[Pathfinder] 104 DPR at level 7 with Summoner

[borg286]

We all know that the Eidolon is the main reason to play a summoner, but just how much damage can you churn out. 
We all know that the fighter sucks, but how much more DPR can a dedicated Synthesist get?

Let's start with how I calculate DPR.
I approximate monster AC with the following 1.3*CR + 11.  From this we can calculate our expected damage against an monster of equal level.
Without taking into account extra damage that doesn't get multiplied on a crit you can calculate your DPR with the following equation.  Feel free to ask me to provide a proof if you want.
(number of similar attacks)*(average damage on a hit)(chance to hit(including chance to crit)) * (1+chance to crit)
Chance to hit = 1-.05*(DC-AB-1)
DC: is AC in this case
AB: attack bonus
Note: this assumes any number you can crit on also implies you hit.  If this is not the case then you probably shouldn't be attacking.

For example:
Thus for a level 7 fighter with +12/+7 dealing 2d6+10 greatsword(19-20/x2).
chance to hit 1: 1-.05*((1.3*7+11) - 12-1) = 0.645 = 64.5% to hit
chance to hit 2: 1-.05*((1.3*7+11) - 7-1) = 0.395 = 39.5% to hit
average damage on a hit: 2d6+10 = 17
DPR = 1*17*.645*1.1 + 1*17*.395*1.1 = 19.45 DPR


Now let's look at a fully optimized Eidolon/Synthesist at level 7
He gets 4 feats: Exotic Weapon Prof(Bastard sword), Multi-weapon fighting, Double Slice, Weapon Focus(Bastard Sword)
Base form: Quadruped; Str 14, Dex 14, Con 13, Int 7, Wis 10, Cha 11;
Stat boosts(Eidolon granted):+3  (I put my attribute boost in Con so I can get a 14 con
Items: 10x +1 masterwork bastard sword,  Belt of giant strength +2
Buffs cast: Enlarge
For his Evolutions: Free: bite(1d6), Free: limbs (legs) (2), Pounce(1), Claws(1), 4x Limbs(2)
AB(Bastard sword): +6(BAB) +5(Str) -1(size) + 2(charge) -2(MWF) +1(WF) = +11
AB(claw):+6(BAB) +5(Str) -1(size) + 2(charge) -2(MWF) -5(secondary natural weapon)= +5
AB(bite):+6(BAB) +5(Str) -1(size) + 2(charge) -2(MWF) -5(secondary natural weapon)= +5
AB(Bastard sword(secondary attack)):+1(BAB) +5(Str) -1(size) + 2(charge) -2(MWF) +1(WF) -5(secondary natural weapon)= +1

Damage(Bastard Sword): 1d10 -> 2d8(large) + 5(str Double Slice) + 1(Enh) = 15 average damage
Damage(Bite): 1d6->1d8(large) + 2(str/2) = 6.5
Damage(Claw): 1d4->1d6(large) + 2(str/2) = 6.5

Being a Synthesist mean I an my Eidolon are one and I gain all of his evolutions, thus I gain 4 pairs of limbs(hands) and his natural attacks.  I have

target AC: 1.3*7+11 = 20

Chance to hit: 1-.05*(20-11/5/5/1 - 1) = .6/.3/.3/.1

DPR calculation
10*15*.6*1.1(10 bastard sword attacks) + 1*6.5*.3*1.05(bite) + 1*6.5*.3*1.05(2x claw) + 1*15*.1*1.1(secondary attack from high BAB)
99 + 2+1.7+1.6=104 DPR

-----------
Now let's take a look at HP
Fighter with a 14 con gets Level*(d10+2+1)
Synthesist with a 14 con gets Level*(d8+d10+2+2+1)
This is due to the way Summoners can redirect damage dealt to their Eidolon to themselves, effectively making 2 tanks. 
A Synthesist gets +20 AC over the course of his career and +4 saves on top of his light armor.
The fighter gets plate and lowers his DPR by using a shield.
Then at level 16 the Synthesist can literally double himself for the whole encounter and effectively get double actions and double DPR.
-----------

