86 replies to this topic

[FatBabyThompkins]

3rdworld, on 30 July 2013 - 11:00 AM, said:

Moreover the sequence is irrelevant. In this thought experiment shot 1 has already been rolled, and the question in hand is what is the chance of shot 2 hitting the same location. Well if that is the CT, the chance is 19.44%.

It is the old brain teaser. I flipped 2 coins, coin 1 landed on heads. What is the chance of coin 2 landing on heads. it isn't 25%.

You care correct in the coin flipping example, when accounting for independent results. Each independent result is 50%. However, when combining the independent results to see the probability as a whole over a given number of tries, the chance to achieve all hits and no misses reduces dramatically, especially given a <50% chance, which in this case is 19.44%. The chance to miss the CT, and hit something else, is >80% making hitting the CT all 4 times statistically unlikely (not impossible, but improbable). In fact, to the tune of 0.14%.

[LoveLost85]

James The Fox Dixon, on 30 July 2013 - 11:03 AM, said:

I've played CoD and Halo as I stated that I've played FPS. Even using the sights doesn't mean you necessarily hit where you are aiming at. Using the sights makes the cone of fire smaller, but doesn't get rid of it.

on games such as that the entire player is one big 'hitbox' that's why it doesn't matter. on mwo, there is multiple, player skill is needed to land shots where its needed and it counts. if your semi-fresh in game except for a rear ST and someone takes the time to aim there and you die, its not convergences fault, that's how its supposed to be, the player was just good.

[3rdworld]

FatBabyThompkins, on 30 July 2013 - 11:08 AM, said:

You care correct in the coin flipping example, when accounting for independent results. Each independent result is 50%. However, when combining the independent results to see the probability as a whole over a given number of tries, the chance to achieve all hits and no misses reduces dramatically, especially given a <50% chance, which in this case is 19.44%. The chance to miss the CT, and hit something else, is >80% making hitting the CT all 4 times statistically unlikely (not impossible, but improbable). In fact, to the tune of 0.14%.

Yes judging the entire sequence would be unlikely. But we already know what shot 1 hit. So if I am trying to discern the probability of shot 2 landing in the same location, it would be = to that rolls probability. The likelihood of the entire sequence isn't relevant to the question.

[FatBabyThompkins]

Master Q, on 30 July 2013 - 11:06 AM, said:

Incorrect.
Assume we have 4 PPCs. Each has to fire at the target and hit. For ease of use let's assume that they all hit (an invalid assumption given a standard Pilot skill of 4, mechs moving for an average of +2 to target number, and possible intervening terrain or distance modifiers, but whatever).

Now we roll on the targeting table:
Front/Rear
2 C. Torso (critical)
3 Right Arm
4 Right Arm
5 Right Leg
6 Right Torso
7 C. Torso
8 Left Torso
9 Left Leg
10 Left Arm
11 Left Arm
12 Head

So only a result of 2 or 7 will give us the result we want (CT). We look at the possible 2d6 rolls from above; there is ONE result (snake eyes) that can give us a result of 2, but SIX results can give us the 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1). So 7 out of the possible 36 results of a 2d6 roll can give us a CT connect.

Probability of a single strike hitting CT will be referred to as P(CT HIT).

Therefore the possibility of four CT hits in a given strike is P(CT HIT) * P(CT HIT) * P(CT HIT) * P(CT HIT), or P(CT HIT)^4.

This is much like flipping a coin. Let's flip one coin: the probability of a Heads result is P(Heads) = 0.5 (one possible result heads, one result tails, we'll dismiss as negligible the "what if it lands on its edge" as astronomically small since on-edge is not normally a valid, stable result and it'll have to fall eventually.)

The probability of two heads in a row is 0.25, because the possible results are: 2 Heads, 2 Tails, Heads+Tails, or Tails+Heads. 4 results, only one of which is 2 Heads. Independent, unrelated events. The Probability of 3 Heads in a row is P(Heads)^3, or (1/2)^3 = 1/6. The probability of 4 heads in a row is P(Heads)^4, or (1/2)^4 = 1/16.

P(CT HIT) = 7/36.
P(CT HIT)^4 = (7/36)^4 = 2401/1679616 = 0.0014294934 = 0.14%

That is the math. They are independent, unrelated events. Not one of them affects the ones that come before or after, BUT the probability of alignment is so small as to be highly improbable.

