Paladin 2 / Wizard (abjurer) X
You said you are willing to take at most a 2 level dip in another class for proficiencies. Have you considered taking these levels in Paladin? Assuming you want to keep the "I'm a Wizard!" flavour, taking your first 2 levels as a Paladin of the god of magic (assuming there is one in your campaign, of course) isn't really out of character. So here's my take on this build. I'll mostly cover melee options, since this is what the question is about, but you should still be able to do anything that another wizard could do, just 2 levels later. This gap can be great at certain levels (Fireball is a great damage upgrade at level 5), but it shouldn't be noticed too much on single target damage (Smite!). It's not the strongest build out there, but it's definitely good enough to be enjoyable!
Benefits of 2 paladin levels :
- Proficiency with all weapons : opens up many solid weapon choices
- Proficiency with all armors and shields : although dex is definitely the best stat in 5E, a melee wizard will require spending spell slots on defence to keep up. Being able to wear a full plate and a shield gives great defensive benefits and costs no daily ressources.
- 6 more HPs : While 2 more level wizard levels would've given you 4 more arcane ward HPs, those only replenish on a long rest or by spending spell slots. Arcane ward is an awesome feature, but real HPs trump it anytime.
- Lay on Hands : Yay for 10 free HPs per day! More than makes up for those 4 lost ward HPs, and can be used on other people, too.
- Fighting style : There are many good options here, but I'd go for protection or defence to increase your utility/survival. Great weapon fighting is a good offensive option if you forgo your shield and grab a great sword, especially since you're going to stack lots of dice on those attacks. This can be somewhat replaced by the Elemental Adept feat, however.
- Access to 1st level paladin spells : One thing you'll have as a wizard is lots of low-level spell slots rather early. Smite spells might not always be the best options, but they can add good damage and other effects on your melee attacks. Paladin also has a few abjuration spells, which gives you back some arcane ward HPs, but the good ones are higher level, sadly. If you have the warcaster feat and can handle your constitution saves, Shield of Faith is also very good as a low-cost defensive boost. While Cure Wounds is a paladin spell, you can cast it using your full spell slots, which means that, although not a cleric, you still have access to some great healing powers if they are needed.
- Divine Smite : Convert spell slots into damage. Given that you can elect to smite after you know the attack hits, and that there is no save for this damage, it's a great way to increase your melee damage. Especially good if you crit...
That being said, given equal gear, you should have the same AC as any other tank, since you're wearing the same stuff they are. As for your damage, the new Sword Coast Adventure Guide cantrips are there for you. Sure, they're not going to out-damage a fighter or a rogue, but they're still very good damage options. Since they require a melee weapon attack, they also trigger class features such as Divine Smite, so you don't miss out too much. Having two attacks could technically mean 2 smites per round, but the added damage of your cantrips will compensate for this quite decently.
- Green-Flame Blade : when fighting multiple enemies, this attack basically gives you the benefit of a second attack without costing anything. Since you're not going to have multiple attacks from class features, this is pretty much as good as you're going to get.
- Booming Blade : Assuming you can make sure your opponent moves willingly each round, this cantrip will give you the same benefits as GFB except on a single target.
Other thing to note is that the secondary damage from these spells automatically hits, no save and no attack roll required, which means that you can strike a minion to land free damage on the BBEG. These spells will thus give you decent damage round after round, leaving you with all your other spell slots to use as you see fit. Your 2 levels of paladin will give you the opportunity to convert your low-level spell slots into more damage as an option, and your wizard powers will allow you to turn these same spell slots into defensive abilities. Shield will grant you +5 AC for one round, which is awesome if you attract the BBEG's attention (especially given that your AC is already high). In Elemental Evil, there is also the Absorb Element spell, which gives you resistance against a single element, also for one round. This gives you defensive options for both physical and most magical attacks. As an interesting addition, both of these spells are abjuration-based, and will thus heal your ward for 2 HPs every time you cast them.
And after all this, you're still an almost full wizard. Your access to spells and features will be delayed for two levels because of multi-classing, which shouldn't reduce your melee effectiveness, but you will still have access to 9th level spells and have spell slots as a 19th level caster. While the Signature Spell capstone is good, the real treat is at wizard level 18 (character level 20 for you), so you don't miss out on much. Indeed, spell mastery will allow you to have 2 low-level at-will spells, which gives you infinite Shield spells, for instance. This should allow you to use your slots for more offensive options, since your defence is free. Infinite Shield spells also means that your arcane ward is always topped off after every combat if you take a minute or so to recharge it after each fight.
