Chapter 1: Statistics
Before we jump straight into action, let's look at statistics around the most common actions in D&D 5th Edition. This information will help us assess and leverage the probability of success for each type of those actions, therefore, giving us a better understanding of the game. Here's what we'll discuss in this chapter:
- Attack vs AC
- Spell vs Saving Throw
- Ability Check vs DC
- Critical Success and Critical Failure
- Advantage and Disadvantage
- How important is it really?
- What does it all mean?
Attack vs AC
An attack is an action that requires you to roll a d20 and add your ability modifier and proficiency bonus relevant to the type of attack. The total of your roll is compared to the Armor Class (AC) of the target of the attack. If the result is equal or higher than the AC, the attack hits, resulting in you applying the effects of the attack to the target (usually, dealing damage).
Since this is the most common action in combat, it is important to have at least a rough estimate of your chances to hit an enemy. For a low-level character that is optimised for making attacks of a certain type total to-hit modifier will be a +5 and an average AC for a low-cr monster is ~15. That puts us at around 55% chance to hit a monster with an attack. This is statistically equal to (a slightly skewed) coin flip, so on average every second attack would hit.
For characters that are trying to make an attack they are not optimised for the chance is halved (25-30%), so most of the time there are better things to do than to try to whack a monster with a weapon or spell you can't use effectively.
Spell vs Saving Throw
Certain offencive spells require their target to make a saving throw: roll a d20 and add an appropriate ability modifier and possibly their proficiency bonus. If the result is equal or higher than the Difficulty Class (DC) of the spell, the spell does not take its full effect (some spells affect creatures even if they pass the saving throw).
Since both monsters and characters can have access to offencive spells, it is important to know the odds for a spell to take effect on a creature. For a low-level character or a low-cr monster the save DC for their spells will be around 12-13. A bonus to the saving throw for a monster can range from +0 to +5. Just as with attacks probability of a spell to not take its full effect is around 40-65%. Most monsters, however, will have their bonuses somewhere in between making the average probability close to a coin flip. Again, there is one in two chance for a creature to avoid the effect of a spell.
Ability Check vs DC
Both inside and outside of combat a character is sometimes required to pass an ability check. In case of spells and attacks the numbers are set by the game. For ability checks, however, the DCs are set by the DM. That being said, most DMs follow certain guidelines while setting difficulties of ability checks.
Mechanically the action is familiar: the character rolls a d20, adds the relevant ability modifier, and possibly their proficiency bonus if they can apply one of their skills of tool proficiencies to the check. If the result is equal or higher than the DC of the check, the character passes, otherwise they fail.
Certain ability checks can mean the difference between life and death or have other substantial consequences. Thus, it is good to know, how likely you are to pass the check before attempting the task.
In most cases an easy task will have a DC of 10, a moderate task will have a DC 15 and a hard task will have a DC of 20. For some tasks the diffculty falls somewhere in between, resulting in DCs of 12 or 18. A character's bonus to an ability check can normally range from +0 to +5, depending on their ability scores and their skill proficiencies.
We will look at the most important case: a character that is fully optimised for the task attempts to pass a moderate ability check (DC 15). Again, the probability of success in that case is close to a coin flip (55%). In the most extreme case of a character attempting a hard task without any relevant bonuses their probability of success is only 5%. I would strongly advise to delegate important tasks to characters that are the most optimised for them.
Critical Success and Critical Failure
In case of attacks (and for most DMs in case of ability checks) rolling a 1 or a 20 results in critical failure and critical success: the action has an additional effect that can change the outcome significantly. The chance of each of those happening is 5%, so they don't happen often. However, due to sheer amount of rolls they will still occur from time to time, so keep an eye on that.
Advantage and Disadvantage
Advantage or disadvantage on a roll lets you roll an additional d20 and choose the best (or worst) result of the two. At first glance this does not look like much, but if we remember that success in most cases is determined by a coin flip, the real advantage (pun intended) for a roll to be successful in case of advantage changes from ~50% to ~75% (the roll fails only if both dice fail), which is a significant increase. But wait, there is more! If we consider critical hits, their chance is effectively doubled, which is great!
How important is it really?
In previous sections we've discussed at length the probabilities of success of most actions in D&D, but how much of a difference does an increase in an attrubute really make? Consider, that you try to optimise the crap out of your character and you sacrifice certain benefits to achieve a sweet +1 in a certain stat. That increase makes your character only 5% more successful in performing tasks that correspond to that stat, which is, let's face it, not a lot. The key here, however, is in performing a lot of tasks, but generally speaking, you don't have to worry to much about a stat increase, if you choose between it and another benefit.
What does it all mean?
You may be wondering 'this is cool and all, but what do I make of all of that?'. Don't worry, I've got you covered. Here's a number of things we can learn from looking at (approximate) statistics:
- As a rule of thumb you can estimate the probability of success on an action of moderate difficulty that you character is optimised for as a coin flip. That should cover questions like 'What are the odds of me finishing that monster in next round?' and 'How many monsters will be affected by my AoE spell?'.
- In most cases, the difference between character being optimised and not optimised for a task is statistically significant. When you as a party are faced with an important challenge, try to delegate the challenge to the character which is optimised for it the most.
- Relying on a coin flip can get you in trouble quickly. Therefore, you should always look for ways of leveraging probability towards your success. Try to gain advantage on your actions and impose disadvantage to the actions of your opponents. Look for ways to bestow other bonuses (or penalties) to those actions. Consider some backup options while performing a task and try to provide those options to your teammates. This requires cooperation, coordination and communication between the party.
- Know your strengths, but most importantly, KNOW YOUR WEAKNESSES. If there is a task you are not optimised for, try to curcumvent having to attempt that exact task and come up with other options to accomplish your goal. Sometimes the best solution is to give up, rethink, regroup and prepare.
- Sooner or later (usually sooner) the dice will sqrew your plans. Roll with it. There will always be situations where dice change the outcome in ways untold. Try to be prepared for that. Always be ready to improvise, have a plan B (and plans C and D, sometimes even E). Try not to have your plans to have a lot of steps that rely on rolls, since the chance of things not going according to plan grows with each extra step. But most importantly, learn to have fun and accept any outcome as an opportunity to tell a better (and a bit crazier) story.
If you're reading this, congratulations! You've actually made it to the end! In the next chapter we'll discuss the concept of action economy, which is one of the most important tactical aspects in D&D and other similar games. But until then, good luck!