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Bonuses, Penalties and Ad Hoc Rules

Post/Author/DateTime Post
#1
the_apologist
Oct 09, 2007 1:06:31 Every DM is familiar with the "DM's Friend" rule: every helpful circumstance grants a +2 bonus, every hindering circumstance assesses a -2 penalty. This works fairly well for most actions. However, as some DMs will attest, it's just not enough in some games, especially when you're a permissive DM and people are trying to do stuff that just can't be reasonably covered in a rules manual that's going to stay within marketable length.

Therefore, I submit the following explanation of what bonuses and penalties mean to characters, both in game terms and in "real world" terms.

And, as always, forgive me if some of my material is already explained in books that I do not own. Gaming is an expensive hobby and I am a man of meager means, so I only have about a dozen books.

What the d20 Mechanic Means

For starters, especially at low levels, the d20 mechanic gives us a fairly simple statistical analysis of "real life" applications of bonuses and penalties. Without getting into anything complicated, the numbers 1-20 are evenly distributed across a d20. Each has a 5% chance of occurring. That means, at any basic task for which the commoner has no knack or shortcoming (I.E. relevant stats are all 10 or 11 and no bonuses or penalties are assessed) a commoner has a percentage chance of successfully completing a task equal to one hundred minus five times the DC. For example, a commoner has a 75% chance of completing a DC 5 task in one try. This doesn't take into account things like tools, circumstances or mechanics such as taking 10 and taking 20, but it's a baseline to start.

Explaining the Bonuses and Penalties

Here I'll boil down what different bonuses and penalties mean to different people. We throw out +1, +2, +4, +10 and +20 bonuses so nonchalantly, but what do they -do-?

+1/-1
A +1 bonus to a check, based on simple low-level math, is a 5% increase in probability of success. Same goes for the opposite: a -1 penalty is a 5% decrease in probability. Depending on the source of the effect, the average guy on the street probably doesn't even notice. A cleric only knows that his Guidance spell works because he has faith that it does; the results are probably not all that noticeable. Likewise, a Flare spell is like seeing spots. It might be the difference between hitting and missing, but for the most part someone who somehow experienced it unknowingly would attribute the miss to other factors.

+2/-2
Much like the +1/-1 entry, but with a slight difference: here we get into what the experienced and attuned might take notice of. Those who are bound and determined otherwise might insist that the cause was something else. The hotshot sword pupil swears that he missed because the sun was in his eyes, but the 65-year old military vet knows it was because his opponent had partial cover. The cleric who claims that his god will not let him suffer the spells of evil ones claims that he is not cursed at all, even if he was. This is not a roleplay guideline, but a possibility. A +2/-2 is noticeable, but it is also ignorable.

+4/-4
This is where things start to get interesting. If the average task has a DC of 10 and commoners roll an unaided d20 to surpass it, this improves a 50/50 shot to a 70/30 shot. For DC 5 tasks this makes success instantaneous and foregone. For opposed checks, this is the little edge that lets a sickly lad (Str 7) out-wrestle the city guard (Str 13) more often than his strapping father (Str 11) can. This is definitely noticeable and hardly ignorable. At low levels (and therefore in everyday terms) a -4 penalty is a very difficult obstacle to overcome. Looked at another way, it's the modifier difference between an ability score of 10 and an ability score of 18. That's bigger than the difference between a farmer and a Navy Seal. Obviously there's other differences (such as specialized training and equipment) that makes the distinction bigger, but in the one capability for which a character has a +4 bonus, he becomes hugely, significantly better than he was. Likewise, a -4 penalty is a really crippling affliction. It makes a regional authority at cobbling (5 ranks) no better than his second-year apprentice. It makes a militia fighter (Str 14, BAB +1, Weapon Focus) as inaccurate or weak as his 15-year old son.