Your melee power also scale quite decently if we compare them to a tank fighter (longsword + shield, defensive fighting style) of equivalent level :
- Level 1-4 : Fighter [1d8 + str] vs GFB [1d8 + str + (int secondary)]
- Level 5-10 : Fighter 2x[1d8 + str] vs GFB [1d8 + 1d8 + str + (1d8 + int secondary)]
- Level 11-16 : Fighter 3x[1d8 + str] vs GFB [1d8 + 2d8 + str + (2d8 + int secondary)]
- Level 17-19 : Fighter 3x[1d8 + str] vs GFB [1d8 + 3d8 + str + (3d8 + int secondary)]
- Level 20 : Fighter 4x[1d8 + str] vs GFB [1d8 + 3d8 + str + (3d8 + int secondary)]
Of course, a fighter has abilities to increase his damage, but so do you (thank you, Divine Smite)! Since the fighter has more attacks, he's more likely to deal some damage each round, whereas your damage all hinges on your single attack landing. This will be especially important if the fighter can get his hands on a weapon that deals extra damage (like a flame tongue), an ability that would be mostly wasted on your single attack per round. The fighter also only requires only one good stat to be 100% effective, while you will need both strength and intelligence. Since your intention is to go melee, I'd consider maxing strength first, especially considered you'll use your spells mostly defensively or in a utilitarian fashion (so lower save DCs are not as bad).
Feats to consider :
- Warcaster : For pretty obvious reasons (casting and adv. on constitution saves). Combined with Booming blade, it's also a boost to damage: when an enemy tries to get away, you booming blade it, which will deal almost double damage if it hits, as the enemy will likely leave the area right after. If they don't, well, your party gets to kill them anyways.
- Shield Master : If you are using a shield, it's a solid defensive feat.
- Heavy Armor Master : +1 strength, reduce most physical oncoming damage by 3. The drawback is that it doesn't work on your arcane ward, as it has it's own HP pool. As such, any damage the ward takes is not "damage that you take" and does not trigger this feat. Still a great option for a tank, especially one that has a wizard's HP pool and requires strength for his attacks.
- Elemental Adept : You're going to cast a lot of fire cantrips, and this feat allows you to ignore resistance and to treat 1s as 2s. This feat does not specify that only the fire damage dice are affected, so it works on your weapon die, your GFB dice, but also on your added Divine Smite dice. Definitely not bad.
- Mage Slayer : Disrupt enemy spellcasters from melee range. The attack granted by this feat is not as strong as a full opportunity attack (as warcaster will allow for a GFB or BB cantrip), but if you can prevent them from casting, it has a lot more utility. Advantage on saves isn't exactly bad either.
Other things to consider :
- Transmuter instead of abjurer : possible proficiency with constitution saves or resistance to one element is a good trade-off for a melee wizard. Not sure that I'd sacrifice arcane ward for it, though. Since Arcane Ward has it's own HP pool, all the damage it soaks isn't counted towards the concentration save DC. Advantage from warcaster should be more than enough, especially if you have some stat bonuses.
- Bladesinger instead of abjurer : A tough one... Since you're going to use cantrips for offense, you're wasting the extra attack feature with that build. But... a dex-based character wearing light armor will have only 1 less AC than a plate wearing character (equal if you cast mage armor instead), so your bladesong will leave you with a net +2 to AC during a fight once you get 20 intelligence (since you're also forgoing your shield). Even if not going for a strength build, you lose none of the advantages of a paladin (smite, armor proficiencies, healing, spells, etc.), but also gain Intelligence bonus to concentration saves and increased combat speed, as well as overall better skills since dexterity is the best stat. I'd personally favour bladesinger, but both options are very interesting.
Expected Average Damage: 641.354, Maximum Damage: 1185
No items or spell components, no special circumstances. Legal for use in Adventurer's League. Attacking with Surprise.