Read my edit from before, but I'll post it here again.

as to the reason why. Given 4 hits, the probability to hit 1 once breaks down to the [probability to hit the CT]*[Prob to miss CT]*[Prob to miss CT]*[Prob to miss CT], which is 10.16%. But you could hit on the first and miss the next three, or miss the first, hit the second, miss the next 2, or any combination resulting in one hit, so the equation becomes [probability to hit the CT]*[Prob to miss CT]*[Prob to miss CT]*[Prob to miss CT]*Combination(4,1), where Combination(4,1) is 4 choose 1, which equals 4.

Broken out: 7/36*(36-7)/36*(36-7)/36*(36-7)/36*(4 choose 1)=40.66%. What you're failing to account for is how you have more chances to get 1 hit than if just rolling one try. You have 4 tires to get 1 result. You don't have 19.44% chance to get one hit, but 19.44% chance times the chance of 3 tries missing times 4 combinations of getting the only hit.

Edit: I hope you do not take my post as flaming, I was merely trying to correct the math. No offence meant.

Edited by FatBabyThompkins, 30 July 2013 - 11:14 AM.

[FatBabyThompkins]

3rdworld, on 30 July 2013 - 11:11 AM, said:

Yes judging the entire sequence would be unlikely. But we already know what shot 1 hit. So if I am trying to discern the probability of shot 2 landing in the same location, it would be = to that rolls probability. The likelihood of the entire sequence isn't relevant to the question.

It is relevant though. The question revolves around pin-point alpha and all shots landing in the same location. The probability to do that in TT is 0.14% with 4 shots on target.

[Master Q]

LoveLost85, on 30 July 2013 - 11:09 AM, said:

on games such as that the entire player is one big 'hitbox' that's why it doesn't matter. on mwo, there is multiple, player skill is needed to land shots where its needed and it counts. if your semi-fresh in game except for a rear ST and someone takes the time to aim there and you die, its not convergences fault, that's how its supposed to be, the player was just good.

Sigh. There's no curing stupid.

Look. The entire design constraints of this game are about limiting convergence. I'll take you through it again. You can bring a horse to water...

• LRM design constraints: redesigned several times because they were too tightly grouped and hitting 1-2 panels.
  
• SRM design constraints: redesigned flight path because of "choke points" that allowed them to hit just 1 panel with an entire salvo.
  
• SSRM design constraints: redesigned targeting because they were hitting nothing but CT.
  
• Laser design constraints: redesigned because lasers going "plink perfect convergence instant damage alpha" were DEEMED OVERPOWERED. They were turned into damage-over-time beam weapons to force the damage to spread across multiple panels.

So with all of this is it ANY surprise that the weapons now seen as overpowered are the ones - AC20, Gauss, PPC - that still do instant damage with perfect convergence when piled into an alpha strike?


This is not a matter of "player skill." Player skill can completely exist without perfect convergence. You want to plant all your shots in the same place? Fire each individually, stay trained on the target, and adjust the reticle for each weapon's known offset. You want to blast an alpha? Accept that your fire pattern is not the size of a single pixel.

It is not "random" and it does not "lessen player skill."

Get that through your skull. Imperfect Convergence does not lessen the need for player skill but it does make for a much more balanced game.

FatBabyThompkins, on 30 July 2013 - 11:13 AM, said:

Read my edit from before, but I'll post it here again.

as to the reason why. Given 4 hits, the probability to hit 1 once breaks down to the [probability to hit the CT]*[Prob to miss CT]*[Prob to miss CT]*[Prob to miss CT], which is 10.16%. But you could hit on the first and miss the next three, or miss the first, hit the second, miss the next 2, or any combination resulting in one hit, so the equation becomes [probability to hit the CT]*[Prob to miss CT]*[Prob to miss CT]*[Prob to miss CT]*Combination(4,1), where Combination(4,1) is 4 choose 1, which equals 4.

Broken out: 7/36*(36-7)/36*(36-7)/36*(36-7)/36*(4 choose 1)=40.66%. What you're failing to account for is how you have more chances to get 1 hit than if just rolling one try. You have 4 tires to get 1 result. You don't have 19.44% chance to get one hit, but 19.44% chance times the chance of 3 tries missing times 4 combinations of getting the only hit.

