Ask a mathie

[rlbell]

I studied mathematics and got the degree.  I am not a great mathematician, but I do like crunching numbers, so if you have a question along the lines of "What is the probability of . . . ", I can take a shot at answering it, and endeavour to show my work.

For a first example, someone once claimed that a good reason to take a Whitworth was that it could force a PSR at LRM ranges (unlike most other forty ton mechs), but how likely is it really to happen?

To force a PSR with its LRM's, a Whitworth must hit with both racks and each must land a full salvo (to inflict the required 20 damage points).  To simplify things, we will assume a gunnery of four, unloading on a shutdown mech, at medium range (14 hexes), so the TN is 3 (actually 2, but snake-eyes always miss).  Scoring a hit 35/36 and landing a full salvo is 3/36 (one way to roll 12 and two ways to roll 11, for a total of 3 successful combinations out of 36).  Hitting with both and scoring full salvos with both is P(hit) squared times p(full salvo) squared, or (35*35*3*3)/(36*36*36*36), or 0.66%.  Not terribly likely.  In fact, the odds of not scoring a PSR after emptying the bins is one minus the odds of failing twelve times in a row:  1 - (1 - 0.0066)^12 = 7.6%.  If a hundred Whitworths unload against a hundred shutdown mechs, you can expect 92 of the shutdown mechs to remain standing.  Between the short range of the ML's and the minimum range of the LRM's, do not bet on a Whitworth forcing a PSR without actually kicking the opposing mech.

[Mattlov]

Double ones do not always miss.  That throws the math off.  If the modified To-Hit number is 2 or less, it is an automatic hit.  Total Warfare: Page 106.

On the same note, Double six does not always hit.

I don't know where people thought these were rule, but as far as I know it has always been this way.

[rlbell]

Double ones do not always miss.  That throws the math off.  If the modified To-Hit number is 2 or less, it is an automatic hit.  Total Warfare: Page 106.

On the same note, Double six does not always hit.

I don't know where people thought these were rule, but as far as I know it has always been this way.

My bad.  This increases the probability of forcing a PSR to 0.69% and the chance of knocking over the shutdown mech, before emptying the bins, to 8%.

[Headshot]

For a first example, someone once claimed that a good reason to take a Whitworth was that it could force a PSR at LRM ranges (unlike most other forty ton mechs), but how likely is it really to happen?

Highly unlikely?
I'm way too lazy to get that deep into the numbers, but the average damage of an LRM10 is 6, for a total of 12 if both actually hit.
Even with the Griffin, trading out one LRM10 for the solid 10 pointer of a PPC, getting that PSR is unlikely enuff that you better not hope on it.
Hell, even the Crusader with two LRM15s is very unreliable with PSRs!
You'll need at least an Archer to somewhat reliably generate 20+ damage with LRMs.
And thats not based on math, but on (counting - oh shit) almost twenty years of practical experience...

[va_wanderer]

Yeah. A Whitworth has a respectable chance to force a PSR with the -S, but that's with SRM's, not LRM's.

Not that I don't like the standard, but it's virtues do not include knock-down firepower with it's LRM racks. In 3025 tech, the real champion of slap-you-silly-at-range goes to only those 'Mechs with dual LRM 20 racks, which isn't many at all.

[SurfRockSteven]

I'm obviously the outlier here, because I've had Whitworth's hit me with both LRM 10s and all 20 missles at long range not once, not twice, but thrice. 

It's kind of humiliating to have an Atlas get taken down at 20 hexes by a Whitworthless.  Humiliating and memorable.

[rlbell]

This installment of "Ask a Mathie" again references a Whitworth, if only tangentially.

In the Fight Night thread Whitworth vs. Vindicator, it came up that there is luck involved, and one bit of luck is two PPC hits to the same location on the Whitworth.

First, we will examine two hits to one location:

HD:    1/36 x 1/36 = 1/1296
CT:    7/36 x 7/36 = 49/1296
LT:    5/36 x 5/36 = 25/1296
RT:    5/36 x 5/36 = 25/1296
LA:    5/36 x 5/36 = 25/1296
RA:    5/36 x 5/36 = 25/1296
LL:    4/36 x 4/36 = 16/1296
RL:    4/39 x 4/36 = 16/1296

So the chance of the first two hits being to the same location is 182/1296, or 14%.

For at least a pair of hits to one location in three hits, we need to enumerate all the ways to hit three seperate locations, and subtract that from one:
The terms are a combination of two locations and the chance of rolling neither for the third one.

HD + Leg (HD+RL, HD+LL, RL+HD, LL+HD) = 4 x (1/36 x 4/36) x 31/36 = 496/46656
HD + side torso (HD+RT, HD+LT, LT+HD, RT+HD) = 4 x (1/36 x 5/36) x 30/36 = 600/46656
HD + arm (HD+RA,HD+LA,LA+HD,RA+HD)= 4 x (1/36 x 5/36) x 30/36 = 600/46656
HD + CT (HD+CT,CT+HD)= 2 x (1/36 x 7/36) x 28/36 = 392/46656
CT + ST (CT+RT,CT+LT,LT+CT,RT+CT)= 4 x (7/36 x 5/36) x 24/36 = 3360/46656
CT + arm (CT+RA,CT+LA,LA+CT,RA+CT)= 4 x ( 7/36 x 5/36) x 24/36 = 3360/46656
CT + leg (CT+LL,CT+RL,RL+CT,LL+CT)= 4 x (7/36 x 4/36) x 25/36 = 2800/46656
Arm + ST (LA+LT,LA+RT,RT+LA,LT+LA,LT+RA,RT+RA,RA+RT,RA+LT)= 8 x (5/36 x 5/36) x 26/36 = 5200/46656
Arm + leg (LA+LL,LA+RL,RL+LA,LL+LA,LL+RA,RL+RA,RA+RL,RA+LL)= 8 x (5/36 x 4/36) x 27/36 = 4320/46656
ST + leg (LT+LL,LT+RL,LL+LT,RL+LT,RL+RT,LL+RT,RT+LL,RT+RL)= 8 x (5/36 x 4/36) x 27/36 = 4320/46656
RT + LT (LT+RT,RT+LT) = 2 x (5/36 x 5/36) x 26/36 = 1300/46656
RL+LL (RL+LL,LL+RL) = 2 x (4/36 x 4/36) x 28/36 = 896/46656
RA + LA (RA+LA,LA+RA) = 2 x (5/36 x 5/36) x 26/36 = 1300/46656

So the total seems to be scoring two hits to one location, in three hits is 37.95%.  It looks like the Vindicator can make its own luck