Half-Orc (Arthur) (Savage Attacks add an extra die of damage on every critical hit)
Divine Soul Sorcerer 4 (Favored by the Gods, Shadow Blade spell, Subtle Spell meta-magic, ASI)
War Domain Cleric 1 (War Priest - make one weapon attack as a Bonus Action)
Assassin Rogue 3 (Assassinate - if surprised, advantage on all attacks, critical on all hits, 2d6 Sneak Attack with Finesse weapons per turn, Expertise: Stealth, Perception)
Battle Master Fighter 3 (Action Surge, 4 Maneuvers, including Precision Attack, Menacing Attack, and Disarming Attack, Fighting Style Dueling)
Paladin 2 (Divine Smite, Divine Sense, Fighting Style Armored)
Divination Tradition Wizard 2 (Portent)
Gloom Stalker Ranger 5 (Dread Ambusher: in the first round you gain an extra attack on every Attack action in the first round, +10 movement, extra 1d8 damage of the weapon's type on this extra attack, Primeval Awareness, Pass without a Trace, Longstrider, ASI, Fighting Style Archery)
Strength 14 + 2 + 2 ASI
Dexterity 13
Constitution 8 + 1
Intelligence 13
Wisdom 13
Charisma 13
- To-Hit: +11, +12-19 with Precision Attack
- Hit Points: 92
- AC: 19 (Breastplate, Armored Fighting Style, Shield)
- Stealth: +23 (Expertise and temporary boost from Pass without a Trace)
- Initiative: +2 (+1 Dexterity, +1 Wisdom from Dread Ambusher)
- Perception: +13 (Expertise)
- Level 10 spellcaster (4 Sorcerer + 1 Cleric + (2 Paladin + 5 Ranger)/2 + 2 Wizard)
- Movement speed: 40 feet (50 feet with Longstrider)
- Darkvision: 90ft
The crux of it is that you have created a truly dreadful ambush character which has significant precision-boosting skills and tracking skills for his enemies. Beyond just being able to hit things hard, they also are able to do so with uncanny accuracy. This character goes patrolling for evil and predators in the woods, using his Primeval Awareness (L1 spell slot) to identify that there is evil in his land. As he uses his hunting ability to stalk his prey, his high perception and natural stealth make it difficult for his quarry to hide and make himself similarly difficult if not nearly impossible to spot. He'd use Pass Without a Trace, perhaps subtly, so that he could sneak up on his quarry. As he draws near and identifies his target, he casts Longstrider from his Ranger spells using the Subtle Spell meta-magic just to give himself that extra boost in movement that he'll need in order to close with his quarry before it realizes the danger. He knows how long it will take him to get into striking range, and stealthily moves to within 50 feet of his target. He has foreseen this day's events, and knows that death awaits his enemy. Patiently, he waits until it's his turn to strike. In terms of the sequence of events, I imagine it would look like this:
Primeval Awareness of the quarry, Subtle Pass without a Trace + Subtle Longstrider during the hunt for the quary. In the preparation round, cast Subtle Shadow Blade L5, from which the surprise round begins. Portent determines the initiative order for the target and the attacker: + Assassinating Critical: Action Surge + Dueling Attacks + Divine Smites + Dread Ambusher + Sneak Attack + Bonus Action War Priest weapon attack with Divine Smite.
Resource Expenditure:
- Spending 2L5, 3L4, 3L3, Spell Slots, all maneuvers, action surge, divine favor, War Priest ability
- Optional for flavor Spend another L2, 2L1 Spell slots: use a level 1 spell slot for Primeval Awareness to identify that your enemy exists nearby, then cast Pass without a Trace and Longstrider using Subtle Spell to hunt them and ambush them successfully.
Order of Events:
Preparation Round:
Level 5 Shadow Blade. (4d8 psychic damage per melee attack)
Surprise Round:
Initiative: Use Portent rolls to guarantee Assassinate feature works.
