Cutting corners with Store TP and weapon skills

Edit: Another table appended.

Last week I referred to "minimum store TP" to achieve so-called n-hit builds from the standpoint of going from 0 to 100 TP in n hits or reaching 100 TP in n - 1 hits starting with sufficient TP return from the previous weapon skill, but practically speaking I should have called it "worst-case scenario store TP if you're using a multi-hit WS." With all the TP you'll get after the first hit (and when was the last time you saw only the first hit land when your WS didn't kill your target?), there aren't too many compelling reasons to maintain "true" store TP totals if it means using equipment you wouldn't touch otherwise. The question is how much store TP to drop while still maintaining a "virtual" n-hit.

As you might have guessed, you can turn to probability to answer this. Consider first the case of a 5-hit polearm with a 5-hit weapon skill. After calculating the probabilities for obtaining sufficient TP returns from a single WS (no need to present such clutter, but I hope I didn't screw up), we can see the relationship between dropping store TP and the lowered probability that you will be able to get 100 TP in n - 1 hits of the next TP-generating "cycle." Of course, these probability calculations are based on the assumption that DA can proc only twice on a multi-hit weapon skill (fewer than seven hits).

I am assuming 95% hit rate for the first WS hit. Since (lack of) accuracy does affect TP return, I thought it would be useful to show the effect of a lower hit rate.

Table 1. Probability of getting 100 TP in 4 hits (after a WS) for a 5-hit polearm (480 delay, 17% double attack rate)

Minimum hits after 1st WS hit	Store TP	95% hit rate		80% hit rate
0	54	.95		.95
1	53	.949996		.948865
1	52	.949996		.948865
2	51	.949677		.930353
2	50	.949677		.930353
3	49	.940513		.815681
3	48	.940513		.815681
4	47	.822485		.490462
4	46	.822485		.490462
5	45	.233998		.105841

You can see there is not much of a drop by shedding up to 6 store TP and still being pretty close to a true 5-hit. Remember that the first hit of a WS can still miss.

The probabilities shown are cumulative probabilities in the sense that, given some amount of store TP, what is the probability that I will be able to get 100 TP in 4 hits after a weapon skill? More specifically, given some amount of store TP, what is the least amount of hits I need to land to be able to get 100 TP in 4 hits with an acceptable probability? Remember that .95 is pretty much as good as it gets.

If you have 95% hit rate, 48 store TP gives you a 94% chance of generating 100 TP in 4 hits, requiring at least a 4-hit return from the previous WS (1st hit TP and TP from at least 3 other hits). If you have a "true" 5-hit build, shedding 6 store TP may be a good trade-off. For example, I've seen 5-hit polearm builds with 49 store TP (including merits), suggesting awareness that 54 store TP is rather superfluous.

If you have 80% hit rate, 48 store TP gives you a 82% chance of generating 100 TP in 4 hits, so you might want at least 50 store TP if being around 80% hit rate is more realistic for whatever you are doing.

This exercise can be repeated for both 6-hit polearm and 6-hit great axe.

Table 2. Probability of getting 100 TP in 5 hits (after a WS) for a 6-hit polearm (480 delay, 21% double attack rate)

Minimum hits after 1st WS hit	Store TP	95% hit rate		80% hit rate
0	29	.95		.95
1	28	.949996		.948948
1	27	.949996		.948948
2	26	.949705		.931688
3	25	.941320		.823837
3	24	.941320		.823837
4	23	.832807		.513000
5	22	.284425		.130744

29 store TP not all that easy to obtain as a warrior (maybe you want to use Aurum Cuirass), but 24 is possible with a bunch of ticky-tack pieces. 15 from /SAM, 5 from Rajas, 1 from Brutal, 1 from Chivalrous Chain, 1 from Ecphoria Ring, and 1 from Engetsuto gives 24 total. Then again, if you're spamming crab sushi, some of these may not be very optimal for Penta Thrust.

Table 3. Probability of getting 100 TP in 5 hits (after a WS) for a 6-hit great axe (504 delay, 21% double attack rate)

Minimum hits after 1st WS hit	Store TP	95% hit rate		80% hit rate
0	22	.95		.95
1	21	.948478		.923695
2	20	.889887		.702636
2	19	.889887		.702636
3	18	.034124		.017160

I have only 6 store TP on equipment for warrior anyway. I can live with 21 store TP if I actually am using /SAM for some reason. What about the likes of 6-hit scythe and 6-hit polearm, both with four-hit weapon skills (like Guillotine and Drakesbane)? The following table compares the minimum TP for a "true" 6-hit build to the minimum TP for a "virtual" 6-hit build.

Table 4. Minimum Store TP requirements for 6-hit builds with 4-hit weapon skills

		Minimum Store TP
Delay	Base TP	True	Virtual
528	14.4	16	14
513	13.9	21	18
501	13.6	23	20
492	13.3	26	23
480	13.0	29	26

With "virtual" store TP builds, the corresponding probability is .9449 given 95% hit rate. (Of course, lower hit rate will lower this probability.) If that .0051-difference in probability really troubles you and is unacceptable, by all means be hyper-conservative.

Dumb thread(s) of the day

Here's a new feature where I talk briefly about crappy replies to decent questions. It would be a lot easier just to take pot-shots all day at shitty FFXI forum threads, which I might just do rather than play with numbers all the time.

Apparently, there is a thread on BG discussing why Allakhazam is so maligned, which usually is done by repeatedly knocking down the straw man that anyone actively endorses TPing in STR or DEX rings. When talking about a signal-to-noise ratio, the noise component is rather substantial on Allakhazam but the signal is pretty small in absolute terms for any FFXI forum, really. Even BG has threads like this, where bald-faced assertions are made without referencing sources and people can say they get 8-hit Drakesbanes with a straight face.

As another example, if you were talking about the relative efficiency of a 6-hit polearm build, you would pretty much get the same content-free, inane answers whether you posited this question on Allakhazam or Blue Gartr. Apparently, it is so difficult to use an average auto-attack damage, use an average WS damage, estimate the time between weapon skills, and use all this information to estimate roughly the relative efficiency of a 6-hit build. (Hint: a 6-hit is not even close to being 20% more efficient than a 7-hit). Instead, you have a reasonable OP followed mostly by dumb-fuck snark and drivel.