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Joined: Mon Jul 18, 2005 9:08 pm
Posts: 356
Location: Beavercreek, Ohio, USA
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I want to come back to this if I may Blarg.
No problem.
In your system, are you only taking the dice rolls into account in isolation of each other then?
I'm not entirely sure of what you're asking about, so let me give this response. ?What I do is calculate what the number of hits would be for one turn's worth of firing from each weapon system, modified by the range of the weapon. ?Once that is done I aggregate everything together for the unit.
It seems to me that you're not applying any modifiers for hulls with multiple shots (Ie: Predators), to take into account that although there may be the same statistical probability of getting 1 hit... Predators also have a truely infinitely higher probability of getting 2 or occasionally 3 hits each.
It seems to me you're not taking this possibility into account in your model?
First off, even though the Predator has multiple weapons it is not statistically assured to get at least one hit unless you are only firing at infantry. ?(3 shots that have a 33.333% chance to hit infantry = 100% chance to hit infantry. ?Of course this is merely statistics, your dice rolls might be skewed from turn to turn such that you might get no hits one turn and 2 hits the next.) ?If this were something like the Gatling Blaster titan weapon, where you have 4 shots and a 50% chance to hit something then statistically you should be averaging 2 hits per turn.
Infinitely higher probablility of getting 2 or occasionally 3 hits each?!?!? ?Technically, yes, you are correct, but that is a twist of logic. ?Since the Predator has a very small chance of getting 2 or more hits in a single turn and the Vindicator has zero chance of getting more than 1 hit in a single turn, you get the situation that something divided by zero = infinity. ?But you are looking at it from a single turn basis. ?By doing that you are trying to glean statistical significance from a sample size that is nowhere near big enough for consideration. ?In our discussion where we are trying to use some statistical information to compare the overall effectiveness of different units we should look at things from a multi-turn perspective.
In my opinion your statistic of "Predators also have a truely infinitely higher probability of getting 2 or occasionally 3 hits each" gives credence to the quote from Mark Twain: "There are three types of lies: Lies, Damn Lies, and Statistics." ?  ?
But hey, let's run the to-hit numbers. ?Since we don't know what kind of target the Predator Destructor will have we will average the to-hit probabilities together, as I did in the earlier statistical analysis. ?The autocannon has a 25% ((33.333% + 16.667%)/2) chance to hit something. ?One of the heavy bolters has a 16.667% ((33.333% + 0.00%)/2) chance to hit something. ?To get both the autocannon and the heavy bolter to both hit on one turn you have a 4.167% (25% of 16.667%, or .25 x .1667 = .041667) chance to hit 2 things. ?If you want to have all three weapons hit then you have a 0.694% (25% of 16.667% of 16.667%, or .25 x .1667 x .1667 = .0069444) chance to hit 3 things. ?The chance to score at least one hit against something is 48.333% for the Predator Destructor, compared to 58.333% chance to hit something for the Vindicator. ?(Remember that the reason why the weapons for both tanks are pretty close in firepower is because the autocannon has a longer range than the other weapons, boosting the Predator Destructor's scoring.)
Now here is where you are probably going to say "But since we know that the Predators's weapons are better against infantry we will always use them against infantry." ?A dangerous assumption to make, but for the sake of intellectual curiosity we'll run those numbers also. ?The autocannon has a 33.333% chance to hit infantry. ?One of the heavy bolters has a 33.333% chance to hit infantry. ?To get both the autocannon and the heavy bolter to both hit infantry on one turn you have a 11.111% (33.333% of 33.333%, or .333 x .333 = .111) chance to hit 2 infantry. ?If you want to have all three weapons hit then you have a 3.703% (33.333% of 33.333% of 33.333%, or .333 x .333 x .333 = .037037) chance to hit 3 infantry.
Also, I'm interested to see what the numbers say when Predators and Vindicators both Sustain.
A quick mental guesstimate gives Predator Destructors a 50%-60% edge in firepower (And even applying the Ignore Cover bonus to Vindicators, they don't have a hope of closing the capability gap).
OK, let's run the to-hit numbers with an additional 16.667% added in to represent the +1 to hit bonus. ?Since we don't know what kind of target the Predator Destructor or the Vindicator will have we will average the to-hit probabilities together, as I did in the earlier statistical analysis. ?For the Predator Destructor the autocannon has a 41.667% ((50.0% + 33.333%)/2) chance to hit something on Sustain. ?One of the heavy bolters has a 25% ((50% + 0.00%)/2) chance to hit something. ?To get both the autocannon and the heavy bolter to both hit on one turn on Sustain orders you have a 10.417% (25% of 41.667%, or .25 x .41667 = .1041667) chance to hit 2 things. ?If you want to have all three weapons hit on Sustain orders then you have a 2.604% (25% of 25% of 41.6667%, or .25 x .25 x .41667 = .02604) chance to hit 3 things on Sustain orders. ?The chance to score at least one hit against something while on Sustain orders is 91.667% for the Predator Destructor, compared to 75% chance to hit something for the Vindicator.
But all of that is just to-hit, and not firepower which takes into account range and Ignore Cover. ?
The Vindicator has the Demolisher Cannon, which has a 30cm range and an AP2+/AT3+ rating on Sustain orders, and the Ignore Cover special ability. ?You average the to-hit probabilities, 83.333% against infantry and 66.667% for armored vehicles, to a 75% chance of hitting something. ?Multiply the probability to kill something by the number of 15cm increments the range of the weapon has, 2 (30cm/15cm increments = 2) by the 75% chance of hitting something to get a 150%-brackets number. ?To factor in the Ignore Cover special ability we'll multiply the final number by 1.16667 giving a final 175%-brackets number.
The Predator Destructor has an autocannon, which has a 45cm range and a AP4+/AT5+ rating on Sustain orders, and two Heavy Bolters which have a 30cm range and a AP4+ rating on Sustain orders. ?The autocannon has a 41.667% chance of hitting something on Sustain orders. ?Multiply this by the 3 range brackets it can reach and you get the number 125%-brackets. ?The heavy bolters have a 25% chance of hitting something on Sustain orders. ?Multiply this by the 2 range brackets they can reach and you get the number 50%-brackets. ?Add all three weapon's numbers together and you get 225%-brackets.
Compare the 2 numbers: 175%-brackets for the Vindicator and 225%-brackets for the Predator Destructor and you see that the Vindicator has 77.77% as much firepower as the Predator Destructor. ?(Or, in other words, the Predator Destructor has a 28.57% edge in firepower.)
Considering the Space Marine's emphasis on moving I don't think that this is a worthwhile analysis, but it is interesting to see how going on Sustain benefits the tank with a higher number of weapons.
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I shot a Deathstrike Missile and destroyed an enemy titan in my pajamas last night. ?How it got into my pajamas I still don't know...
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