Let's take a look at level 1 non Synthesist Summoner with nothing fancy
Base form: Quadruped; Str 14, Dex 14, Con 13, Int 7, Wis 10, Cha 11;
For his Evolutions: Free: bite(1d6), Free: limbs (legs) (2), Pounce(1), Claws(1), Improved Damage: Claws(1)
AB(claw):+1(BAB) +2(Str)+ 2(charge) = +5
AB(bite):+1(BAB) +2(Str) + 2(charge) = +5

Damage(Bite): 1d6+ 2(str) = 5.5
Damage(Bite): 1d4 + 2(str) = 4.5

target AC: 1.3*1+11 = 12

Chance to hit: 1-.05*(12-5 - 1) = .7

DPR calculation
1*5.5*.7*1.05(bite) + 2*4.5*.7*1.05(2x claw)
4+6.6=10.6 DPR
===
Now let's compare that with a 2-handed weapon fighter
AB: +1(BAB) +4(Str) + 1(Weapon focus) +2 (charge)= +8

Damage: 2d6+7(str*1.5) = 14

target AC: 1.3*1+11 = 12

Chance to hit: 1-.05*(12-8 - 1) = .85

DPR calculation
1*14*.85*1.1 = 13.1 DPR


Thoughts?

[Mixster]

Dwarven Waraxe deals more damage on average than a Bastard Sword, but spending two feats on something you could essentially get with the Heirloom Weapon trait is probably also a bad ideal.

While in your combat form, you don't qualify for double slice, but you seem to have forgotten to add it in anyway, it would have added +3 damage per claw.

If you assume DR 5/Magic. Which is reasonable at this level, your damage plummets while the THF fighters stays about the same.

[borg286]

I did have a miscalculation.  I forgot to take an additional -2 penalty for weilding a 1-handed weapon instead of a light weapon.  I'll redo my calculation now.


AB(Bastard sword): +6(BAB) +5(Str) -1(size) + 2(charge) -4(MWF) +1(WF) = +9
The secondary attacks add little to damage

Chance to hit: 1-.05*(20-9 - 1) = .5

10*15*.5*1.1(10 bastard sword attacks) =  82.5 DPR



as per the DR, true, my DPR would drop to 55 and his to 13.7
Still a factor of 4

Before I was doing 4.23 times as much damage, now due to the DR I'm only doing 4 times as much damage as the 2 handed fighter.

If it was DR 10 let's see how we fare
8 DPR for the fighter
27.5 DPR for the synthesist
I'm doing 3.44 times as much damage.
I'm not seeing the argument for DR.  If I were weilding short swords and didn't have Double Slice (which doesn't work on natural weapons by the way) I can see your point, but that's why we use the bastard sword and double slice.

==========
How do the dwarven waraxes do more damage than a bastard sword?  I'm honestly not seeing it.
DPR for an /x2 weapon is (average damage)*(chance to hit)*(1+chance to crit)
DPR for an /x3 weapon is (average damage)*(chance to hit)*(1+2*chance to crit)
they always balance /x2 weapons with /x3 weapons by trading 1 point of multiplier for 1 more threatening number ((20)-> (19-20) -> (18-20))
ie. 18-20/x2 = 19-20/x3 = 20/x4
and 19-20/x2 = 20/x3   <--bastard sword vs. war axe
1+.1(bastard sword) = 1+2*.05(waraxe)
The only argument I can see is the fact that you have to hit to confirm the critical, and my equations do not reflect the scenario where you can roll a number within the crit range but still not hit.  For example if you have a 25% chance to crit, but only a 10% chance to hit my equations would be wrong, whereas with the x3 weapon getting into the scenario where the equation doesn't hold up would be less likely for he would only have a 10% chance to crit.

