[RPG] Can you cast the Fireball spell to target a point such that its area affects an opponent next to you but not yourself

Here are some examples of the areas affected by a 15-foot cone cast at different angles.

The point of origin is shown at an intersection between squares (as recommended in the DMG), and also centered on the side of the square for attacks in a cardinal direction (which is more intuitive).

Here are all the squares that are touched by the cone:

Here are all the squares that are 50% or more covered:

This is probably as close as you can get to the standardized shapes of previous editions.

A more generous interpretation in keeping with the spirit of the rules would be to say that the cone hits any creature whose circular base is overlapped:

Boy, so many people lining up to tell you "don't do it that way it's badwrongfun!" I'll offer a differing perspective, which is yes, absolutely, use a house rule to this effect. It has the desired effect of adding verisimilitude without "nerfing" or "ruining" anything. I shall offer up real play experience and not pure opinion to demonstrate this.

I used this exact kind of house rule during all of my AD&D 2e days (a decade) and from time to time in 3e/Pathfinder days for the same reason; adding some verisimilitude to combat - far from negating the need for tactics, it instead makes you have slightly better tactics because you aren't relying on things being exact (like artillery and infantry in the real world). Planning for the possibility of friendly fire makes for incorporation of real world techniques which is always desirable to me (learning about real world weapons, tactics, history, science, etc. is one of the best benefits of RPGs that many people seem to want to stomp out nowadays). Also, adding a little bit of randomness to magic makes it not so overwhelmingly better than the martial options - some of the martial/magic power differential comes from "I have to roll all the time" vs "I just do it", so by making your mages roll to do things you equalize the playing field a bit.

House Rule Option 1: Grenade-Like Missiles

But to do this you need something that best as I can tell is missing in 5e, which is what previous editions call "grenade-like missile," "scatter diagram," or the "throw splash weapon." In 1e AD&D it was under Grenade-Like Missiles in the DMG (p.64) - you'd roll d8 for direction and d4 (short range) d6 (mid range) d8 (long range) for how far it landed from the target.

In its most recent 3.5e incarnation, it's written like this:

To attack with a splash weapon, make a ranged touch attack against the target. Thrown weapons require no weapon proficiency, so you don't take the -4 nonproficiency penalty. A hit deals direct hit damage to the target, and splash damage to all creatures within 5 feet of the target.

You can instead target a specific grid intersection. Treat this as a ranged attack against AC 5. However, if you target a grid intersection, creatures in all adjacent squares are dealt the splash damage, and the direct hit damage is not dealt to any creature. (You can't target a grid intersection occupied by a creature, such as a Large or larger creature; in this case, you're aiming at the creature.)

If you miss the target (whether aiming at a creature or a grid intersection), roll 1d8. This determines the misdirection of the throw, with 1 being straight back at you and 2 through 8 counting clockwise around the grid intersection or target creature. Then, count a number of squares in the indicated direction equal to the range increment of the throw. So, if you miss on a throw out to two range increments and roll a 1 to determine the misdirection of the throw, the splash weapon lands on the intersection that is 2 squares away from the target in the direction toward you. See the accompanying diagram.

After you determine where the weapon landed, it deals splash damage to all creatures in adjacent squares.

In other words, roll to hit the target place, and use d8 to scatter direction on a miss.

So, super helpful for those thrown mundane firebombs, but you can also use it for area effect spells that don't usually require a hit roll - you just require that touch attack on their target or target square. (You have to interpret what "range increment" means for the spell, I usually just did 1 square if it was dropping in short spell range, 2 squares medium, 3 squares long). You can use a real ranged hit roll or sub in something like an Arcana check at your discretion. (Sometimes in 3e I've used Spellcraft instead of a to-hit).

A fireball is most likely still going to hit that main guy you throw it at. It is less likely to perfectly get every one of a group of enemies, and it's also more dangerous to try to crisp everyone including the enemies in direct melee with your party members.

Then you get to apply other bonuses/penalties like you would for ranged attacks. I'm running a Pathfinder pirate game where PCs are often trying to heave fireballs and lightning boats at enemy ships while going full speed in a ship heaving up and down on the waves through a rainstorm. Those additional to-hit penalties make it really exciting, especially if some of their crew has already flown over onto the enemy ship! Similarly, if players play smart and set out ranging stakes and practice, then when the hordes of wild elves attack their encampment they could get advantage on the placement roll.

House Rule Option 2: Proximity Saves

One of my current Pathfinder GMs handles this same problem just by making all party members in close combat with anyone getting AoEd make a save for half/no damage, for the same reason. This works OK but I don't like it as much, mainly because it takes all the control away from the wizard. "Having to roll to hit" is not onerous and expected of other classes, but just saying that they can't really try to place it better and you just have to save if you're around is a bit odd and tends to just make AoEs one radius bigger. "How come an enemy in contact doesn't have to save too?" Although rogues and monks and such enjoy being able to use evasion with impunity in these situations.

Why This Isn't A Huge Mistake

The theoretical problems levied against house ruling this by other posters are invalid.

1. "This takes control away from the player!" Only to the degree that control is taken away from any character (especially the fighty types) from having to roll a die to determine success. That's arbitrary, and other d20 derived games do have spellcasters roll for success and it doesn't "ruin" them.

2. "This obviates the point of using a grid with its numerological perfection." No it doesn't, again, any more than fire bombs or ballista or anything else having to roll to place on a grid does. You don't have to go Theater of the Mind to get a little bit of imprecision. You could, but that's not a necessary solution.

3. "This removes the need for tactics!" Really? Removing randomness removes tactics? Counterexample: the real world. Rather than removing tactics this instead ensures more realistic tactics.

4. All kinds of tactical tips for your monsters to not bunch up and not get all fireballed. All fine, do those too, but does not bear on the validity of this house rule. Encounter design is an entirely different topic.

5. "It's not RAW." No one cares; your game is your rules. See How do you help players not focus on the rules?

6. "This must mean you are a meanie and are against your players." I assume you'll use the same rule when monsters fireball, so that's not really valid, and it assumes bad faith in that you don't really just want more realism like you say but you want to "stick it to mages." Plus, does it mean you hate fighters because you make them roll for stuff?

From my experience, all this house rule does (both variants) is make a) casters not drop AoEs sometimes in risky situations, and b) make martials have to be a little smarter because they can't rely on pinpoint spellcaster artillery precision. It changed the game a little, but not in any way any of the participants thought was "unbalanced." Instead, it ended up more realistic, which is one of my core gaming principles (YMMV). I haven't used these in 5e, but I am familiar enough with 5e to say I don't see any way in that this would have a different effect (as to be expected, as 5e is closest to a 2.5e in practice).