MathHammer Part 4. Rolling to Hit

 

     This post is to answer a question about the MathHammer calculator. Kai asked me to explain the formula I used to determine the probability to hit with blast weapons. So here it goes. And if you have any thoughts on how this could be improved, or any other questions feel free to leave a comment! More below...

     So first lets review the process of shooting a blast weapon. So we place the blast marker over our intended target. Next we roll the scatter dice and two D6. The scatter dice has 2 out of 6 faces which are hits and the other 4 are scatters. So we have a 1/3 chance of hitting straight off the bat and 2/3 chance of scattering 2D6. when we scatter 2D6 we subtract the ballistic skill of the shooter. Now that I've repeated what everyone already knows, lets look at the math.

      In this example, we are shooting at a group of Imperial Guard with our frag missile. The mathhammer calculator shows that we have a 61% chance of hitting. this isn't quite as straightforward as hitting with something like a boltgun, so i will explain the math i used to estimate this.

      So to determine the probability we start with the 1/3 chance of rolling a hit. Next we add the probability of hitting when we roll a scatter instead of a hit. To calculate this we start with the 2/3 chance of rolling a scatter multiplied by the probability of the total of the 2D6 being small enough to still hit. To do this in excel I had to do things a little differently by graphing out the probabilities of 2D6 results.

     This graph is the cumulative probability of 2D6 results. For example if we need a 6 or less we can see from the graph that there is about a 40% chance. I used a third order polynomial as the trend line which gives a function that we can use to finish off our equation.

     Now the probability of rolling a small enough number is determined by the polynomial function where x is the minimum distance needed which is determined by the BS plus the radius of the blast marker and the radius of the base of the target. The blast size is divided by 2 to get from the diameter to the radius and the base is divided by 50.8 to convert from the diameter in millimeters to the radius in inches (1in=25.4mm).

     This picture shows a quick example of how this works. say we are aiming for the middle model but roll a scatter and a total of 7 on 2D6. For the equation to see if we still hit the original target we take the 7 that we rolled. We then subtract the BS of 4, half of the 3" blast (1.5in), and half of the base width (about 0.5in) for a total of 4+1.5+0.5=6". So as the math shows exactly what we see in the example, we missed the original target by 1inch. 

     And back to the original mathhammer calculation. We plug in the stats for our firer and the target along with the size of the blast (usually 3 or 5 inches) and the size of the target's base (25, 40, 60mm etc. The model base could also be the size of a tank). All this info goes into the equation we described earlier and bam, we have a pretty decent estimation of our chances to hit.

     So that's about it! As you may have noticed, there are a few limitations of this equation. first of all, since it uses a best fit trend line as the 2D6 probability, it isn't exact. It is however a pretty decent estimation (and we really don't need any more than an estimation for what we're doing). The second limitation is having more than one enemy fall under the blast marker since it is really only set up to calculate the chances of killing one model. In the example above, the equation would have said we missed completely, but we really hit another guy. Unfortunately this calculation can't really determine the chances of hitting other models since there are so many possible places that other enemy units could be placed.
     Okay, sorry about the long winded explanation, but hopefully it was somewhat interesting/informative. Thanks for reading!