Edit: I hope you do not take my post as flaming, I was merely trying to correct the math. No offence meant.

I think you were kind of talking past the idea.

The point was to analyze what happens every time in MWO (4 shots, same location) and not the "chance of one shot hitting the location."

Chances of individual shots hitting a location are all fine and good. Heck, it's what the game is built on. Overall pattern of shots spreading, though, is needed for the "slug" weapons to be balanced against the "beam" and "spread" weapons.

Edited by Master Q, 30 July 2013 - 11:28 AM.

[James The Fox Dixon]

Master Q, the One Click Wonders think that hitting a single panel with a single mouse click for multiple weapons is more skill than a person firing multiple weapons with several mouse clicks to hit a target. You can't fix the One Click Wonders.

Edited by James The Fox Dixon, 30 July 2013 - 11:25 AM.

[3rdworld]

FatBabyThompkins, on 30 July 2013 - 11:17 AM, said:

It is relevant though. The question revolves around pin-point alpha and all shots landing in the same location. The probability to do that in TT is 0.14% with 4 shots on target.

The question I responded to, was that no weapon should hit the same location.

Which tells me there are at least 2 weapons.

and I would know the hit location of at least 1 of the previous shots.

In which case the chance of landing a follow-up to that shot, the probability is = to that 2d6 roll.

James The Fox Dixon, on 30 July 2013 - 11:25 AM, said:

Master Q, the One Click Wonders think that hitting a single panel with a single mouse click for multiple weapons is more skill than a person firing multiple weapons with several mouse clicks to hit a target. You can't fix the One Click Wonders.

[REDACTED]

Edited by Destined, 30 July 2013 - 11:34 AM.
Insulting

[Master Q]

3rdworld, on 30 July 2013 - 11:28 AM, said:

The question I responded to, was that no weapon should hit the same location.

Which tells me there are at least 2 weapons.

and I would know the hit location of at least 1 of the previous shots.

In which case the chance of landing a follow-up to that shot, the probability is = to that 2d6 roll.

If you fire an "alpha strike", you know the location of NONE of the shots at the time you decide to squeeze the trigger. You have an idea that you might have a high probability for one location, but you shouldn't have foreknowledge that all 4 are automagically going to land in one spot absent some really extant circumstances.

[3rdworld]

Master Q, on 30 July 2013 - 11:29 AM, said:

If you fire an "alpha strike", you know the location of NONE of the shots at the time you decide to squeeze the trigger. You have an idea that you might have a high probability for one location, but you shouldn't have foreknowledge that all 4 are automagically going to land in one spot absent some really extant circumstances.

why? are my sights off? If so I should get my techs working on that.

[FatBabyThompkins]

Master Q, on 30 July 2013 - 11:06 AM, said:

The probability of two heads in a row is 0.25, because the possible results are: 2 Heads, 2 Tails, Heads+Tails, or Tails+Heads. 4 results, only one of which is 2 Heads. Independent, unrelated events. The Probability of 3 Heads in a row is P(Heads)^3, or (1/2)^3 = 1/6. The probability of 4 heads in a row is P(Heads)^4, or (1/2)^4 = 1/16.

I wanted to single this out as it is a normal source of confusion as the success probability for coins is 50%. Let us assume 4 coin flips. What are the odds of getting 4 heads? .5*.5*.5*.5=1/16. Sounds familiar. Let us look at is another way. [Prob of getting heads]*[Prob of getting heads]*[Prob of getting heads]*[Prob of getting heads]*[Combination of Heads], which results in the same equation we saw before. But now let us examine with 4 flips would it would be like to get exactly 3 heads from 4 flips. You are saying that it is .5*.5*.5=1/8, but where did the probability to get that last miss go? It should be counted somewhere, it didn't go anywhere. What if the first die roll were a miss? Or the second? How do you account for that? Well, looking back to the equation I provided, we can see that it is [Prob of getting heads]*[Prob of getting heads]*[Prob of getting heads]*[Prob of getting tails]*[Combination of Heads], which is .5*.5*.5*.5*(4 choose 3)=.25, not .125.