====

The real interesting thing to see is how much more DPR can a character get with each +1 to hit granted.

let's take a look a the fighter attacking a prone target
His DPR increases from 19.45 to 27 or 7.55/+4 bonus or +1.9 DPR per +1 granted
The Synthesist/Summoner increases from 82.5 to 115   or  32.5/+4 bonus = or +8.12 DPR per +1 granted

[borg286]

At 11th the summoner or synthesist will take improved share spells and then get a hold of a wand of lead blades.  This will increase his weapon damage 1 more step.  Unlike other spells the spell does not specify 1 or 2 weapons, or 1 natural attack, but all weapons.  Sadly the class feature of share spells does not work here because it specifically calls out it only works for spells on the summoner's spell list.  For improved share spells there is no such requirement.

I'll post here in case anyone needs it the weapon size progressions assumming you have exotic weapon prof

   1d6    1d8   2d6   3d6   4d6 : best weapon: Wakizashi, light, 18-20 crit
   1d8    2d6   3d6   4d6   6d6 : best weapon: Katana, 1-handed 18-20 crit
   1d10   2d8   3d8   4d8   6d8 : best weapon: Bastard Sword, 1-handed, 19-20 crit
   1d10   2d8   3d8   4d8   6d8 : best weapon: Dwarven waraxe, 1-handed, /x3 crit

And to really complicate any DPR calculations there Deadly Juggernaug

[borg286]

You can however, as a synthesist, use a wand of Lead blades and cast it on yourself.  Since it's the synthesist that gained his eidolon's evolutions, it is the synthesist that has gained the extra limbs and not his eidolon, therefore the weapons he's weilding and attacking with are his, not his eidolon's.
The earliest I can see casting from a wand is level 3

1   11   1 rank, +3 trained, +4 Cha, +3 skill focus(1/2 elf)
2   3   1 rank, masterwork tool +2
3   4   1 rank, +2 used it before (bless + guidance for first time), +1 skill boosting item
-----------
+18 rolling a 2 = 20 UMD check

Pretty mean buff at level 3

For everyone else they can take the trait that gives UMD as a class skill and grants a +2 to it.  Combine that with an extra level or 2 and anyone can cherry pick this spell.

[Ed-Zero]

Both Deadly Juggernaut and Lead Blades are amazing, haven't seen them before.

[Sobolev]

I'm fascinated by this idea, but I don't know why you're making 10 Bastard Sword attacks.  You bought Arms 4 times, which should give you 8 arms, not 10.  And you're a quadruped in order to get Pounce, so you're certainly not starting with 2.  The only thing I can think of is that you are assuming that you keep your original two arms, which is not how I read the ability, but I guess that's possible.  Please keep up the work, I am enthralled with the idea.

[borg286]

1d8, 19-20/x3, light)), 1: Multi-weapon fighting, 3: Double Slice, 5: Arcane Strike, 7: Weapon Focus
Evolutions: free: Bite(1d6), free:2x limbs(legs), Pounce(1), 10x limbs(hands)

Attack bonus(off hands): 6(BAB) + 5(Str)+1(WF)+2(charge)+1(enhancement) -2(MWF with light weapon) = +13
Attack bonus(bite): 6(BAB) + 5(Str)+2(charge)-7(MWF and secondary natural weaopn) = +7
Attack bonus(High BAB secondary attack): 1(BAB) + 5(Str)+1(WF)+2(charge)+1(enhancement) -2(MWF with light weapon) = +8

Target AC: 20

Chance to hit: 1-.05*(20-13/7/8-1) = .7/.4/.45

Damage
12x off hands: 1d8 + 5(str) + 1(enh) + 2(arcane strike) = 12.5
3x claw/bite: 1d6 + 2(str/2)  = 5.5
as a synthesist I have my pair of hands and I have 5 other pairs of limbs

