Steve Jackson Games Forums - Question about the maths behind attack roll and defense rolls

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Re: Question about the maths behind attack roll and defense rolls

Quote:

Originally Posted by Landwalker (Post 966888)

Why would you expect two master swordsmen to rapidly dismember each other instead of to have a long, drawn-out duel?

i wouldn't expect them to, but under my previous understanding of the rules, I would PREFER they chop each other up quickly as opposed to having a net 5% chance to hit per turn.

Re: Question about the maths behind attack roll and defense rolls

Quote:

Originally Posted by laguna (Post 966900)

i wouldn't expect them to, but under my previous understanding of the rules, I would PREFER they chop each other up quickly as opposed to having a net 5% chance to hit per turn.

So, as I understand it, you want them to dismember each other because it's quicker and more convenient for you, as opposed to adhering to realistic expectations?

(I'm not saying there's anything wrong with wanting convenience, I'm just verifying what your position is.)

And in any case, even if you bump them up to Skill 26, the 5% hit chance is hyperbolic.

Skill 26 means Parry 16 (and what the heck, let's give them Combat Reflexes and Enhanced Parry 1, for a Parry of 18).

The attacker can take a -16/-8 Deceptive Attack, dropping both the attack and the parry to Effective Skill 10, and there would be a 25% chance of successfully striking the defender.

A -14/-7 deceptive attack: 27.8%

-12/-6: 24.4%

So the -14/-7 is the optimal point, giving you a 27.8% chance of success per turn.

If you adhere to the "one-second turn" idea, then that means that there will be about one strike per four seconds per swordsman. It's not unreasonable, then, that such an encounter might last 15 seconds or less.

That's also disregarding other attack options. If the attacker uses a Committed Attack (Determined), he can get up to 37.1% with a -16/-8 Deceptive Attack, but he'll be in a bad spot defending afterwards.

And then of course there are Feints (and Beats and Ruses), dozens of techniques, rapid strikes, etc.

Re: Question about the maths behind attack roll and defense rolls

Right... okay, I forgot the formula... ungh... I think, and I hope I got it right this time, it's...

(((Chance to hit)-(Crit Chance))*(Chance to fail Active defense))+(Chance to Crit)

And when you have combat reflexes, you have probably within 5% of one out of three chance to hit the target... sorry I got things backwards.

The idea is that two master swordsman attacking each other several times before first blood may seem unattractive to some... if it is, you can always fast-draw first if you havethe higher speed and slice the guy with a deceptive All-Out Attack (Double) and get him before he does anything... I mean that's what I'd do if I was put into the situation... unless he already has his blade ready, then I would throw something and run, hide behind the corner and get him when his back is turned... or something else delightfully cheesy.

If you want it to take longer, take enhanced block, a shield, and wear the heaviest armor you can afford... and this just skims the surface...

...and I'm way off topic by now.

Re: Question about the maths behind attack roll and defense rolls

@landwalker you are correct, i am willing to sacrifice realism for (in this case) game flow. but as i said, i didn't understand the significance of deceptive attack so this particular fudging won't be necessary when my game starts.

Re: Question about the maths behind attack roll and defense rolls

Quote:

Originally Posted by Landwalker (Post 966907)

And in any case, even if you bump them up to Skill 26, the 5% hit chance is hyperbolic.

The 5% hit chance was before I drew his attention to Deceptive Attack.

Re: Question about the maths behind attack roll and defense rolls

This is what it means.

The first table has the percentages as they stand today. The second table has the percentages if you use the quick contest rules.

In quick contest, the only thing that matters is the difference between the stats that are compared, so the listed a margin is the difference between attack and defense. And it shows the percentages of how often the character with the higest stat will win.

Code:

        Attack                                                                                        

Defense        5                    6                    7                    8                    9                   10                    11                    12                  13                  14                  15                 16

5        4,501028807        8,916323731        15,53926612        24,81138546        35,84962277        47,77091907        59,69221536        70,73045267        80,00257202        86,6255144        91,16941015        94,03292181

6        4,372427984        8,573388203        14,87482853        23,69684499        34,19924554        45,54183813        56,88443073        67,38683128        76,20884774        82,51028807        86,96844993        89,91769547

7        4,179526749        8,058984911        13,87817215        22,02503429        31,7236797        42,19821674        52,67275377        62,37139918        70,51826132        76,33744856        80,6670096        83,74485597

8        3,909465021        7,338820302        12,48285322        19,68449931        28,25788752        37,51714678        46,77640604        55,34979424        62,55144033        67,69547325        71,84499314        75,10288066

9        3,587962963        6,481481481        10,82175926        16,89814815        24,13194444        31,94444444        39,75694444        46,99074074        53,06712963        57,40740741        61,34259259        64,81481481