+10/-10
This gets even more significant than before. A +10 bonus to a check turns Danny Normal into an olympic champion. It makes DC 10 checks automatic successes, and makes DC 20 tasks, normally almost impossible except for the trained few, a coin-flip away. On the other hand, a -10 penalty makes the incredibly knowledgeable local librarian as ignorant as an uneducated farmer, and the county strongman as weak as a six-year-old girl. If people can feel a +4 bonus or -4 penalty, they absolutely feel a +10 bonus or -10 penalty. Imagine that you woke up tomorrow and sort of knew what D&D was about, but otherwise had no knowledge about it whatsoever, at all. You had to look up every rule, you couldn't name any classes, you had to read every feat... that's a fraction of what a -10 penalty does. It makes a man who has dedicated his life to a pursuit no better than a newcomer. On the other hand, imagine you woke up tomorrow able to fly a fighter jet. That's a +10 bonus. It imparts an average adult lifetime of knowledge into your head. (Note that all of this assumes the average adult master of a technique is an elderly person with 10 ranks in something, generally 7 levels in an NPC class. Of course there will be exceptions that reach level 18 commoner or expert, but they are very rare.)

+20/-20
Here we hit the ridiculous and almost unimaginable. This is the stuff of Felix Felicis: no matter what you do with a +20 bonus in something, you can do no wrong within the parameters of normal usage. Basic commoners can't roll above 20 on a check. A basic commoner with a +20 bonus can't roll below 20. A great master with 10 ranks and a +20 bonus can roll up to DC 50 checks. A child can fight better than the king's knights. A clumsy oaf with a +20 to AC or Reflex saves can ninja backflip over AAMRAAM missiles. Likewise, a -20 penalty makes the world's strongest man weaker than a squirrel. It makes the world's wisest man dumber than a lizard. This is the stuff of grand dreams and terrible nightmares. A +20 makes the unthinkable possible for the average man. A -20 makes a great legend into a weeping babe.

Ad Hoc DMing

Hopefully the preceding information will be useful when determining what bonuses and penalties to ad hoc when DMing the unusual, and make what bonuses and penalties do get thrown out seem less arbitrary. With a solid mental picture of what bonuses and penalties mean to the average man it's much easier to assess the correct one. In addition, an understanding of bonuses and penalties can turn, "Darn, now my character might not be able to hit very often" or "Awesome, I got a buff spell!" into a viable roleplay opportunity. I look forward to an excellent conversation based on the veracity or inaccuracy of my numbers and descriptions, and welcome the helpful comments sure to come.
#2
empirate
Nov 13, 2007 8:51:16 I think you're under a wrong impression if you think that +1 bonuses are almost negligible. They don't only provide a +5% to the chance that you succeed, but rather much more.

Say you're a 1st level fighter fighting Orcs straight from the Monster Manual. You have an attack bonus of, say, +5 (+1 base, +2 from Str 15 with the Elite array, +1 from Weapon Focus, +1 with a Masterwork weapon). The Orc has an AC of 13. You need an 8 to hit, and this means that 65% of your swings will hit.

Now you receive a Bless spell from your friend, the 1st level Cleric. Suddenly, you only need a 7 to hit, meaning that 70% of your attacks will connect. A flat increase of 5%? Let's do the math: 70 divided by 65 equals 1.077, meaning that your chance to score a hit goes up by 7.7%, not 5%.

Now say you're fighting not an Orc, but something tougher. Say you're in your boss fight, and you're facing a Bugbear. This particular Bugbear is a tough mother, and has ditched his leather armor for chainmail. His AC is 20 (+1 Dex, +3 NA, +5 chainmail, +1 small shield). You need a 15 to hit him, which will happen 30% of the time. Your Cleric casts Bless, increasing that to 35%. How much has your chance to hit the Bugbear actually gone up? 35 divided by 30 is 1.167. Your chance to hit the Bugbear is increased by 16.7 percent, or exactly one sixth. If you bash this Bugbear for six rounds, you're granted one full hit more than you otherwise would by a mere Bless spell.

Now this Bugbear's brother is the elder, and he has access to some really good equipment. He uses full plate along with a large shield. He also has the Dodge Feat, and declares its use against you. His AC is 25 (+1 Dex, +3 NA, +2 large shield, +8 full plate, +1 Dodge), meaning you hit him on a natural 20 only. What does Bless do now? It actually doubles your chances of hitting! Instead of a nat 20 only, you now hit the Bugbear on a 19, too! A meager +1 bonus increases your chances to hit by a full 100%!