--1 main +11x off hands-------bite/claw---------1x secondary attack from high BAB
DPR: 12*12.5*.7*(1+2*.1) + 3*5.5*.4*(1+.05) + 1*12.5*.45*(1+2*.1) = 140 DPR



Good buffs to have cast as buff:

• Lead Blades: increase weapon damage size by 1 step for all your weapons
• Enlarge Creature: +2 str, -1 attack, increase weapon damage die as usual

If these are active the DPR goes up to 233.06 DPR and 300 DPR vs. a prone target meaning he has a +16.8 DPR / +1 bonus granted

======

Now let's upgrade to 8th level where the Large evolution is available, throw on these buffs and reallocate our evolutions.
We'll also spend a bunch of money on 10x +1 keen Sawtooth Sabre so we can have a 17-20/x3 crit range

Evolutions purchased: pounce(1), large(4), 4x limbs(2) from 13 evolution points(2 of which came from being a 1/2 elf)

Str: 14(base) + 1(ability score increase @5th) +3(8th level eidolon) +2(belt of mighty strength) +2(enlarge creature) + 8(large evolution)= 30 Str (+10)

Attack bonus(off hands): 6(BAB) + 10(Str)+1(WF)+2(charge)+1(enhancement) -2(MWF with light weapon)-2(size) = +16
Attack bonus(bite/claw): 6(BAB) + 10(Str)+2(charge)-7(MWF and secondary natural weaopn)-2(size) = +10
Attack bonus(High BAB secondary attack): 1(BAB) + 10(Str)+1(WF)+2(charge)+1(enhancement) -2(MWF with light weapon) -2(size) = +11

Target AC: 21

Chance to hit: 1-.05*(21-16/10/11-1) = .8/.5/.55

Damage
10x off hands: 4d6 + 10(str) + 1(enh) + 2(arcane strike) = 27
1x bite: 2d6 + 5(str/2)  = 13
as a synthesist I have my pair of hands and I have 4 other pairs of limbs

---------10x off hands-------bite    ---------1x secondary attack from high BAB
DPR: 10*27*.8*(1+2*.2) + 1*13*.5*(1+.05) + 1*27*.55*(1+2*.2) = 330 DPR
and 398 DPR vs. a prone target meaning I get a +16.78 DPR / +1 bonus to attack granted

======

As per the DR 5/magic I have arcane strike and my weapons count as magic, so I can pierce through that.
But I'll calculate it anyways
Level 7 with no buffs: 80 DPR vs. fighter's 13.7
Level 8 with buffs: 267 DPR

[Sobolev]

I think you misunderstood what I was saying.  I wasn't disagreeing that you gain 2 arms when you buy the Arms evolution, what I was saying is that at level 1, with no evolutions, you have 4 legs and no arms.  You do not have your 2 arms for being a biped normally, because you are "translucently inside your eidolon" who is a quadruped.  Then you buy 10 arms, and you have 10 arms, not 12.

Also, I must be missing something.  I see why the Sawtooth Sabre is light, but I still thought it was 19-20/x2, not x3.

Edit: I'm about to join a PF game at level 1.  I might actually try this.  At level 1, I'm reasonably sure this can't function at all (I'm skeptical you can even qualify for MWF at level 1 with only three evolution points as a quadruped).  But you can always just hang out as a great cat until level 3, and then take off from there.  The real question becomes, what feat do you take at level 1.  Perhaps that's when you take Weapon Focus?  I'm not sure.

