Game design trap - Starting too close to zero.

[Sunseeker]

Somewhere a lonely mathematician dies every time someone repeats the idea that a smaller bonus makes the die roll more important.



So any of the following would work:

Fighter has +0 to hit, commoner AC is 5.
Fighter has +5 to hit, commoner AC is 10.
Fighter has -5 to hit, commoner AC is 0.
Fighter has +100 to hit, commoner AC is 105.

Considering that the Fighter still has to roll the same number on the die, a 5, yes those are all effectively the same.

 

[Minigiant]

Somewhere a lonely mathematician dies every time someone repeats the idea that a smaller bonus makes the die roll more important.



So any of the following would work:

Fighter has +0 to hit, commoner AC is 5.
Fighter has +5 to hit, commoner AC is 10.
Fighter has -5 to hit, commoner AC is 0.
Fighter has +100 to hit, commoner AC is 105.

But which one of those is more likely to actually be in the game.

 

[Pyromantic]

But which one of those is more likely to actually be in the game.

I think the point is that none of those actually has anything to do with what you were previously referencing: how important the die roll becomes. They all lead to exactly the same probabilities.

 

[Minigiant]

I think the point is that none of those actually has anything to do with what you were previously referencing: how important the die roll becomes. They all lead to exactly the same probabilities.

It does.
I see many times over many topics that many people want:
1) To start bonus at zero
2) To keep DCs high
2) To keep bonuses low.

Having 1, 2, and 3 makes the dice roll (luck) the more important factor than character ability. Fighters with +3 attack swinging against 16+ AC with a d20.

 

[Pyromantic]

It does.
I see many times over many topics that many people want:
1) To start bonus at zero
2) To keep DCs high
2) To keep bonuses low.

Having 1, 2, and 3 makes the dice roll (luck) the more important factor than character ability. Fighters with +3 attack swinging against 16+ AC with a d20.

But mathematically it doesn't matter in terms of how likely you are to hit.

If I understand what you're saying correctly, you're referencing the idea that if you have a larger bonus for a larger difficulty, then the random portion of your check is "smaller" relative to the impact of skill. Which has absolutely no foundation whatsoever beyond aesthetics, since the ratio of those numbers is irrelevant.

The probability of success on a d20 roll with a +0 bonus and DC of 5 is identical to one with a +10 bonus and DC of 15. As such, the impact of the die roll is also identical.

 

[Crazy Jerome]

First off, you seem to be stuck in 3e mode and projecting that onto 5e. If the 3e skill system goes away (as I hope it will) then all of what you wrote in that example becomes moot.

Other than that I just don't see what you're getting at. What is there in the game that multiplies in such a way that a bonus of +6 vs. +0 vs. -3 presents any kind of problem? And, if there is no difference, why not keep the bonuses/penaitles as small as possible?

For combat, I would in fact posit that for all bonuses (and penalties) smaller is always better. If I'm fighting a foe that has 20 h.p.* and I'm doing a straight d8 every time I hit (thus on average I need 5 hits to put it down but it might only take 3 and could take 20 if I'm really unlucky), the math works much different than if the foe has 70 h.p. and I'm doing d8+10. On average I'll still put it down on 5 hits, but it's gonna take me at least 4 and can't possibly take more than 7. The actual die roll has become far less meaningful. To me, this is bad.

* - for these purposes let's assume death at 0 h.p. and ignore crits and fumbles.

Lan-"what determines the grind value is AC; how long it takes to get those 5 hits in"-efan

On the skill point thing, context, context! I mentioned it in passing as an example from 3E of the kind of problem. It was disputed. I then elaborated. None of the rest of the things I have discussed have anything in particular to do with 3E. So what have you read here that makes you think I'm stuck on 3E?

As for the hit point example and how long it takes to put a foe down, it is true that changing the starting damage alone won't get you there. The smaller range and generally lower hit points of early D&D is also a huge help--really the main help. Changing the lower bound is more about truncating the extremes. After all, you could have 20 hit points, do 1d20, and get a range from 1 to 20 rounds. I think most people would find that too far the other way.

And of course how much randomness we want in that process is somewhat of a playstyle question. The difference between 1d4+1 and 1d6 brings up the same issue. Ideally, the ranges chosen would support some variation.