Always remember this: a +1 bonus doesn't equal five percent. Depending on the difficulty of the attempted task, it can up to double your chances of succeeding. The easier the task, the less a +1 does for you; the harder the task, the more welcome a little bonus can be.

Most of the time, you'll be trying something that can be accomplished about half of the time. In these circumstances, a +1 bonus increases your chances to succeed by 10%, no less. I've come to think of +1 as +10% because of this. Do the math.
#3
highbulp
Nov 18, 2007 10:16:18
I think you're under a wrong impression if you think that +1 bonuses are almost negligible. They don't only provide a +5% to the chance that you succeed, but rather much more.

You're looking at a different statistic. I'll use the "needing a 20" example because it's simpler.

If you need to roll a 20 to hit somebody, then you have a 5% chance of rolling that high on the die and hitting them. By getting a +1 bonus and only needing a 19 to hit, you now have a 10% chance of rolling that high on the die and hitting them. Yes, the odds of you rolling a hit has doubled (+100%), but the chances of the event actually happening has still only gone up by 5%.

I'm sure there is a technical term for this, but I'm not sure what it is at the moment. The point is, a +1 bonus is always a 5% gain. Now how much of an improvement that 5% is can vary (as you have pointed out), but it's still only a 5% increase in odds.
#4
empirate
Nov 20, 2007 12:10:42 Of course you're right from the outside perspective. But for the PC (or NPC) who actually is in the situation, +1 does more than up his chances of succeeding by 5%. The outside perspective of "chances of event X occurring" are largely academic to PCs in most circumstances.
If something takes you seven rounds to accomplish, and your chances to do your per-round average go up one-sixth because of a +1 bonus, you take one round less, on average. You don't take 5% overall rounds less to do it (which would be 0.35 full rounds), but one full round less (or 14.29% overall rounds less). Six instead of seven rounds.
#5
billthemaniac
Nov 20, 2007 16:40:46 First, a nitpick on the OP: Your math is off by 5%. The actual value is 5%x(21-DC)
You're looking at a different statistic. I'll use the "needing a 20" example because it's simpler.

If you need to roll a 20 to hit somebody, then you have a 5% chance of rolling that high on the die and hitting them. By getting a +1 bonus and only needing a 19 to hit, you now have a 10% chance of rolling that high on the die and hitting them. Yes, the odds of you rolling a hit has doubled (+100%), but the chances of the event actually happening has still only gone up by 5%.

I'm sure there is a technical term for this, but I'm not sure what it is at the moment. The point is, a +1 bonus is always a 5% gain. Now how much of an improvement that 5% is can vary (as you have pointed out), but it's still only a 5% increase in odds.

Yeah. The thing is, you have a 5% increase in probability as a percentage of all possibilities, which is a 100%-5.25% increase as a percentage of the original probability.

There's no real term for the multiplicative increase in probability because it would be too confusing.
#6
etarnon
Nov 21, 2007 2:45:39
this means that 65% of your swings will hit.

Now you receive a Bless spell from your friend, the 1st level Cleric. Suddenly, you only need a 7 to hit, meaning that 70% of your attacks will connect. A flat increase of 5%? Let's do the math: 70 divided by 65 equals 1.077, meaning that your chance to score a hit goes up by 7.7%, not 5%.

The chance increase is 70-65 / 100, Sorry that's just the truth, doing the math.
#7
empirate
Nov 22, 2007 11:57:03 You don't have to be sorry because we're talking about different things.
You're talking about the absolute chance of the (hit/successful bluff/whatever) occurring. I'm talking about the relative chance. "Doing the math" varies, depending on what you want to know.
To me, the knowledge that, if I cast [x], I'll have a 5% higher base chance to do [y] isn't as important as the knowledge what that +1 will do for me, namely, increasing the likelihood of succeeding by one-sixth. After all, I have to decide whether I want to cast [x] or not!
#8
the_apologist
Dec 02, 2007 16:19:59 Yeesh. Alright, so I'm not a statistician and phrased my idea wrong. Sorry.

The point is, the fighter isn't going to appreciably notice a +1 bonus to his skill. He can feel a +4. He can only feel the +1 if he's mentally convinced himself that he can. Same thing for a -1 penalty. If he's convinced it's not there, he can ignore it. Not so with a -4 or -10.