10        3,240740741        5,555555556        9,027777778        13,88888889        19,67592593        25,92592593        32,17592593        37,96296296        42,82407407        46,2962963        50                53,7037037

11        2,893518519        4,62962963        7,233796296        10,87962963        15,21990741        19,90740741        24,59490741        28,93518519        32,58101852        35,18518519        38,65740741        42,59259259

12        2,572016461        3,772290809        5,572702332        8,093278464        11,09396433        14,33470508        17,57544582        20,57613169        23,09670782        24,89711934        28,15500686        32,30452675

13        2,301954733        3,0521262        4,177383402        5,752743484        7,628172154        9,653635117        11,67909808        13,55452675        15,12988683        16,25514403        19,3329904        23,66255144

14        2,109053498        2,537722908        3,180727023        4,080932785        5,15260631        6,310013717        7,467421125        8,53909465        9,439300412        10,08230453        13,03155007        17,48971193

15        1,980452675        2,19478738        2,516289438        2,966392318        3,502229081        4,080932785        4,659636488        5,195473251        5,645576132        5,967078189        8,830589849        13,3744856

16        1,903292181        1,989026063        2,117626886        2,297668038        2,512002743        2,743484225        2,974965706        3,189300412        3,369341564        3,497942387        6,310013717        10,90534979

Code:

Margin        High Wins

0        45,35751029

1        54,64248971

2        63,68955761

3        72,06147119

4        79,41529492

5        85,5366941

6        90,35279492

7        93,92361111

8        96,41203704

9        98,03240741

10        99,00977366

Re: Question about the maths behind attack roll and defense rolls

Quote:

Originally Posted by DukeofDellot (Post 966919)

(((Chance to hit)-(Crit Chance))*(Chance to fail Active defense))+(Chance to Crit)

Yup thats it but it gets more comlicated quickly!

I jsut finished my first few web pages on the subject (Check my sig). I even have a google spreadsheet dedicated to the cause.

(Chance of a Crit) + (Chance of a Hit thats not a Crit)(Chance of Failed Defense)

there is also the matter of how likely you are to penetrate armor. (The odds your DMG exceeds theri DR).

Its all under the GURPS and game Balance link.

Nymdok

Re: Question about the maths behind attack roll and defense rolls

Quote:

Originally Posted by Landwalker (Post 966888)

Why would you expect two master swordsmen to rapidly dismember each other instead of to have a long, drawn-out duel?

This could be quite accurate though. Skill improves, but in GURPS your hit points don't. And as a fighter becomes more and more effective at doing high damage, the human biology doesn't keep pace with the ability to absorb damage (no matter what DnD and its 100+ HP characters would have you believe).

This may not apply to all fighting styles, but I'd say it's an accurate model for several. In fencing matches it's been my experience and observation that mid-level fencers give the most "entertaining" matches. The high-level fencers strike so quickly that one or the other has blown through to their target in a handful of seconds. (Granted, this is under competition-safety conditions where the round is over upon a successful hit - but I can only imagine the real-life swordfight experience wouldn't be much different. Once you start taking damage, you're into the vicious cycle of injuries hampering performance, leading to more injuries.)

Re: Question about the maths behind attack roll and defense rolls

Quote:

Originally Posted by Landwalker (Post 966888)

Why would you expect two master swordsmen to rapidly dismember each other instead of to have a long, drawn-out duel?

When I've seen two master martial artists fight, I don't notice that bouts go on longer. If anything, they're shorter than novice v novice fights (the novices spend a lot of time moving around doing utterly ineffective things).

Turning my observations to GURPS, what I've seen is that good practitioners basically throw Deceptive attacks that bring their hit chance down to a net of 13-14 as a matter of course (after footing, which is almost always good, and hit location and use of Techniques are accounted for). You throw the bestest blow you can without flailing, and you do it every time it matters.

The only time you don't do this is when you're using lower skill than you have in order to teach...

Re: Question about the maths behind attack roll and defense rolls

Quote:

Originally Posted by Landwalker (Post 966907)

And in any case, even if you bump them up to Skill 26, the 5% hit chance is hyperbolic.

If you're talking about Critical Hits that goes to 6 or less at Skill 16 or approx. 10%.

To use the numbers from Basic Critical hits go from 1.9% at 14 or less to 4.6% at 15 to 9.3% at 16. Skill 16 also drops Crit Fails from 17-18 to just 18.

So the chance of getting in that fight-ender more than double by going from 14 to 15 and double again from 15 to 16. The chance of spazzing out goes down by a factor of 4 too. That's actually a very sharp delineation in "real" Skill levels.

So fights between masters really might be shorter.