[borg286]

Your BAB is overridden by the eidolon and is thus +1.  =See if you can get the 1/2 elf variant racial swap of exotic weapon prof for your choice of

   1d6 Wakizashi, light, 18-20/x2 crit
   1d8 Katana, 1-handed 18-20/x2 crit
   1d8 sawtooth sabre, light 19-20/x2

[borg286]

Weapon   dam.   crit multiplier
Wakizashi   3.5   1.15
sawtooth   4.5   1.1
      
katana   4.5   1.15
falcata   4.5   1.2
bastard   5.5   1.1
waraxe   5.5   1.1

It looks like the sawtooth is better for light weapons
for the 1-handed weapons if you have a static damage modifier of 5 and no magical properties  the bastard sword and waraxe are always better than the katana and falcata even when you get gargantuan weapons.
When you have a static damage modifier of +10 the falcata is better on a medium creature, but the bastard sword edges ahead as you increase in size.  The same if your static damage is +20.

If you apply keen on all the weapons the falcata is better on a medium, but the bastard sword edges out as you increase in size.  As you get a static damage modifier of +10 and up the falcata becomes king for all size.  But only slightly.

My preference is for accuracy rather than straight damage so as to make your damage distribution probability tighter.  ie. you are more likely to do less damage more consistently rather than more damage less likely, but with the same expected damage in the end.
Because of this I'd favor the sawtooth.  Otherwise I'd go for the bastard swords as they're cooler than axes.

[Mixster]

There is, IIRC no 18-20/x3 weapon in pathfinder. Unless you use the backwards yadda yadda and use a Kaorti Resin Katana, which would then be a 18-20/x4 weapon.

I think the fighter you are comparing this too is too generic. And would like to come up with a proper fighter build. However, I find relying solely on damage to be a bad melee tactic, and would thus probably make a Kusari-Gama tripper.

Just for the record, I don't disagree that the synthetist is one of the best combat classes out there, and probably better than most fighter builds. It does have full BAB, a ton of floating improvements and up to 6th level spells. But the fighter does have some nice stuff for pure damage purposes in pathfinder, especially around level 8. It gets especially good with Teamwork tricks.

[borg286]

The level 6 spells is misleading.  While the summoner does classify them as level 6, they are equivilant to level 8 and 9 spells for the wizard.  His spell endurance is quite limited though.  Instead of being able to have a toolbox of spells at your fingertips there a few wonderful spells that open up more.  The evolution spells can give you spontaneous problem solving.   lesser gives you Climb, Swim, under water breathing, Reach, Scent, Skilled(+8 to any skill, take that, Mr. Factotum), Ability Increase(+2 to Cha for example), Energy Attacks if you're a natural attack kind of synthesist, Flight, Immunity to an elemental damage type, detect chaos/evil/good/law, and Tremorsense.  any for a level 2 spell

For his 3rd level spell(achieved at 7th level) he can get Blindsense, burrow, lesser restoration, see invisibility,  cure moderate wounds, Breath Weapon for minion clearing, Fast Healing to heal a minimum of 110 HP, Incorporeal Form(touch attacks + MWF/multiattack = dead) for the ultimate assassin, Spell Resistance, arcane sight, cure serious wounds,  gaseous form,  major image, and stinking cloud.

Albiet there are some level requirements on these evolutions.  The fact that he can call on any of these with either lesser evolution or evolution.  Greater evolution simply gives you 2 of them for the price of 1 high level spell.  That's some pretty good problem solving capability.

You're right that I didn't do a fair comparison against the fighter.  I know it's useless to compare to the fighter, but I had to establish a baseline and the fighter seemed a good candidate.

[Sobolev]

Yeah, at level 1 if your DM says you can't use your arms and its arms at the same time the answer seems to be Improved Natural Armor, Claws and Pounce.  If they do Pounce and Limb (Arms) seems to be the answer.  I'm not sure what your feat should be if you're going the way without the extra arms at first level.  You can't get Double Slice at first level, because you don't have MWF yet.  Power Attack is underwhelming.  Arcane Strike is less than stellar at such a low level.  Extra Evolution is a possibility?  I'm not sure what it could be spent on however.  

If Sawtooth Sabres are unavailable, what is a good offhand weapon for this?  I feel like offhanding a regular weapon (that is, not a light weapon) is too large a penalty, but maybe mathematically it pays off in the end.