Post/Author/DateTime	Post
#1 the_apologist Oct 09, 2007 1:06:31	Every DM is familiar with the "DM's Friend" rule: every helpful circumstance grants a +2 bonus, every hindering circumstance assesses a -2 penalty. This works fairly well for most actions. However, as some DMs will attest, it's just not enough in some games, especially when you're a permissive DM and people are trying to do stuff that just can't be reasonably covered in a rules manual that's going to stay within marketable length. Therefore, I submit the following explanation of what bonuses and penalties mean to characters, both in game terms and in "real world" terms. And, as always, forgive me if some of my material is already explained in books that I do not own. Gaming is an expensive hobby and I am a man of meager means, so I only have about a dozen books. What the d20 Mechanic Means For starters, especially at low levels, the d20 mechanic gives us a fairly simple statistical analysis of "real life" applications of bonuses and penalties. Without getting into anything complicated, the numbers 1-20 are evenly distributed across a d20. Each has a 5% chance of occurring. That means, at any basic task for which the commoner has no knack or shortcoming (I.E. relevant stats are all 10 or 11 and no bonuses or penalties are assessed) a commoner has a percentage chance of successfully completing a task equal to one hundred minus five times the DC. For example, a commoner has a 75% chance of completing a DC 5 task in one try. This doesn't take into account things like tools, circumstances or mechanics such as taking 10 and taking 20, but it's a baseline to start. Explaining the Bonuses and Penalties Here I'll boil down what different bonuses and penalties mean to different people. We throw out +1, +2, +4, +10 and +20 bonuses so nonchalantly, but what do they -do-? +1/-1 A +1 bonus to a check, based on simple low-level math, is a 5% increase in probability of success. Same goes for the opposite: a -1 penalty is a 5% decrease in probability. Depending on the source of the effect, the average guy on the street probably doesn't even notice. A cleric only knows that his Guidance spell works because he has faith that it does; the results are probably not all that noticeable. Likewise, a Flare spell is like seeing spots. It might be the difference between hitting and missing, but for the most part someone who somehow experienced it unknowingly would attribute the miss to other factors. +2/-2 Much like the +1/-1 entry, but with a slight difference: here we get into what the experienced and attuned might take notice of. Those who are bound and determined otherwise might insist that the cause was something else. The hotshot sword pupil swears that he missed because the sun was in his eyes, but the 65-year old military vet knows it was because his opponent had partial cover. The cleric who claims that his god will not let him suffer the spells of evil ones claims that he is not cursed at all, even if he was. This is not a roleplay guideline, but a possibility. A +2/-2 is noticeable, but it is also ignorable. +4/-4 This is where things start to get interesting. If the average task has a DC of 10 and commoners roll an unaided d20 to surpass it, this improves a 50/50 shot to a 70/30 shot. For DC 5 tasks this makes success instantaneous and foregone. For opposed checks, this is the little edge that lets a sickly lad (Str 7) out-wrestle the city guard (Str 13) more often than his strapping father (Str 11) can. This is definitely noticeable and hardly ignorable. At low levels (and therefore in everyday terms) a -4 penalty is a very difficult obstacle to overcome. Looked at another way, it's the modifier difference between an ability score of 10 and an ability score of 18. That's bigger than the difference between a farmer and a Navy Seal. Obviously there's other differences (such as specialized training and equipment) that makes the distinction bigger, but in the one capability for which a character has a +4 bonus, he becomes hugely, significantly better than he was. Likewise, a -4 penalty is a really crippling affliction. It makes a regional authority at cobbling (5 ranks) no better than his second-year apprentice. It makes a militia fighter (Str 14, BAB +1, Weapon Focus) as inaccurate or weak as his 15-year old son. +10/-10 This gets even more significant than before. A +10 bonus to a check turns Danny Normal into an olympic champion. It makes DC 10 checks automatic successes, and makes DC 20 tasks, normally almost impossible except for the trained few, a coin-flip away. On