Let's consider your examples for the d4 guy. The one with straight d4 versus 20 hit points will take from 5 to 20 rounds, and average of 8 rounds. (I realize that the extremes in the 5 to 20 are extremely unlikely here.) Meanwhile, our d4+10 guy versus 70 hit points is an average of just under 6 rounds, for an extreme range of 5 to 7. Pretty tight--probably too much.

Of course, we are assuming in this example that the d4 guy is going to get that same +10. (He probably will not.) And we are assuming that the 5 round average was important enough to preserve, so that the hit points scaled from 20 to 70. Maybe the 70 hit points should be somewhat less, the d8+10 guy is still thus seeing more variance, and his nice d8+10 attack is putting down opponents a bit faster than 5 rounds on average.

No matter where you set it, however, if you make the die all important for long periods in the starting range, the fact is that d4s might as well not exist. And maybe that would be a better answer for the kind of game you want. I think that was mentioned earlier. Maybe get rid of d4s and d6s as common attacks, and go with things like d8 as the starting point, with d10, 2d6, etc. occurring more often. That puts the average damage well away from zero, and you get the same nice effects as bumping the base mod to +4.

 

[Minigiant]

But mathematically it doesn't matter in terms of how likely you are to hit.

If I understand what you're saying correctly, you're referencing the idea that if you have a larger bonus for a larger difficulty, then the random portion of your check is "smaller" relative to the impact of skill. Which has absolutely no foundation whatsoever beyond aesthetics, since the ratio of those numbers is irrelevant.

The probability of success on a d20 roll with a +0 bonus and DC of 5 is identical to one with a +10 bonus and DC of 15. As such, the impact of the die roll is also identical.

My issue is not that the chance is identical, it is that the chance of the talented, the skilled, and the untrained are practically identical. Then making the chances not match the fluff.

Over many threads here and over places, I've seen many people suggest that an untrained has a +0 and the trained at a little +2; granting a mere 10% increase of chances.

Part of this is because people think Zero when they think untrained. But when when these same people are asked what trained is and you offer a +5 they go "TOO HIGH!" and opt for the +1 or +2 option.

Then you ask for the DC they come up with high values of 15 and up.

And we get druids who cant build themselves a shelter to wait out a rainstorm or a fighter with a ~60% chance of missing the orc. And that's why I hate low level. You can't do jack reliably unless you powergame because all the bonuses are +0 and +1 but the DCs are much higher.

 

[Crazy Jerome]

That's fair. Options should definitely be considered.

I would suggest however that you underestimate the negative impact of scaling everything in this way. Keeping numbers smaller when possible does have an aesthetic appeal and an approachability factor, even in cases where it may not matter mathematically. Some people really hate the +1/2 level on 4E for the simple fact that they hate dealing with +20-something on die rolls all the time. May not make any difference for a lot of people, but some find it unwieldy.

I see 4th's changes to hit point and damage scaling at 1st level as an improvement, even if the way it progresses needs some work, but I'm not sure exactly what you want to do with it. Would you increase all stat modifiers, so that an "average" score of 10 gives something like a +5 modifier? Or are you saying that specific instances of game mechanics (like damage expressions or skill acquisition) should generally start on a larger scale?

I guess I'm saying that I don't see that what you're asking can be entirely removed from specifics. And given the history of changes in hit point/damage in 4th edition, and the fact that WotC has already openly discussed the question of starting hit points, I think this is certainly a consideration for them already.

Well, I certainly would not scale everything this way. That's total overkill. I wouldn't even scale most things this way. And for that matter, I wouldn't even consider it in a system with as wide a scale as 4E (though I guess once hit points are going into the mulitple hundreds, doing +4 versus +1 damage at start is rather beside the point).

Having stat mods be a flat +1 per 2 points in the ability score (so +5 at a value of 10) is definitely something I've considered as an easy way to both eliminate a set of negative numbers, deal with this issue on a systematic basis, and pick up some other niche benefits that are indirectly related. It does nothing to dampen rampant stat inflation when it comes to attack bonuses (as has been discussed several times already), and thus would need to be watched on that basis. But it would certainly make the damage bonus from high stats worth a bit less than it is now. Main problem with it is that if stats are producing that much of the bonus +5 to +10, say, then it doesn't leave much room for skill, while keeping a tight system inside the meaningful d20 range. I'd prefer mods stay within +10 normally, and within +20 on the outside. Can't do that if you have stats give +8 to +10 easily.

