Your cantrips do not do poor damage, and you have plenty of slots.
4.5 damage is not good damage at 3rd. It is terrible, terrible damage, far below average, bordering on pathetic.
You have 7-8 slots and some of them you are using to prop up the social pillar. There are 20 rounds of combat in a normal day (although you will probably be unconscious some of them). You will not be using leveled spells a lot combat.
Remember the idea is to be
GOOD at all 3 pillars. IF a 3rd level Wizard with a 10 dex, not shield, no mage armor who spends slots on non-combat encounters is "good" at the combat pillar, then a fighter with a 10 Charisma and no proficiencies is "good" at the social pilar, because that is about how effective you will be compared to other characters.
Maybe not enough to cover eight combat encounters,
I am figuring 6 combat encounters, lasting 3-4 rounds each, or about 20 rounds of combat total, and most PCs do have the health and resources to survive that. Further anyone who wants to contribute in combat usually can without using resources.
If your Wizard had a 16 Dex he would be helping every turn in combat with his crossbow. He would still be on the low side in terms of damage, but that low water mark is nearly 70% higher than you will be doing.
Besides, you asked for a 3rd level mage, of course they aren't doing their best yet.
I stated any Character who took a 16 in Constitution on point would not be good at all 3 pillars and they aren't.
Three or four Goblins? Unless they all shoot the wizard (which, they could theoretically survive) then they are going to drop at least one goblin on their turn. Assuming the rest of the party can manage at least that, the wizard will be fine.
Four Goblins. They need a 6 to hit you, they will likely surprise the party, they have a higher dex and initiative than you do and most of the time they will be rolling with advantage because they are hidden from you most of the time. The second you shoot a spell they will all fire at you (or all that are remaining alive will).
Also keep in mind with nimble escape and a +6 stealth there will be some difficulty targeting them with some of your spells.
This is a fight designed for 1st level and you have a significant chance of going down in it. On average 6 shots at you will take you down. Figure one in the first round while you are surprised and the goblins fire is split, three in the second round (after you cast a spell and one of the Goblins is dead). Two more shots at you in the 3rd round and you probably die.
I don't think it is definite, but I do think you are at a high risk. Poor stealth rolls by them, good attack rolls by the party will go to your favor.
I never insisted on the 16 constitution. You did. You specifically demanded I have it
What I am pretty sure I said was a fighter who takes a 16 Constitution on point can't be good at all 3 pillars, but neither can a Wizard or any other class except Bard, Rogue or Ranger. If those are not my exact words, it is pretty close.
My point is if you dump your other stats and throw a bunch of points into constitution you will be weak at least one of the pillars, having a 16 in Constitution is essential to the counter argument against that.
And, you are just declaring things with no reason here. Ray of Frost is a good cantrip, decent damage and a utility effect.
It is not decent damage at 3rd level. The only cantrip that is decent at this level is EB with AB.
4.5 damage with a +5 attack stat is less than 3 DPR. Considering Nimble Escape, that 3rd level Wizard in the goblin encounter above would take on average 4 rounds with ROF to kill a single Goblin.
Every time I use it, I'll be meaningfully contributing.
You will be contributing less than when a fighter with an 8 Wisdom and no perception proficiency searches a room.
Also, do you think something like Grease is only around for a single turn? That is a concentration spell, and can be effective for multiple turns.
Ok to start with Grease is not concentration. If it was concentration it would not likely stay around for long given how many concentration checks you will be making with a 10AC.
Grease lasts a minute, but it only affects a 10 foot area, enemies are not going to stay in it unless it gives them an advantage to do so or they have no choice.
I am not saying it is an awful spell, it is a good spell for 1st level only because it is a control that you do not need to concentrate on, but it is not as good as other concentration spells and typically does not give a lasting significant effect.
Additionally, only decent at the social pillar? Did you even read what I wrote? OR do you only count raw persuasion rolls as social and nothing else, like disguises, reading minds, illusions, misdirection, or any of the other things I built this character to actually do?
The character you built is good at the social pillar.
Yeah, and? I'm identifying a plant while looking through my familiar's eyes. Why would I be using my familiar's scores,
Because RAW it takes an action to look through your familiar's eyes and it only lasts until the start of your next turn. It takes another action to make the skill check.
Read find familiar -
" ..... While your familiar is within 100 feet of you, you can communicate with it telepathically. Additionally, as an action, you can see through your familiar’s eyes and hear what it hears until the start of your next turn, ...."
You take an action to look through your familiar's eyes, that ability stops at the beginning of the next turn before you make your skill check.
