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Kensan_Oni
Joined Oct 2005
4680 Posts

I have a 20 sided dice. I am going to roll. Let's say I need a coinflip. 50/50. What number do I need to roll or better to get 50%

If you said 10, you're wrong. 1-10 is 10 numbers out of 20. That would make it 55 percent. 11-20 would make it 50%.

So why are they giving everyone an extra 5%? Seems like lazy math to me...

(Direct Ref: Saving throws 4E page 2 section 10 What you Need to Know Handout)
Nautilus
Joined Jan 2007
129 Posts
I believe the true reason lies inside one of James Wyatt's Excel spreadsheets. When aiming at the optimum period for conditions to last, they must have found that a 55% break chance was ideal. There's really nothing special about 50%, in itself.
Krusk
Joined Nov 2005
6173 Posts
All of these are reasonable assumptions

Because rolling a natural 10.5 is impossible.
because they wanted to give players a small edge
Because PCs will need the edge with how nasty some effects will be

"In a way, you are worse than Krusk"                               " As usual, Krusk comments with assuredness, but lacks the clarity and awareness of what he's talking about"

"Can't say enough how much I agree with Krusk"        "Wow, thank you very much"

"Your advice is the worst"                                                  "I'd recommend no one listed to Krusk's opinions about what games to play"

Kensan_Oni
Joined Oct 2005
4680 Posts
Eh, I know, it's only a 5%... it just bugs me cause of all the times I've had to tell people 10 on a d20 is not equal to 50%, that's all.
bobthedog
Joined Aug 2007
1336 Posts
Eh, I know, it's only a 5%... it just bugs me cause of all the times I've had to tell people 10 on a d20 is not equal to 50%, that's all.

Dividing by two is overrated, anyway. :D
sphyre
Joined May 2003
1054 Posts
So why are they giving everyone an extra 5%? Seems like lazy math to me...

Because it's easy to remember? Single digits: Fail. Double digits: Succeed. Why the extra 5%? Because it's not particularly fun to have ongoing effects forever. The little bonus is there to end the effect.

It's easy enough to house rule, as it is to keep at 10+ saves.
lordofnightmares_dup
Joined Dec 2004
1107 Posts
Because DC 10 sounds like a good baseline for average difficulties.
Kensan_Oni
Joined Oct 2005
4680 Posts
But DC 9 probably works better.
neceros
Joined Nov 2005
299 Posts
But DC 9 probably works better.

That depends on your mind set. Mathematically, we don't want it to literally be a 50/50, even if we say it constantly.

Players are supposed to be heroic in the sense that they can continue onward through thick and thin. Giving them an additional 5% is hardly anything to get upset over, but it's enough to give most people that edge to stay alive.

Plus, it's easy to remember.
Neceros' Character Sheets
Many sheets for many systems.
kjakan
Joined Feb 2005
112 Posts
Because DC 10 sounds like a good baseline for average difficulties.

Indeed.

Sure, they could have made the d20 with a 0 instead of a 20, or they could rule that the DC is the number to beat, not to match. That way (without modifiers) a DC 0 check would be an automatic success, DC 10 is fifty-fifty and DC 20 is impossible.

I don't think that would be a very good idea, though. It's more interesting to have a "nearly impossible" succeed on a roll of 20 against DC 20.

-K
Joined Jun 2002
126 Posts
If people would start numbering at zero instead of one, these problems wouldn't arise. ;)
eldritch_lord
Joined Jul 2006
4412 Posts
If people would start numbering at zero instead of one, these problems wouldn't arise. ;)

Well, not everyone can be as logical as us computer programmers, I suppose....
shamsael
Joined Oct 2007
90 Posts

I have a 20 sided dice. I am going to roll. Let's say I need a coinflip. 50/50. What number do I need to roll or better to get 50%

If you said 10, you're wrong. 1-10 is 10 numbers out of 20. That would make it 55 percent. 11-20 would make it 50%.

So why are they giving everyone an extra 5%? Seems like lazy math to me...

(Direct Ref: Saving throws 4E page 2 section 10 What you Need to Know Handout)

Well, on a DC 10 action with no bonuses in 3e, you have that same 55% chance to succeed, so it's not that new.
decivre
Joined Apr 2007
6177 Posts
I think the bigger problem lies with attack rolls. All bonuses for attacker and defender equal, the attacker still has a mild edge over his opponent of 55%. It doesn't stop there either. Apparently you building up perception all this time isn't as important as the guy building up stealth... while you use passive perception he has a 55% chance of succeeding with equal bonuses. A person with bluff has a 55% chance of beating someone with passive insight. A trap has a 55% chance of beating your passive perception if it rolls (does it roll?) with the same bonus.