Another way to write it is to [Prob of getting heads]*[Prob of getting heads]*[Prob of getting heads]*[Prob of getting tails]*[Combination of Tails], which is .5*.5*.5*.5*(4 choose 1)=.25. If your mind isn't blown that 5*.5*.5*.5*(4 choose 3)=.5*.5*.5*.5*(4 choose 1) then you have a good grasp of the concepts. If it is blown, then I would recommend reading up on combinatorics and binomial distribution.

[Master Q]

3rdworld, on 30 July 2013 - 11:32 AM, said:

why? are my sights off? If so I should get my techs working on that.

You are attempting something the equivalent of holding one paintball gun in each hand, sitting on the bed of a truck with work out shocks, bouncing along off-road in a field, taking potshots at 10-30 foot wide targets from a distance of between 100 and 1000+ meters.

Does that start to give you an idea of what the difficulty should be? You should feel lucky you HAVE sights, not demand that you can hit a pixel from half a mile away.

[FatBabyThompkins]

Master Q, on 30 July 2013 - 11:35 AM, said:

You are attempting something the equivalent of holding one paintball gun in each hand, sitting on the bed of a truck with work out shocks, bouncing along off-road in a field, taking potshots at 10-30 foot wide targets from a distance of between 100 and 1000+ meters.

Does that start to give you an idea of what the difficulty should be? You should feel lucky you HAVE sights, not demand that you can hit a pixel from half a mile away.

I would follow this up with taking anyone to a gun range where even in the most calm of environments they would likely miss paper at 200m, much less hit the bulls eye. Or putting 3 shots one on top of the other at 50m. There is a reason weapons and shooters are rated in MOA (Minute of Arc) and the Robin Hood case (shooting an arrow into another arrow) is so exemplary.

[3rdworld]

Master Q, on 30 July 2013 - 11:35 AM, said:

You are attempting something the equivalent of holding one paintball gun in each hand, sitting on the bed of a truck with work out shocks, bouncing along off-road in a field, taking potshots at 10-30 foot wide targets from a distance of between 100 and 1000+ meters.

Does that start to give you an idea of what the difficulty should be? You should feel lucky you HAVE sights, not demand that you can hit a pixel from half a mile away.

it isn't like that at all.

more like this but from the year 3000

Edited by 3rdworld, 30 July 2013 - 11:41 AM.

[mania3c]

too much math which means nothing at all..

if for once we could put math, probability, TT rules and real-life nonsense aside and really talk about pros and cons of non-perfect convergence.. It's hard for many of us to contribute something when most of these posts are about math and statistics..

[FatBabyThompkins]

Master Q, on 30 July 2013 - 11:23 AM, said:

I think you were kind of talking past the idea.

The point was to analyze what happens every time in MWO (4 shots, same location) and not the "chance of one shot hitting the location."

Chances of individual shots hitting a location are all fine and good. Heck, it's what the game is built on. Overall pattern of shots spreading, though, is needed for the "slug" weapons to be balanced against the "beam" and "spread" weapons.

Like my edit said, I was only trying to correct the math. Nothing more. Your final result was correct, but the intermediary were not. What your results shows were if 1 shot lands, this is the probability of it hitting the CT. If 2 shots land, this is the probability of both shots hitting the CT. If 3 shots land, this is the probability of all three shots hitting the CT...

mania3c, on 30 July 2013 - 11:43 AM, said:

too much math which means nothing at all..

if for once we could put math, probability, TT rules and real-life nonsense aside and really talk about pros and cons of non-perfect convergence.. It's hard for many of us to contribute something when most of these posts are about math and statistics..

But math and probability were the defining balancing mechanism behind the TT rules, which was the base line for MWO. PGI is starting to diverge from that base line, which is upsetting some people. You don't have to understand all the math (most of the math I introduced was for educational benefit and correction, nothing to do with actual game play balance, mind). Contribute what you can. Bring your strengths to the table and don't let anyone railroad you into submission through "the truth of math". All have a say here.

[Pht]

James The Fox Dixon, on 30 July 2013 - 05:58 AM, said:

The main problem with the current Meta is the pin point high alpha builds aka the PPCx2/Gauss.

Actually, the high-damage alpha builds aren't the main problem. They're the symptom that the current combat mechanic is the underlying cause of, and the current combat mechanic is the result of their approach to how to make an MW video game.

