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Let us take a +2 enemy as an example:
We have +26 to hit and the enemy has 37 AC.
Regular true strike hit (critting excluded) is 69.75% and the crit chance is 9.75%. The crit chance doubles the damage (we're gonna exclude crit effects for simplicity here) so our total damage is 0.8925x where x is the avg damage of our attack.
With keen our regular chance to hit with true strike becomes 64% and the crit chance becomes 19% for a total damage of 1.02y where y is the average damage for this attack.
So for the non keen attack to do more damage in this scenario (true strike vs an enemy with 11 more AC than your hit rate) it needs to do 12.5% more damage.
The average damage of an elemental rune is 3.5.
3.5/0.125 is equal to 28 so if the keen attack does more than 24.5 (28-3.5) damage it will outdamage an elemental rune while spellstriking in this scenario.
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Let us take a +2 enemy as an example:
We have +26 to hit and the enemy has 37 AC.
Regular true strike hit (critting excluded) is 69.75% and the crit chance is 9.75%. The crit chance doubles the damage (we're gonna exclude crit effects for simplicity here) so our total damage is 0.8925x where x is the avg damage of our attack.
With keen our regular chance to hit with true strike becomes 64% and the crit chance becomes 19% for a total damage of 1.02y where y is the average damage for this attack.
So for the non keen attack to do more damage in this scenario (true strike vs an enemy with 11 more AC than your hit rate) it needs to do 12.5% more damage.
The average damage of an elemental rune is 3.5.
3.5/0.125 is equal to 28 so if the keen attack does more than 24.5 (28-3.5) damage it will outdamage an elemental rune while spellstriking in this scenario.
Just keep in mind that if your odds of hitting are just slightly better than your example (needing to roll a 9 to hit instead of an 11), the Keen rune doesn't help you at all because rolling a 19 is already a crit for you (as you beat the AC by 10).
Yes, it would be a boss-killer rune for that build. But even then status bonuses, status maluses and flanking may make the rune redundant except vs the toughest enemies.
It does make a second attack much stronger. Hit - true strike - hit.
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Using True Strike on a secondary attack is a plain bad idea.
If you're considering keen icm with true strike, doing it for the second attack is much better than for the first attack, because keen adds little to the first attack, where a 19 can be a crit already.
But spell strike is 2 actions already, so the answer would be that keen is not the most effective rune for true strike / spell strike combo.
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If you're considering keen icm with true strike, doing it for the second attack is much better than for the first attack
Nope. The first attack will at least have the same chances of critical success than the second. If you want to fish for crits, use True Strike on the first attack.
Overall, that's a bad idea to use True Strike on the second attack. For a normal martial it starts being better against a level -5 opponent or an at level opponent with a +7 bonus to hit, for a Fighter a level -4 opponent or an at level opponent with a +5 to hit. You roughly need to hit on a 2 for the second attack to be a better choice for True Strike.
For Stab and Blast you really want to hit the first attack since you don't get to make the second attack if you miss, therefor I would 100% True Strike on the first attack on Stab and Blast (if I wanted to use True Strike).
the keen rune is very situational if not pretty useless since it only nets you a +5% damage (one chance in 20 to double your damage) in the case you can still hit but not crit on a 19. Let us analyze some scenarios:
-your first attack is accurate enough to crit on a 19 or less by itself
then the keen rune is only useful on the second and third attack. You should almost never do three attacks except some very specific cases so we could say it is a +5% damage per round if you attack twice, a +2,5% damage per attack if you want (+3,3% if you attack 3 times). This in my opinion is the most probable scenario with a decently competent team (able to use buffs, flanking and debuffs) and if your GM does not love single very high level monster fights.
-Your first attack is not accurate enough to crit by itself on a 19
This is the best case scenario for the rune. Both your first and second attack can benefit from it so it nets you a +5% increase in damage per attack (unless you attack three times but as i said you probably should not).
To make a comparison, an elemental rune that deals 3,5 damage on average is a +7% damage if your base strike deals 50 damage. Unless my math is skewed (and it might, i'm no math making man guy) it feels a bit bad compared to the others. I mean, the better you are at critting the worse the critting rune gets? That is some weird design if you ask me.
I made a homerule that changes the keen rune to allow a crit if you pass the armor class of your enemy by 9 or more instead of 10. It feels a LOT better.
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You are mixing up percentage units with percentage, 5 percentage units more to crit might result in more than 5 percent of total damage increase.
However your general analysis of use cases for the rune is of sound logic to me.
As Onkonk said, you need to compare the one extra chance to hit to your actual chances to hit.
For example, unbuffed non-Fighter martials tend to hit on a 9 on their first attacks against same level enemies. So their second attacks hit on a 14: 6 chances to hit and 1 chance to crit. Getting to 5 chances to hit and 2 chances to crit (considering a crit as the double of a hit) gives a damage increase of 12.5% on your second attack. Second attack that accounts for roughly 35% of your damage on a double attack scenario, so you gain 4-5% damage in total. Way more in line with your elemental rune.
Also, you'll obviously choose such rune when your weapon has the Deadly/Fatal trait or if you have some great Critical Specialization, ending up with the rune efficiency being very close to the Elemental Rune.
The Keen Rune is not a bad rune. On crit builds, especially those with very high damage by default (Barbarian for example), it's a good rune.