Why punish the defender at all? Especially if they were aiming for a good defense?
bazra
Joined Mar 2008
1 Post
To be honest I´ve grown to dislike d20 given how large spread of different results it can give making game very "swingy". I´m probably going to see if I could eliminate it alltogether and replace it with 3d6 roll.
nom
Joined Jan 2004
2095 Posts
To be honest I´ve grown to dislike d20 given how large spread of different results it can give making game very "swingy". I´m probably going to see if I could eliminate it alltogether and replace it with 3d6 roll.

As odd as this sounds, reducing the probability of single-instance good or bad events actually makes the game more swingy, as those events become less predictable. A better way to reduce swingyness is to reduce the impact of each sample, which gives the players more time to react.

Stats warning:
Mean of binomial distribution = np
Variance of binomial distribution = np(1-p)

For 10 samples at 0.5, mean is 5, variance is 2.5, stdev is ~1.6, which is 31% of the mean.
For 10 samples at 0.1, mean is 1, variance is 0.9, stdev is ~ 0.95, which is 95% of the mean.

Let's say we want to average 10 points over 10 samples. With p = 0.5, we'd set a 'success' at 2 points. 1 standard deviation on each side is ~7 - 13. With p = 0.1, we'd set a 'success' at 10 points. 1 standard deviation on each side is ~ 0.05 to 19.5. High-yield low-probability events are much more "swingy" than low-yield moderate-probability events.
Stuntman
Joined Sep 2001
3576 Posts
Eh, I know, it's only a 5%... it just bugs me cause of all the times I've had to tell people 10 on a d20 is not equal to 50%, that's all.

First of all, you do not have to know that having to roll 10 on a d20 to success is 55% in order to have fun. Second, not everyone is as strong as you in mathematics. Third, it bug me too, but I get over it. Fourth, enlightening those people do not necessarily make the game better or more fun for everyone and is probably wasted effort.
<\ \>tuntman
mr_teapot
Joined Jan 2007
649 Posts
Why punish the defender at all? Especially if they were aiming for a good defense?

Because action is interesting and lack of action/failure is less interesting. Hitting someone is cool to do and to watch. Swinging and missing is not. Having your character unable to act because of a status effect sucks. Being able to do something in combat is better. Favoring the things you want makes the game more fun and interesting.

If the game favored defense, less would happen and it would lead to static, boring situations rather than interesting, dynamic situations. (The difference in this case is small but can have a decently large effect in aggregate.)
jaelis
Joined Apr 2004
4737 Posts
As odd as this sounds, reducing the probability of single-instance good or bad events actually makes the game more swingy, as those events become less predictable. A better way to reduce swingyness is to reduce the impact of each sample, which gives the players more time to react.

I'm not sure I get your point here. Rolling 1d20 and rolling 3d6 both have the same mean, 10.5. 1d20 certainly does have the higher variance though (5.7 vs I believe 3.) So if you do as Bazra suggests and replace d20s with 3d6's you will indeed make things less swingy, in the sense of reducing the variance.

I guess you're saying that if you need to make a 16 or better, the fluctuations in whether you win or not will be larger, relative to the number of times you succeed, with the 3d6 method. (With the d20, you'll win 25 +/- 5 times out of 100, with 3d6 you'll win 4.6 +/- 2 times out of 100.)

But on the other hand, the absolute fluctuations will be smaller (+/- 2 compared to +/- 5). I don't know why the relative fluctuations would be the important thing. I would have said that the 3d6 is less swingy simply because the unlikely thing (winning) is less likely to occur.
jimprofit
Joined Oct 2007
933 Posts
Eh, I know, it's only a 5%... it just bugs me cause of all the times I've had to tell people 10 on a d20 is not equal to 50%, that's all.

I know this, and it's precisely why I sway my GM.