Action: Attack action (2 attacks from Ranger, +1 attack from Dread Ambusher feature)
*Bonus Action: 1 attack through War Priest
Action Surge: Attack action (2 attacks from Ranger, +1 attack from Dread Ambusher feature)
The Math on the Damage:
(All dice are doubled because these are critical hits because of Assassinate)
Every attack that hits results in this: 2\$\times\$4d8 Psychic (Shadow Blade, Level 5) + 1d8 Savage Attack + 2 Dueling Fighting Style + 5 Strength modifier = 9d8 + 7 Psychic damage
7 attacks (3 attacks per action, plus 1 attack from War Priest) yield: 63d8 + 49 Psychic damage
Gloom Stalker Ranger allows us to adds 1d8 damage of the original weapon's damage type to the extra attack of every Attack action we take in the first round of combat through the Gloom Stalker feature. Since we take two Attack actions through Action Surge, we get extra 2d8 Psychic damage, which is doubled since they're critical hits. 67d8 + 49 Psychic damage
Assassin Rogue allows us to add 2d6 Sneak Attack damage because Shadow Blade is a Finesse weapon. Sneak attack rules for rogues do not require you to use Dexterity when using Finesse weapons. Since the attack is a critical hit, the damage gets doubled. 67d8 + 4d6 + 49 Psychic
As a paladin, every successful hit allows us to add 2d8 + (spell slot level-1)\$\times\$1d8 radiant damage, maxing out at 5d8 for an L4 spell slot or higher. As a 10th level spellcaster, after casting Shadow Blade at level 5, we can use 3 L4 spell slots, 1 L5 spell slot, and 3 L3 spell slots. All of this, of course, gets doubled on critical hits, which these will be. This results in the following additional damage: 2\$\times\$(3\$\times\$5d8 + 1\$\times\$5d8 + 3\$\times\$4d8) = 64d8 Radiant damage
Damage Total:
(67d8 + 4d6 + 49 Psychic) + (64d8 Radiant) = (67\$\times\$4.5 + 4\$\times\$3.5 + 49 Psychic) + (64\$\times\$4.5 Radiant) = 364.5 Psychic + 288 Radiant = 652.5 total
In order for the Assassinate feature to work, during the first round of combat the Assassin must act before their quarry. By having access to Portent, we will have two dice rolls which can be used for any ability check, which includes initiative. Because the quarry has a +0 to their initiative and our character has a +2 to initiative, regardless of what we roll, we can substitute the lower of the two Portent rolls to the target and use the higher of the two rolls for ourselves.
Damage, adjusted for accuracy:
The following probability calculations below were made with the help of the table in the article "D&D 5e: Probabilities for Advantage and Disadvantage" to figure out the likelihood of rolling particular numbers on a 20-sided die with advantage.
At least one attack will always hit. It's true that it's mathematically possible for a 1 to be rolled on every single attack die (7 attacks, all with advantage), but the odds of that are ridiculously low: \$\left(\left(\frac{1}{20}\right)^2\right)^7\$ = 0.0000000000000000006103515625. In other words, the Sneak Attack will always be added.
Precision Attack maneuvers and the Favored by the Gods feature allow the player to use them after the attack roll is made and any of these three abilities can be used in conjunction with one another.
With our target having an AC of 20, and our character having a starting +11 to hit, we need to roll 9 or higher in order to successfully land a hit, which from the table we can see that we have an 84% likelihood through advantage.
The Precision Attack maneuver from the Battle Master, adds 1d8 to attack rolls, yielding 4.5 average increase in likelihood. This can be used on 4 attacks, resulting in +15.5 to attack rolls, since we have 4 superiority dice from the Battle Master. In addition, the Favored by the Gods Divine Soul Sorcerer feature will allow us to add 2d4 to one attack that misses, turning it into a hit on average, due to effectively adding +5 to hit (resulting in a +16 to hit) for one of the two attacks which we cannot add the Battle Master die to. As a result, for 1 attack we need to roll 4 or higher through advantage to score a hit, and for 4 of the other 5 attacks we need to roll 4.5 or higher through advantage in order to score a hit.
The optimal strategy of their use should look something like this:
- Our attacks, whenever possible, should be sequenced from most damaging to least damaging, in order to take advantage of our ability to lazily add attack bonuses.
- Similarly, we should use our spell slots for Divine Smite in a decreasing progression. The Bonus Action attack will use the L5 spell slot, the first three attacks of the first Attack action will each use an L4 spell slot, and the three attacks of the second Attack action will each use an L3 spell slot.
- If an attack misses and we still have a superiority die, we should use the Precision Attack adds an average of 4.5 to the attack roll.
- If the total for the attack roll is still too low and we still can use Favored by the Gods, we should use it.
- If the number of attacks remaining is less than the number of superiority dice remaining and we haven't applied a maneuver to the attack, we should apply a damaging maneuver like Menacing Attack or Disarming Attack.