OTOH, I believe that one time when I suggested starting at +0 mod with a 1 in the score, I advocated something like 1 (+0), 2-3 (+1), 4-6 (+2), 7-10 (+3), 11-15 (+4), 16-21 (+5), etc. That happens to work very effectively for a simple point-buy of 1 point per point in score, while discouraging extremely high scores.

That does bring up another point which may have been misconstrued several times, and probably should extend my previous answer to Lanefan. I would also advocate that the bonus to damage grow relatively slowly, such that the d8+10 thing is not something that would happen quickly. That is, such a system would not change the wizard/fighter base from d4/d8+3 to d4+5 to d8+10 to compensate the fighter. Part of the point is to bring the classes closer together. If the 10 Str wizard is d4+4 or d4+5, then the 16 Str fighter is d8+7 or d8+8--and that is assuming that we stick with +1 mod per 2 points in the score, which I'm also not convinced is a good idea (however it is changed).

Go back to the Basic/AD&D formula with its -3 to +3 range, or use something like I had above with +1 to +5 range, and now we are talking d4+3 verus d8+5. We aren't used to seeing that as valid, because 40 years of D&D has taught us that it can't possibly work for the fighter. But maybe if the wizard can hit like that, he can be forced to wait for the powerful magic until higher levels? Or maybe the fighter can get some other things to compensate?

 

[Pyromantic]

I want to take a time out here and mention one falsehood that I believe is popping up repeatedly in discussions of damage. Namely, that if you take a person's hit points and divide by the expected damage of a hit, then you get the expected number of attacks to drop them. There's a reason I used flat values in an example above rather than rolled, as it generates some very complex calculations. I'm not an expert in probability but have seen enough of it to be careful.

Consider a simple example. A person does d2 damage per hit and wants to drop someone with 3 hit points. You might think: "well, a d2 does 1.5 damage on average, so I expect it to take 2 hits to get 3 damage total." Right?

Nope.

You can see pretty quickly that the minimum number of hits required is 2, but it could also be 3, so the expected number must be between these values. It actually works out to be 2.25.

Edit:

Meanwhile, our d4+10 guy versus 70 hit points is an average of just under 6 rounds, for an extreme range of 5 to 7. Pretty tight--probably too much.

Here's an example of what I mean. The expected number of hits required to defeat the 70 hit point opponent is actually above 6. That's because the probability of it requiring only 5 rounds is less than the probability of it requiring 7. It actually works out to about 6.02.

 

[Pyromantic]

My issue is not that the chance is identical, it is that the chance of the talented, the skilled, and the untrained are practically identical. Then making the chances not match the fluff.

Over many threads here and over places, I've seen many people suggest that an untrained has a +0 and the trained at a little +2; granting a mere 10% increase of chances.

Part of this is because people think Zero when they think untrained. But when when these same people are asked what trained is and you offer a +5 they go "TOO HIGH!" and opt for the +1 or +2 option.

Then you ask for the DC they come up with high values of 15 and up.

And we get druids who cant build themselves a shelter to wait out a rainstorm or a fighter with a ~60% chance of missing the orc. And that's why I hate low level. You can't do jack reliably unless you powergame because all the bonuses are +0 and +1 but the DCs are much higher.

What you're discussing then is not about starting away from 0, but the size of the interval between what we consider baseline and proficient. There's no reason that +0 is the baseline, and indeed it isn't in many cases. (IIRC a 3.5 individual with average strength, no BAB and lacking weapon proficiency is looking at -4 to hit. A 1st-level fighter with weapon focus is probably around +6.)

The size of this interval varies quite a bit depending on which edition you're referencing and which task specifically. If anything, I would say the range of starting values for 4th edition skills is too high. Bonuses over +10 are not uncommon for 1st-level characters (a good stat, training, and any bonus from background or race gets you there easily), but neither is a -1 modifier. How much it should vary is subjective.