the other hand, a -10 penalty makes the incredibly knowledgeable local librarian as ignorant as an uneducated farmer, and the county strongman as weak as a six-year-old girl. If people can feel a +4 bonus or -4 penalty, they absolutely feel a +10 bonus or -10 penalty. Imagine that you woke up tomorrow and sort of knew what D&D was about, but otherwise had no knowledge about it whatsoever, at all. You had to look up every rule, you couldn't name any classes, you had to read every feat... that's a fraction of what a -10 penalty does. It makes a man who has dedicated his life to a pursuit no better than a newcomer. On the other hand, imagine you woke up tomorrow able to fly a fighter jet. That's a +10 bonus. It imparts an average adult lifetime of knowledge into your head. (Note that all of this assumes the average adult master of a technique is an elderly person with 10 ranks in something, generally 7 levels in an NPC class. Of course there will be exceptions that reach level 18 commoner or expert, but they are very rare.) +20/-20 Here we hit the ridiculous and almost unimaginable. This is the stuff of Felix Felicis: no matter what you do with a +20 bonus in something, you can do no wrong within the parameters of normal usage. Basic commoners can't roll above 20 on a check. A basic commoner with a +20 bonus can't roll below 20. A great master with 10 ranks and a +20 bonus can roll up to DC 50 checks. A child can fight better than the king's knights. A clumsy oaf with a +20 to AC or Reflex saves can ninja backflip over AAMRAAM missiles. Likewise, a -20 penalty makes the world's strongest man weaker than a squirrel. It makes the world's wisest man dumber than a lizard. This is the stuff of grand dreams and terrible nightmares. A +20 makes the unthinkable possible for the average man. A -20 makes a great legend into a weeping babe. Ad Hoc DMing Hopefully the preceding information will be useful when determining what bonuses and penalties to ad hoc when DMing the unusual, and make what bonuses and penalties do get thrown out seem less arbitrary. With a solid mental picture of what bonuses and penalties mean to the average man it's much easier to assess the correct one. In addition, an understanding of bonuses and penalties can turn, "Darn, now my character might not be able to hit very often" or "Awesome, I got a buff spell!" into a viable roleplay opportunity. I look forward to an excellent conversation based on the veracity or inaccuracy of my numbers and descriptions, and welcome the helpful comments sure to come.
#2 empirate Nov 13, 2007 8:51:16	I think you're under a wrong impression if you think that +1 bonuses are almost negligible. They don't only provide a +5% to the chance that you succeed, but rather much more. Say you're a 1st level fighter fighting Orcs straight from the Monster Manual. You have an attack bonus of, say, +5 (+1 base, +2 from Str 15 with the Elite array, +1 from Weapon Focus, +1 with a Masterwork weapon). The Orc has an AC of 13. You need an 8 to hit, and this means that 65% of your swings will hit. Now you receive a Bless spell from your friend, the 1st level Cleric. Suddenly, you only need a 7 to hit, meaning that 70% of your attacks will connect. A flat increase of 5%? Let's do the math: 70 divided by 65 equals 1.077, meaning that your chance to score a hit goes up by 7.7%, not 5%. Now say you're fighting not an Orc, but something tougher. Say you're in your boss fight, and you're facing a Bugbear. This particular Bugbear is a tough mother, and has ditched his leather armor for chainmail. His AC is 20 (+1 Dex, +3 NA, +5 chainmail, +1 small shield). You need a 15 to hit him, which will happen 30% of the time. Your Cleric casts Bless, increasing that to 35%. How much has your chance to hit the Bugbear actually gone up? 35 divided by 30 is 1.167. Your chance to hit the Bugbear is increased by 16.7 percent, or exactly one sixth. If you bash this Bugbear for six rounds, you're granted one full hit more than you otherwise would by a mere Bless spell. Now this Bugbear's brother is the elder, and he has access to some really good equipment. He uses full plate along with a large shield. He also has the Dodge Feat, and declares its use against you. His AC is 25 (+1 Dex, +3 NA, +2 large shield, +8 full plate, +1 Dodge), meaning you hit him on a natural 20 only. What does Bless do now? It actually doubles your chances of hitting! Instead of a nat 20 only, you now hit the Bugbear on a 19, too! A meager +1 bonus increases your chances to hit by a full 100%! Always remember this: a +1 bonus doesn't equal five percent. Depending on the difficulty of the attempted task, it can up to double your chances of succeeding. The easier the task, the less a +1 does for you; the harder the task, the more welcome a little bonus can be. Most of the time, you'll be trying something that can be accomplished about half of the time. In these circumstances, a +1 bonus increases your chances to succeed by 10%, no less. I've come to think of +1 as +10% because of this. Do the math.