FAQ agrees with me about the arms thing: http://paizo.com/paizo/faq/v5748nruor1fz#v5748eaic9obe

[borg286]

Just do the dpr calculation.  I just read the faq and I see his point.  I'll have to redo my dpr yet again.  I'd recommend bastard sword.  Best increase in damage with a single size increase.  Since the synthesist doesn't get 2 extra hands I'm wondering why go synthesist?  1/2 feats rather than 1/3 feats, lead blades wand would go away.  Hrm

[Sobolev]

Just do the dpr calculation.  I just read the faq and I see his point.  I'll have to redo my dpr yet again.  I'd recommend bastard sword.  Best increase in damage with a single size increase.  Since the synthesist doesn't get 2 extra hands I'm wondering why go synthesist?  1/2 feats rather than 1/3 feats, lead blades wand would go away.  Hrm

From a practical standpoint, as a Synthesist the monster has to go through your eidolon to kill you.  And you only have to cast Mage Armor once a day!  But you lose out on those extra actions.

[borg286]

If you can convince your DM to allow you to change Two-weapon fighting to multi-weapon fighting when you have multiple arms there is a nice solution:

At level 1 you simply don't have your eidolon out at all, ever.  This allows you to cast spells (remember that you can't cast any spell with somantic components while fused with an eidolon that has no hands), open doors(you need hands for that too), shake someone's hand, wipe your butt...
Provided you have a 15 dex at level 1, you take Two-weapon fighting and the 1/2 elf exotic weapon training (your mom was a lawful evil red mantis assassin, your dad was a chaotic good sorcerer who eventually divorced.  While at your mom's she taught you how to use sawtooth sabers.  While at your dad's you learned conjuration...)
Then at level 2 your eidolon's physical stats(overriding yours while fused now) qualify you to keep two/multi-weapon fighting.  At level 2 you will have 4 evolution points.  limbs(2), limbs(2) and just get pounce next level.

It's a bit expensive and redundant, but it ensures you qualify for everything starting at level 1(provided your DM is leniant with the two->multi-weapon fighting).

[borg286]

Just wanted to show off a cool finding.  This is more of how powerful UMD is, and how a Synthesist, and to a lesser extent a Summoner, can gain some huge versatility with UMD.
Here is how I would plan getting my UMD high
1: 9= 1(rank) + 3(trained) +4(cha) +1(guidance)
2: 12= 2(rank) + 3(trained) +4(cha) +2(masterwork item)
3: 15= 3(rank) + 3(trained) +4(cha) +2(masterwork item) +2(skill boosting item) +1(guidance)
4: 24= 4(rank) + 3(trained) +4(cha) +2(masterwork item) +2(skill boosting item) +8(skill evolution) +1(guidance)
5: 27= 5(rank) + 3(trained) +4(cha) +2(masterwork item) +2(skill boosting item) +8(skill evolution) +3(circlet of persuasion)
6: 28= 6(rank) + 3(trained) +4(cha) +2(masterwork item) +2(skill boosting item) +8(skill evolution) +3(circlet of persuasion)
7: 30= 7(rank) + 3(trained) +5(cha) +2(masterwork item) +2(skill boosting item) +8(skill evolution) +3(circlet of persuasion)
... just in ranks, nothing more

Under UMD: Use a scroll, "In addition, casting a spell from a scroll requires a minimum score (10 + spell level) in the appropriate ability"  Seeing that all wizard spells are also sorcerer spells, and that all cleric spells are also Oracle spells, you therefore have the Cha to cast them.
Therefore we only need to worry about the UMD 20 + caster level to cast the spell as though the spell were on our spell list