Just like when we use a d6 for a d3 we do it 1/2=1, 3/4=2, 5/6=3

To be truly even it'd have to go
1=1
2=2
3=3
4=1
5=2
6=3

But who want's to remember that mess? And it's just a friggin d3 anyway...
jimprofit
Joined Oct 2007
933 Posts
If people would start numbering at zero instead of one, these problems wouldn't arise. ;)

1's suppose to mean epic fail anyway lol!
nom
Joined Jan 2004
2095 Posts
I'm not sure I get your point here. Rolling 1d20 and rolling 3d6 both have the same mean, 10.5. 1d20 certainly does have the higher variance though (5.7 vs I believe 3.) So if you do as Bazra suggests and replace d20s with 3d6's you will indeed make things less swingy, in the sense of reducing the variance.

In the middle of the range, the difference is unimportant. What is interesting is what happens at the ends of the range.
I guess you're saying that if you need to make a 16 or better, the fluctuations in whether you win or not will be larger, relative to the number of times you succeed, with the 3d6 method. (With the d20, you'll win 25 +/- 5 times out of 100, with 3d6 you'll win 4.6 +/- 2 times out of 100.)

Not quite. My point is more sophisticated.

Means are important, but we're not so much interested in the mean of the sample as the probability of success for a given target number. In general, the designer picks a target number, figures the probability of success, and then weights the reward for success such that the mean reward comes out correctly.

Note that the process of picking a target number removes any consideration of what the original distribution looks like. You collapse the distribution down to a binomial trial (or bernoulli event). The repeated samplings thus form a binomial distribution.

The "swingyness" of a system is not represented by the mean, but the standard deviation. More interestingly, it's represented by the standard deviation as a fraction of the mean. For a binomial distribution, the more extreme (away from 0.5) your probability, the larger the deviation relative to the mean and the more likely you are to have results that differ markedly from the mean. Factor in the risk-reward function described above and you get a highly swingy system at the extremes, especially for low probality, high payoff events.

Short version: The chance of winning 200 is much higher for 10 samples at 10% paying 100 than for 10 samples at 50% paying 20. Both have a mean of 100, but scoring 200 in the latter case has a ~0.01% chance, while scoring 200 or more in the former has a ~26% chance. That said, the latter case also has a ~0.01% chance of getting 0, while the former has a ~35% chance of getting 0.

Tangent: non-uniform distributions have another nasty side effect where the value of a modifier varies by the target number. On a d20 uniform distribution, +1 is always worth absolute 5% (as long as you don't hit a limit). On a 3d6 distribution, it varies wildly.
jaelis
Joined Apr 2004
4737 Posts
Maybe I understand... you're saying that if you design a system where there is a small probability of a very important thing happening, then the fluctuations in whether that happens or not will be really significant.

For instance, in the d20 vs 3d6 example, you're suggesting that if a roll of 20 on the d20 gives double damage, a designer might make a roll of 18 on 3d6 be an auto-kill, since it is so much less likely to occur. And that would be bad, because whether or not you roll an 18 would have a huge impact on a given fight.

But I still think that's not quite to Bazra's point. Because if you don't change the reward to reflect the smaller probability, then the system really does become less swingy as you reduce the variance. For instance, if you just have an 18 do double damage in the 3d6 system, then it has no more impact than rolling a 20 did before, but happens much less often. Even more extreme, if you didn't change the target values at all, so you still had to roll a 20 to get a crit, then you would never crit at all and that source of variability would be removed entirely.

I think that if you do simply replace all d20 rolls by 3d6 rolls without changing any DCs or other target values, then you really would have a less swingy system. More boring perhaps, but less swingy.
Steely_Dan
Joined Mar 2007
10154 Posts
I think that if you do simply replace all d20 rolls by 3d6 rolls without changing any DCs or other target values, then you really would have a less swingy system.

That's a UA variant, but of course I know you know that.
gotbrain
Joined Aug 2006
302 Posts
Tangent: non-uniform distributions have another nasty side effect where the value of a modifier varies by the target number. On a d20 uniform distribution, +1 is always worth absolute 5% (as long as you don't hit a limit). On a 3d6 distribution, it varies wildly.

And this is very important because in order to maintain balance things need to scale relatively equally. A +1 on that armor adds equal value as it increase to +5 vs. the attackers +'s on a d20 system. But on a 3d6 system each + is worth a whole lot more than the previous because the odds of rolling the higher number are that much less.
nom
Joined Jan 2004
2095 Posts
Maybe I understand... you're saying that if you design a system where there is a small probability of a very important thing happening, then the fluctuations in whether that happens or not will be really significant.

For instance, in the d20 vs 3d6 example, you're suggesting that if a roll of 20 on the d20 gives double damage, a designer might make a roll of 18 on 3d6 be an auto-kill, since it is so much less likely to occur. And that would be bad, because whether or not you roll an 18 would have a huge impact on a given fight.