The Bonus Action weapon attack will average (2\$\times\$4d8 + 1d8 + 7) Psychic + 2\$\times\$5d8 Radiant = 47.5 Psychic + 45 Radiant = 92.5 damage. Adjusted for the likelihood of a natural 1, the accuracy adjustment reduces the expected damage total by: -92.5*(1-0.84) = -14.8
When using Favored by the Gods, our to hit becomes +16 on average, which means we need to roll 4 or higher through advantage. On the referenced table, we see that for this we have a 97.8% likelihood. The damage for this attack will be (2\$\times\$4d8 + 1d8 + 7) Psychic damage and (2\$\times\$5d8) Radiant = 9d8 + 7 Psychic + 10d8 Radiant = 47.5 Psychic + 45 Radiant = 92.5 damage. Adjusted for accuracy, this means that the damage total is lessened by -(1-0.978)\$\times\$92.5 = -2.035.
When using the Precision Attack maneuver, since the AC of the target is 20 and we will need to roll "5.5", the average (I think) will be (97.8% + 96%)/2 = 96.9%. This means that each of the 4 attacks with maneuvers has a 96.9% chance to hit. So, we will on average do 96.9% of the expected damage for those 4 attacks. The damage of these 4 attacks of the two Attack actions is: 4\$\times\$1d8 + 2\$\times\$4\$\times\$4d8 + 2\$\times\$1d8 + 4\$\times\$7 Psychic + 2\$\times\$(4d8 + 4d8 + 5d8 + 5d8) Radiant = (38d8 + 28) Psychic + (36d8 Radiant) = 199 Psychic + 162 Radiant = 361 total damage. Adjusting for accuracy, this means that the previously mentioned "total damage" is also lessened by -361\$\times\$ (1 - 0.969) = -11.191
On each of the 4 attacks on which we use a superiority die, if the attack doesn't need the accuracy boost, we can apply the die to the damage by using a different maneuver, such as Disarming Attack, doubling it because of the critical hit. This results in 2\$\times\$1d8 damage = 9 damage. How often would we get to add this extra damage? Since the original to-hit modifier is +11, hitting AC 20 would happen 84% of the time. Thus, 84% of the time, we can substitute a damaging maneuver instead of the Precision Attack Battle Master maneuver. Thus, the expected damage is increased by: 0.84\$\times\$9 onto every attack, for four attacks: 0.84\$\times\$9\$\times\$4 = +30.24
The 3rd attack from the second Attack can do (2\$\times\$4d8 + 1d8 + 7) Psychic damage and (2\$\times\$4d8) Radiant = 9d8 + 7 Psychic + 8d8 Radiant = 47.5 Psychic + 36 Radiant = 83.5 damage. As such, the damage expected for the last attack will be 83.5*(1-0.84) = -13.36.
Result:
Adjusted for accuracy, then, this means that the expected average damage of this character is 652.5 -14.8 - 2.035 -11.191 + 30.24 -13.36 = 641.354 total damage
Hope this math was relatively easy to follow, and hope you guys enjoyed the character and story setup as well. And be aware, the optimal use of the superiority dice and Favored by the Gods could improve this by a few more points.
*Note: Originally, I came up with a slightly higher number by using a Quickened Booming Blade. However, that spell is from Sword Coast Adventurer's Guide, and because many of the other features referenced here are from Xanathar's Guide to Everything, in Adventurer's League we wouldn't be able to use both for this character. *
It's worth noting, since the original poster mentioned this looking like a Death Knight, that this build would probably work even better against a Death Knight, because the latter's shield and sword can be removed through the Disarming Attack maneuver, thus lowering his AC and removing its ability to parry with his reaction.
*Note: Another poster, Herohersh (https://rpg.stackexchange.com/a/138689/49041), cleverly suggested that based on the guidelines for this math problem you could use your action to Create Bonfire during the setup round when you're casting Shadow Blade, step into the bonfire in order to trigger Absorb Elements through your reaction, and then proceed to attack using the bonus damage of Absorb Elements. In addition to probably not working mechanically due to stipulations regarding casting any other spell during the same round during which a Bonus Action spell is cast, for my personal taste I find this unsatisfying because it breaks the immersion and idea that you could still be hidden from your enemy the round before you attack if you conjure a bonfire that gives away your position. *
Best Answer
While the question you ask is theoretically simple, there are a lot of factors that need to be taken into account when dealing with this. The difference between the two builds isn't just "Oh, I'm going to change out a couple of levels and have basically the same character!" There's a lot of differences, and there can be a lot of things that change between the characters. For simplicity, all of the characters will share the same race and ability scores. This means that I can calculate the same attribute bonuses how I like, and basically make the character have the skills we need.
