcomes, 6 of which are unique.


We can visualize this with the following probability tree:

So how do we interpret these data?  The probability of 5 avoidances in a row is the same probability at level 4 as 3 successes is at level 1, and your chance of being hit all 5 times drops from 32.7% to almost one third of that at 11.6%!  Visualizing data can be difficult with hard numbers, so below is a bar graph comparing level 1 to level 4 Blur.

Finally, if we go back to our original example of 2 attacks, Mortred will have:

.35 x .65 or a 22.75% chance of dodging one in two attacks,
.35 x .35 or a 12.25% chance of dodging both, and
.65 x .65 or a 42.25% chance of being hit twice

This is as opposed to the 16%, 4%, and 64% of level 1 Blur, respectively. 

That's a lot of missed attacks!

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