You've got it exactly. My example wasn't quite complete, because the real swingyness in my example can be seen if you figure each encounter should require 100 points to win. At 20 points per "success" you cannot win an encounter in less than 5 rolls. At 100 points per "success", you can win on any roll.

Reducing the effect of any given check has two effects:

(1) it makes the "Law of Large Numbers" more effective, which results in encounters tracking the mean result more closely.

(2) it gives players time to evaluate the direction the encounter is going and make changes accordingly.
I think that if you do simply replace all d20 rolls by 3d6 rolls without changing any DCs or other target values, then you really would have a less swingy system. More boring perhaps, but less swingy.

1d20 vs 3d6 has very little to do with "swingyness", since swingyness is primarily determined by the magnitude of the effect of a single sample, especially a single unlikely sample. A one-in-a-million event is still "swingy" if it can cause major disruption if it occurs.
And this is very important because in order to maintain balance things need to scale relatively equally. A +1 on that armor adds equal value as it increase to +5 vs. the attackers +'s on a d20 system. But on a 3d6 system each + is worth a whole lot more than the previous because the odds of rolling the higher number are that much less.

This was a "feature" of BattleTech, which used 2d6. Moving the target number from 6 to 8 (11/36) had more impact than moving it from 4 to 6 (7/36). Viewed another way, going from 19 to 20 on d20 halves the expected damage, but going from 11 to 12 cuts it by 2/3. Going from 17 to 18 on 3d6 reduces expected damage by 3/4.
journeyman777
Joined Jun 2005
586 Posts
While the mathematical analysis is indeed interesting. I mean that, the concepts and their implications do have a great deal of significance to the overall game. However, the question I find slightly more pressing is: Why 10 and not (10+1)? A non-scaling chance of success does not seem conducive to verisimilitude or mechanical differentation between classes. This doesn't much support the "heroic fantasy roleplaying" experience in any way I can think of.

Scenario: Archmage (lv30) demonstrates a lv1 damage over time poison spell to his apprentice (lv1). (for convenience, assume a true strike effect is used to hit, but not crit). The mage cast the spell on his apprentice (55% chance the apprentice throws off the "epic" archmage's spell? WTF?). An apt pupil, the apprentice successfully casts that same spell on his master (an archmage only has a 55% chance of negating a spell from a lv1? Doesn't seem very "epic" to me.) Having too much fun with his new spell, the apprentice also casts it on an adventuring buddy of his master's and the guy's own apprentice. (The big, strong, amazingly tough, "epic" fighter who kills green dragons for fun has a barely better than even chance of throwing off a lv1 poison effect? His utterly inexperienced apprentice has those exact same odds? Having Con 18+ or 8- doesn't matter? Being a dwarf doesn't help? WTF?)

It just doesn't feel right to have a variable chance (based on class, feats, abilities, ect) to get the initial effect, but then have a single unchanging percentage for the rest of the effect. It's like having the first strike in a full attack rol d20 against AC, but all following strikes you just flip a coin, heads you hit, tails you didn't. Has anyone seen a blog entry, interveiw, or something to explain the reasoning behind this? I can see the logic to allowing a save every round (that way the player can at least feel like they are trying to do something), but the flat chance just looks like an overreaction to save or suck effects (which seem to have been mostly slowed down to take place over several rounds) and massive save DC cheese.
nom
Joined Jan 2004
2095 Posts
Rewrite your example in 3E terms: The spell effect lasts 1d4 rounds, regardless of who it is applied to. 4E uses a hypergeometric distribution instead of a linear one and standardises the mechanic across all "short duration" effects. This standardisation allows for additional mechanics, such as powerful creatures having save bonuses or abilities that grant additional saving throws.

In both editions, other factors apply.

Firstly, you have to actually apply the spell. In 3E, this requires a DC vs saving throw check. In 4E, it requires an attack roll vs defense check.

Secondly, the amount of damage applied by the spell often varies by the power of the caster, and similarly the hit points (or equivalent) varies with the target. An effect dealing 10 damage per round to a 30 hp creature is (relatively) a lot more dangerous than an effect dealing 5 hp per round to a 60 hp creature.
journeyman777
Joined Jun 2005
586 Posts
This standardisation allows for additional mechanics, such as powerful creatures having save bonuses or abilities that grant additional saving throws.