The first decision is to assume we are going a strength-based character. We could do a bow Fighter, and it would work well especially with the long-range of the bow, but I am still trying to max out the Champion aspect of the Fighter/Wizard, and using a Str-Based character with a Greatsword means that the critrange of 19-20 is helped out that much more by 2d6 melee over 1d8 ranged damage from a Longbow.
The goal for the Knight is to get to basically max Str/Int for damage purposes, and then either 18 Con + Tough for max HP, or 20 Con for 25 less HP than the tough mode and gain +1 Con Mod.
For the Fighter/Wizard, we want to maximize damage. While this class should still have a fair bit of melee ability, we need to maximize the offensive abilities best we can. Trying to max out Str/Int first is good, and then having the rest of the ability score increases (which there are only 5 of) to round out the HP gives the Fighter/Wizard a significantly worse HP.
We are going to use a Mountain Dwarf. Since we only need Int, Str, and Con as our stats to max now, since Wis, Cha, and Dex don't matter, we want to maximize those values. Mountain Dwarf gives +2 to Str and +2 to Con, so we can start out with a 17/8/17/15/8/8 character. With the Eldritch Knight, it's impossibly easy to get 11 points of Attributes out of the 7 attribute increases.
Itemization will be the same. They will both have 2 +1 Longswords/Shortswords and +1 Full Plate (for defensive purposes). This will give them max AC and max damage for now.
The target will be an Ancient Red Dragon. It has 22 AC, which to my knowledge is the hardest thing to hit at the moment.
From there, it becomes a simple measure of planning and building the characters.
Elder Rich Level 20 Mountain Dwarf Fighter (Eldrith Knight)
Charisma: 8 (-1)
Start: 17/8/17/15/8/8
Features: Two Weapon Fighting (Fighting Style), Second Wind, Action Surge (Two Uses), Weapon Bond, Extra Attack (3), Indomitable (three uses), Weapon Bond (Eldritch Knight), Improved War Magic (Eldritch Knight), Eldritch Strike (Eldritch Knight), Arcane Charge (Eldritch Knight)
Feats: Tough, Dual Wielding, Heavy Armor Master
Main Hand: +1 Longsword (+12 Attack, 1d8 + 12 Damage (16.5 Avg. Dmg.), 2d8 + 12 Crit (21 Avg. Dmg. Crit))
Rich is probably going to be able to deal a fair bit of damage. Each single Main Hand Longsword strike will deal an average of 16.5 Damage on a hit. Against a Red Dragon, that's a 55% chance to hit (and 5% to crit), so 9.3 damage per swing accounting for accuracy (and crit). The offhand is 10.5 damage on average, so a 6 damage per swing accounting for accuracy (and crit). That means every attack action is going to be 15.3 damage per swing. Considering that Rich will get 4 attacks per turn, this is 61.2 DPR on just a basic set of attacks. With an Action Surge, that damage jumps to 122.4, which is approximately 22% of an Ancient Red Dragon's max HP. Two turns right after each other, Rich Alone could easily bloody the Dragon with slightly lucky rolls.
The main hand weapon used to be a +1 Greatsword. Compared to the current build, it did less damage on Rich's turn (10.8 damage per Attack action, 43.2 damage per turn vs. 15.3 per Attack Action, 61.2 per turn), but had a higher reaction -> opportunity attack damage. This is because it had an average damage of 19 Damage (Crit 26). These extra points of damage could stack up well, but to be honest, the lack of 2.5-5 points of damage on the 1 reaction per round loses out to the heavily increase DPR thanks to the dual wielding. The Greatsword also had a higher Improved War Magic damage, thanks to being able to attack only with your main-hand weapon. Again, while the loss of 2-5 damage per Spell -> Attack is known, the heavy increase in overall DPR from the multiattack functionality of Fighters is much more useful.
Fig Tier Wiz Level 20 Mountain Dwarf Fighter (10)/Wizard (10)
Charisma: 8 (-1)
Start: 17/8/17/15/8/8
Features: , Second Wind, Action Surge (One Use), Improved Critical, Extra Attack, Remarkable Athlete, Indomitable (one use), Great Weapon Fighting (Additional Fighting Style); Arcane Recovery, Arcane Tradition, X Savant, 3 Arcane Tradition Features (Arcane Ward, Projected War, Improved Abjuration || Sculpt Spell, Potent Cantrip, Empwered Evocation)
OPTION 1:
OR
OPTION 2:
So here I've given out 2 builds for Fig that both can work. We only have 5 Ability Score increases, so it is much more difficult to max out Str and Int and get a high Con score. Technically, Heavy Armor Master can be exchanged for any feat that gives +1 Str, Con, or Int, but the DR 3 on non-magic weapons seems like a huge deal.