#3 highbulp Nov 18, 2007 10:16:18	I think you're under a wrong impression if you think that +1 bonuses are almost negligible. They don't only provide a +5% to the chance that you succeed, but rather much more. You're looking at a different statistic. I'll use the "needing a 20" example because it's simpler. If you need to roll a 20 to hit somebody, then you have a 5% chance of rolling that high on the die and hitting them. By getting a +1 bonus and only needing a 19 to hit, you now have a 10% chance of rolling that high on the die and hitting them. Yes, the odds of you rolling a hit has doubled (+100%), but the chances of the event actually happening has still only gone up by 5%. I'm sure there is a technical term for this, but I'm not sure what it is at the moment. The point is, a +1 bonus is always a 5% gain. Now how much of an improvement that 5% is can vary (as you have pointed out), but it's still only a 5% increase in odds.
#4 empirate Nov 20, 2007 12:10:42	Of course you're right from the outside perspective. But for the PC (or NPC) who actually is in the situation, +1 does more than up his chances of succeeding by 5%. The outside perspective of "chances of event X occurring" are largely academic to PCs in most circumstances. If something takes you seven rounds to accomplish, and your chances to do your per-round average go up one-sixth because of a +1 bonus, you take one round less, on average. You don't take 5% overall rounds less to do it (which would be 0.35 full rounds), but one full round less (or 14.29% overall rounds less). Six instead of seven rounds.
#5 billthemaniac Nov 20, 2007 16:40:46	First, a nitpick on the OP: Your math is off by 5%. The actual value is 5%x(21-DC) You're looking at a different statistic. I'll use the "needing a 20" example because it's simpler. If you need to roll a 20 to hit somebody, then you have a 5% chance of rolling that high on the die and hitting them. By getting a +1 bonus and only needing a 19 to hit, you now have a 10% chance of rolling that high on the die and hitting them. Yes, the odds of you rolling a hit has doubled (+100%), but the chances of the event actually happening has still only gone up by 5%. I'm sure there is a technical term for this, but I'm not sure what it is at the moment. The point is, a +1 bonus is always a 5% gain. Now how much of an improvement that 5% is can vary (as you have pointed out), but it's still only a 5% increase in odds. Yeah. The thing is, you have a 5% increase in probability as a percentage of all possibilities, which is a 100%-5.25% increase as a percentage of the original probability. There's no real term for the multiplicative increase in probability because it would be too confusing.
#6 etarnon Nov 21, 2007 2:45:39	this means that 65% of your swings will hit. Now you receive a Bless spell from your friend, the 1st level Cleric. Suddenly, you only need a 7 to hit, meaning that 70% of your attacks will connect. A flat increase of 5%? Let's do the math: 70 divided by 65 equals 1.077, meaning that your chance to score a hit goes up by 7.7%, not 5%. The chance increase is 70-65 / 100, Sorry that's just the truth, doing the math.
#7 empirate Nov 22, 2007 11:57:03	You don't have to be sorry because we're talking about different things. You're talking about the absolute chance of the (hit/successful bluff/whatever) occurring. I'm talking about the relative chance. "Doing the math" varies, depending on what you want to know. To me, the knowledge that, if I cast [x], I'll have a 5% higher base chance to do [y] isn't as important as the knowledge what that +1 will do for me, namely, increasing the likelihood of succeeding by one-sixth. After all, I have to decide whether I want to cast [x] or not!
#8 the_apologist Dec 02, 2007 16:19:59	Yeesh. Alright, so I'm not a statistician and phrased my idea wrong. Sorry. The point is, the fighter isn't going to appreciably notice a +1 bonus to his skill. He can feel a +4. He can only feel the +1 if he's mentally convinced himself that he can. Same thing for a -1 penalty. If he's convinced it's not there, he can ignore it. Not so with a -4 or -10.