If they fix the symptom, another one will pop up. The underlying causes needs to be fixed, and the root cause is the non-systematic way that the developers appear to have been going about things.

For starters, they took numbers from the TT which were built for a non-fps style combat mechanic, and put them into a FPS/shooter combat mechanic; with the obvious and predictable result that the 'mechs would die very fast, so they doubled the internal and external armor, but that threw off weapons balance, so they tweaked the rates of fire on the weapons ... which caused more problems ... and so on.

Fixes in a non-systematic setup by defintion cause unintended consequnces; and unintended consequences = things for people to min-max/munchkinize.

Bryan Ekman said:

stjobe: Every ballistic weapon has had about a 50% increase in damage per ton of ammo, except for the MG, which got an 80% decrease in damage per ton of ammo. What was the reasoning behind treating the Machine Gun differently from all other weapons in the conversion from BattleTech to MWO?

A: We don’t have a standard conversion rule of thumb. We as ses each weapon, how it’s being used, what the desired role we want for MWO, and tune it accordingly. With each new `Mech we add, or new feature, we have to reevaluate the performance of every weapon.

Quote

In order to fix this problem we must look at the mech hard points themselves. In all of the art and what is currently in game are the weapon hard points in the torsos being fixed in place.

The art is actually very low on the rung as far as defining things in the lore.

We actually have it in black and white that the 'mechs can and do bring each individual weapon to bear. So, you're sort of onto the right direction, but the flavor might need to be a bit different if you're looking for a lore reason to change things.

IE: instead of just changing it for the torsos vs arms, it would actually need to be done for each individual weapon as a simulation of the 'mechs ability to bring those weapons to bear under any given condtion.

Edited by Pht, 30 July 2013 - 12:07 PM.

[LoveLost85]

Master Q, on 30 July 2013 - 11:23 AM, said:

Sigh. There's no curing stupid.

Look. The entire design constraints of this game are about limiting convergence. I'll take you through it again. You can bring a horse to water...

• LRM design constraints: redesigned several times because they were too tightly grouped and hitting 1-2 panels.
  
• SRM design constraints: redesigned flight path because of "choke points" that allowed them to hit just 1 panel with an entire salvo.
  
• SSRM design constraints: redesigned targeting because they were hitting nothing but CT.
  
• Laser design constraints: redesigned because lasers going "plink perfect convergence instant damage alpha" were DEEMED OVERPOWERED. They were turned into damage-over-time beam weapons to force the damage to spread across multiple panels.

So with all of this is it ANY surprise that the weapons now seen as overpowered are the ones - AC20, Gauss, PPC - that still do instant damage with perfect convergence when piled into an alpha strike?



This is not a matter of "player skill." Player skill can completely exist without perfect convergence. You want to plant all your shots in the same place? Fire each individually, stay trained on the target, and adjust the reticle for each weapon's known offset. You want to blast an alpha? Accept that your fire pattern is not the size of a single pixel.

It is not "random" and it does not "lessen player skill."

Get that through your skull. Imperfect Convergence does not lessen the need for player skill but it does make for a much more balanced game.



I think you were kind of talking past the idea.

The point was to analyze what happens every time in MWO (4 shots, same location) and not the "chance of one shot hitting the location."

Chances of individual shots hitting a location are all fine and good. Heck, it's what the game is built on. Overall pattern of shots spreading, though, is needed for the "slug" weapons to be balanced against the "beam" and "spread" weapons.

lols, so now im stupid cause I believe fired shots should land where I aim, weird

[FatBabyThompkins]

LoveLost85, on 30 July 2013 - 01:11 PM, said:

lols, so now im stupid cause I believe fired shots should land where I aim, weird

You're not stupid, but being naive if you think any shot should land where your reticule is, much less multiple weapons firing to one point on a target hundreds of meters out. Personally, I am for 1:1 convergence if it takes time and risk to accomplish it. You shouldn't have 1:1 convergence if you're moving and shouldn't have it immediately after stopping your movement either. Stand out of cover for 2 seconds, take your shot. Or take a snap shot and hope 1 or 2 of your "bullets" hit.

[Erata]

3rdworld, on 30 July 2013 - 11:40 AM, said:

it isn't like that at all.

more like this but from the year 3000

Have you seen the 4X zoom module? Video camcorders are Lostech.