This is the crux of my complaint, I've neither seen or heard mention of anything that actually grants a bonus (or penalty) on a saving throw. Right now it's looking like the odds are always 55% regardless of everything else. (I see your example, but random durations were pretty rare in 3e.)
balseraph
Joined Jun 2003
84 Posts
because they wanted to give players a small edge

Over any period of time longer than a single encounter, won't the monsters have the edge? I imagine that, like in 3.5e, the PCs will be forcing more saves than they will be having to make them.
The_Stray
Joined Dec 2003
1320 Posts
This is the crux of my complaint, I've neither seen or heard mention of anything that actually grants a bonus (or penalty) on a saving throw. Right now it's looking like the odds are always 55% regardless of everything else. (I see your example, but random durations were pretty rare in 3e.)

The Eladrin premade character from the 4E XP packet has an ability that gives him a +5 bonus on saving throws vs. Charm.

When the Cat's a Stray, the Mice will Pray

lurker88
Joined Sep 2007
115 Posts
The Eladrin premade character from the 4E XP packet has an ability that gives him a +5 bonus on saving throws vs. Charm.

The halfling also gets one vs. fear, the dwarf gets one vs. poison and an immediate save against being knocked prone plus there's a human racial feat that gives a generic +1 to everything. The paladin and cleric have abilities that trigger immediate and/or improved throws and there's an item that gives bonuses once per encounter as well.

All in all, they seem to be rather common.
journeyman777
Joined Jun 2005
586 Posts
Excellent. Assuming there are ways to (effectively) increase the DC as well, I may not need to houserule this after all. Many thanks for the info.
lostdm
Joined Jan 2004
129 Posts
I ran some quick numbers. Under the current system a chance of the effect lasting 5 or more rounds is 4%.

If you made players roll for 11 it would be 6.25%.

My theory is that 10 was chosen so that the chance of an effect lasting that long would be less than a chance of a crit.

On a side note. With the +5 like with halflings and fear- it seems to shave two rounds off the effect. By that I mean, the chance of a halfling suffering a fear effect 3 or more rounds is 4%
subedei
Joined Dec 2005
1255 Posts

11 is just an inelegant number.

We prefer to count by 10's and multiples of 10.

Why are the changing the bonus/penalty progression from 1-2-4-etc to 1-2-5 etc? For the very same reason.

Notice vulnerabilities and ongoing damage are also in multiples of 5. Higher level abilities will probably skip directly to 10 rather than stopping at 7 or 9. 5's and 10's are just easier to add and they FEEL more symmetrical and natural.
hecscrivener
Joined Aug 2007
246 Posts
Excellent. Assuming there are ways to (effectively) increase the DC as well, I may not need to houserule this after all. Many thanks for the info.

You'd spend time and energy houseruling this?
Kensan_Oni
Joined Oct 2005
4680 Posts
Why are the changing the bonus/penalty progression from 1-2-4-etc to 1-2-5 etc? For the very same reason.

Not that I wanna really argue with you, but I'm all for a -2-5-7-10 progression of penalties. I kinda miss the success tables from TORG, to be honest.
nihzlet
Joined Aug 2006
314 Posts
wow, someone else who has played TORG. i dont see those very often.

Posted by JimProfit:
I know this, and it's precisely why I sway my GM.

Just like when we use a d6 for a d3 we do it 1/2=1, 3/4=2, 5/6=3

To be truly even it'd have to go
1=1
2=2
3=3
4=1
5=2
6=3

But who want's to remember that mess? And it's just a friggin d3 anyway...

err... that makes no sense. the chances of getting any given number from 1-3 are dead equal either way you do it. how is that the same as the debate concerning that extra 5%?
Just thought you should know. the countdown continues...
setantus_dup
Joined Nov 2007
56 Posts
error
journeyman777
Joined Jun 2005
586 Posts
You'd spend time and energy houseruling this?

I'm most of the way through a BA in Game Design. If I'm going to be spending time and energy tweaking game mechanics anyway, I might as well focus on numbers my "test group" use often enough for the effect minor variances have on the actual play experience to become evident.
hecscrivener
Joined Aug 2007
246 Posts
I'm most of the way through a BA in Game Design. If I'm going to be spending time and energy tweaking game mechanics anyway, I might as well focus on numbers my "test group" use often enough for the effect minor variances have on the actual play experience to become evident.

Wait, they have BAs in Game Design?! What have I been doing reading all these dead Brits for the past four years?