I'm the one taking the action.
No it is 2 actions you are trying to take on one turn.
I believe the only two ways to do this RAW as you describe are by using Time Stop or if you have 2 fighter levels and use action surge to do it.
Note how your entry says that they cover DIFFICULT situations that you encounter WHILE climbing.
That is what ability checks are for.
Athletics is the ability you use to make climbing checks. Not when climbing stairs, or climbing a ladder or climbing on to a horse, but any time you are going to make a check.
So yeah, my 8 strength wizard can climb a tree or a rocky cliff just fine. Might struggle with climbing up a waterfall or a smooth wall though. Which can be handled with pitons and rope.
No character needs to roll to do something trivial.
I don't need to roll persuasion to buy a mug of ale or perception to find the sun on a clear sunny day either.
I would argue that the tree and rocky cliff are not so clear and I know ROFM calls for athletics checks for climbing a cliffs, and TOA requires it for climbing a tree. So it would seem that official WOTC 5E content does in fact require you to make such a check for trees and cliffs at times.
No they don't, unless I am somehow soloing the encounter with no allies.
If you are soling this encounter 1 vs 4 you are almost certainly dead, despite it being an "easy" encounter RAW. As I said earlier, it is 4 turns on average to kill a single goblin using ROF and it is 6 attacks on you before you are down.
You mathematically still have a decent chance of going down if you are at 3rd level supported by 3 other 1st level characters. I said you have a decent chance of dying, and that is not actually true considering death saves, but you do have a mathematically significant chance of going down to 0 hit points in that fight and that is what I actually meant to say.
Here is what you are suggesting I change it to:
16 Str --> +3
10 Con --> +0
12 Charisma --> +1
16 Wisdom --> +3
13 Dex --> +1
8 INT --> -1
That is not what I am suggesting. As you qouted I said I would "dump" Strength or Dex, on point buy I would set one of those to 8 if I wanted to be good at all 3 pillars.
Do you... do you not know how maneuvers work? IF you are doing this per the fighting style, you get 1 die. 1 > 8, no matter how you cut that.
I don't think you know how maneuver dice work because you have the numbers wrong.
I assume you do realize that 8 number above includes the Wizard's short rest recharge through AR?
Maneuver dice all recharge on a short rest, which means from the fighting style alone he has 3 of them on a standard adventuring day with 2 short rests, not 1. That more slots than you are going to be able to spend on skill checks since you need to save most of your slots for combat.
Finally you can decide to spend the maneuver dice or not, whereas the spells you mention all need to be cast ahead of time.
So, to have "more manuevers" you need to be battlemaster.
No to have more maneuvers to spend on skill checks, while still being good at combat I just need the fighting style.
If I was building for this specifically at 3rd level I would have 4 more PER SHORT REST from subclass or 15 total per day.
But lo, I never picked a subclass for the wizard. So are we changing this so that you get to be a battlemaster who just happens to perfectly always use their dice ideally, while I'm a subclassless wizard?
So pick a subclass! It is not going to change it.
And as for contributing in every round of combat... that encounter with the goblins in the forest, do you know who has been the least effective every time I've run that? Melee combatants.
But you are probably not running it with a 10 Dex Wizard with no defensive options.
Because the goblins are hidden in the underbrush, at a distance, so the melee characters have to run in, deal with difficult terrain, and the goblins generally just keep kiting and shooting them then hiding. So, how effective is your fighter in any round of combat they can't reach a target? Are they always going to reach their target 100% of rounds of combat? Not in my experience.
At 1st level melee characters are still pretty good throwing things at the ranges the Goblins are at on that map and they are doing substantially more damage doing that than your Wizard. A sword and board with superior technique loses 1 point of damage throwing weapons at 1st level, a heavy weapon build with superior technique loses no damage at all considering they can go hand axes and throw one with a bonus action (1 attack 2d6+3 or 2 attacks totaling 2d6+3).
The reason a 1st level fighter will last longer than your Wizard is their AC is much higher and they can heal themselves.
And I love how you just go "sure" to a character who needs six skills, when their background and class will combine to give them 4. And will also need to break the rules for character creation to have unusually high stats. And you still need to assume Battlemaster, and not any other type of fighter.
I never said they needed 6 skills, nor that they needed to play a Battlemaster. Playing a Battlemaster is an option, and at this level it is the best one for this purpose, but I did not preface it with that assumption. My assumption is you need a good Wisdom and Charisma and some Wisdom and Charisma Skills with some exrtras to boost those checks.