For the following Summoner levels we should have a good chance of casting a spell from a scroll(this is not taking into account the caster level requirements(bolded items), I'll do that in a sec).
3: 1(75%), 2(65%), 3(don't try)
4: 1(95%), 2(95%), 3(95%), 4(90%), 5(80%), 6(70%)...
5: 1(95%), 2(95%), 3(95%), 4(95%), 5(95%), 6(85%), 7(75%), 8(65%)
6: 1(95%), 2(95%), 3(95%), 4(95%), 5(95%), 6(90%), 7(80%), 8(70%)
7: 1(95%), 2(95%), 3(95%), 4(95%), 5(95%), 6(95%), 7(90%), 8(80%), 9(70%)

For sorcerer/oracle spells, because they're delayed a level behind the wizard/cleric, you'll need to have a caster level equivilant to theirs when they could first cast the spell.  Just because your UMD check is high enough to make the scroll believe the spell is on your spell list, it does not waive the CL requirement.
For this there's nothing we can do to boost it.

3: 1(100%), 2(95%), 3(85%), 4(75%), 5(65%), 6(55%), 7(45%), 8(35%), 9(25%),
4: 2(100%), 3(90%), 4(80%), 5(70%), 6(60%), 7(50%), 8(40%), 9(30%),
5: 2(100%), 3(95%), 4(85%), 5(75%), 6(65%), 7(55%), 8(45%), 9(35%),
6: 3(100%), 4(90%), 5(80%), 6(70%), 7(60%), 8(50%), 9(40%),
7: 3(100%), 4(95%), 5(85%), 6(75%), 7(65%), 8(55%), 9(45%),
8: 4(100%), 5(90%), 6(80%), 7(70%), 8(60%), 9(50%),
9: 4(100%), 5(95%), 6(85%), 7(75%), 8(65%), 9(55%),
10: 5(100%), 6(90%), 7(80%), 8(70%), 9(60%),
11: 5(100%), 6(95%), 7(85%), 8(75%), 9(65%),
12: 6(100%), 7(90%), 8(80%), 9(70%),
13: 6(100%), 7(95%), 8(85%), 9(75%),
14: 7(100%), 8(90%), 9(80%),

Now if I multiply these together(chance of getting both) we can achieve the chance to cast any sorcerer/oracle spell from a scroll
Level: Spell(Chance%)
3: 1(75%), 2(61.75%), 3(46.75%), 4(33.75%), 5(22.75%), 6(13.75%), 7(6.75%), 8(1.75%), 9(1.25%)
4: 2(95%), 3(85.5%), 4(72%), 5(56%), 6(42%), 7(30%), 8(20%), 9(12%)
5: 2(95%), 3(90.25%), 4(80.75%), 5(71.25%), 6(55.25%), 7(41.25%), 8(29.25%), 9(19.25%)
6: 3(95%), 4(85.5%), 5(76%), 6(63%), 7(48%), 8(35%), 9(24%)
7: 3(95%), 4(90.25%), 5(80.75%), 6(71.25%), 7(58.5%), 8(44%), 9(31.5%)
8: 4(95%), 5(85.5%), 6(76%), 7(66.5%), 8(51%), 9(37.5%)
9: 4(95%), 5(90.25%), 6(80.75%), 7(71.25%), 8(58.5%), 9(44%)
10: 5(95%), 6(85.5%), 7(76%), 8(66.5%), 9(51%)
11: 5(95%), 6(90.25%), 7(80.75%), 8(71.25%), 9(58.5%)
12: 6(95%), 7(85.5%), 8(76%), 9(66.5%)
13: 6(95%), 7(90.25%), 8(80.75%), 9(71.25%)
14: 7(95%), 8(85.5%), 9(76%)

If we follow the 90% chance line we get the following spell level progressions
3:1st
4:2nd
5:3rd
6:3rd
7:4th
8:4th
9:5th
10:5th
11:6th
12:6th
13:7th
14:7th
...

I know that purchasing scrolls is very expensive, but as for having a toolbox of spells like the artificer would, I'd say we're doing pretty good for ourselves.