Option 1 is what I had originally come up with for Fig and Rich. The idea is to max out damage thanks to Str and Int, and use a Greatsword for combat. Because of that, you can take the Defense Fighting Style for +1 AC. The damage for this character is 10.8 Damage per attack accounting for accuracy against an Ancient red Dragon, and therefore a 43.2 Damage per turn.
Option 2 is more like Rich, wanting to use two weapons. The best/only options for max 1-handed light damage is Shortsword basically. As with Rich, the damage is greater over the course of a round than using the Greatsword because of the multiple hits you get in per attack, but you have a lower amount of damage on a reaction, by about 2 points (3.5 points on a hit, 7 points on a crit). This build sacrifices 1 AC to get an increase of damage at close range.
(As an aside, Option 2 could also possible use an 18/8/18/20/8/8 final ability score with 2 +1 Longswords and Dual Wielding. I checked the numbers, and while you do get +1 AC thanks to dual weilding, you actually lose damage overall. This is because while you do get to go from 1d6 weapons to 1d8, you lose +1 to your Attack Modifier and +1 to your damage. The mainhand would be +11 to attack, 1d8 + 11 Damage (15.5 Avg. Dmg), 2d8 + 11 Crit (20 Avg. Dmg. Crit)). As you can see, the main hand would basically lose 5% on normal attacks, while the Average Crit damage increases by 1. This is the same for the off hand. The only difference is basically that you lose 5% to-hit to gain a marginal benefit when you crit.)
So right off the bat we see that Fig is lacking in a couple of areas compared to Rich. He's already at a much lower HP thanks to the levels in Wizard only giving +4 to HP per level instead of +6. In addition, the lack of ability score increases means that hitting 18 Con + Tough or 20 Con is almost impossible without sacrificing damage. With 60 HP less than Rich, it's a fair bit of damage that is not turned lethal.
Second, the lack of Action Surges and Extra Attacks means that Fig won't be able to attack more than twice a turn. This is huge when you compare the two characters. The lack of Dual Weilding for Fig means no "natural" dual wield longsword, and therefore a fair bit of loss of damage. On top of that, you can only deal ~28.2 damage per turn, ~56.4 with your single Action Surge. The damage that Fig is going to be putting out is on the level of a 10th level fighter, not a 20th Level Fighter/Wizard.
Speaking of the Wizard side, you are still not a super-powerful spellcaster when it comes to spells. What you give up from the Wizard Side to "splash" 10 levels in Figher means that you only have access to 5th level spells. While not an issue for the most part, 5th levels spells will need to greatly make up for the damage deficit that the lack of extra attacks the fighter should have incurs. You also "only" have 2 5th level slots and 2 4th level slots over the Knight. I put "only" in quotes because while I can attempt to downplay those slots, they represent a level of power the Knight cannot achieve. If we are talking about pure damage, the Knight can cast 1 4th level spell, but will probably want to prefer to use his spells as support spells to further lock-down his targets while he beats the heck out of them. The Wizard can use those 4 extra slots to provide a lot of utility to the party.
For comparison of the spell casting abilities, we need to look at the damage between the classes. Because spell damage is only based onthe spell, not your For now, I think the best option to check for spell damage is going to be the Spell Damage Comparison Chart put out by Rhaegar83 on /r/dndnext.
Looking at the spells, it's clear that no 5th level spell can match the single-turn damage of a 20th Level Eldritch Knight attacking the crap out of a single target. While you do get access to some nice 5th level AoE spells like Cone of Cold and Flame Strike, the Eldritch Knight can easily hit 2 targets for similar Damage if he is able to get between the two using his move.
The end result is that Rich, the Eldritch Knight is going to end up tankier (HP and AC) and able to deal more single-target damage thanks to his quad-attack. Fig is going to be able to deal more AoE damage, single by virtue of having access to 5th level spells, as well as 2 more 4th level spells slots. Fig is also going to be able to be more of a controlling presence on the battlefield, if he is going to take at least some support/control-y spells.