OK, so hit rate of 95%, and a Zanshin proc rate of 45%: Probability of a Zanshin swing connecting is thus 0.05 * 0.45 * 0.95 = 0.021375 (Probability of Miss * Probability of Zanshin Proc * Probability of Zanshin Hit Landing)
Assuming a 5-hit build, you can either start a build to 100TP with 20TP (WS Hit) or 0TP (WS Miss). Zanshin doesn't proc on a WS miss. Also, if you are on 80TP, an Ikishoten enhanced Zanshin swing won't get you to 100TP any faster than a regular Zanshin hit, so I am going to exclude these cases.
Possibilities (Note: Z=Ikishoten enhanced Zanshin swing):
WS Hit-Z-Hit-Hit = 0.95*0.021375*0.95^2 = 0.018326
Note that there are 3 possible ways to have the scenario of WS Hit, a Zanshin proc, and 2 other Hits, so multiply probability by 3 to give 0.054979.
WS Miss-Z-Hit-Hit-Hit= 0.05*0.021375*0.95^3 = 0.000916
Note that there are 4 possible ways to have the scenario of WS Miss, a Zanshin proc, and 3 other hits, so multiply probability by 4 to give 0.003665.
Add the two together and you get 0.054979 + 0.003665 = 0.058644 which is about 6%. I don't bother with all the other situations where a Zanshin could occur (like WS Hit-Z-Miss-Hit-Hit) because their probability is rather low and I'm just doing a quick estimate. Now remember all that neglects double attack and triple attack. Zanshin can't proc on those, so any double or triple attack would reduce that frequency. So, that is how I got that number. Feel free to pick it apart.
Edit: If you are curious, adding 5 Zanshin merits to bring you to 50% Zanshin activation rate would bring the 0.058644 up to 0.065161, or about 6.5%.
Edit 2: Dustin, rereading what you wrote, the difference between our numbers comes from the fact that you need to consider the WS as part of the hit build. It can hit or miss, but Zanshin cannot proc on those misses. Also, you need to consider that a Zanshin swing can miss. Your numbers seem to be also talking about something slightly different than mine. You are talking about benefiting from Zanshin in general, while I am talking about the odds that having Ikishoten merits will reduce your time to 100TP. The only difference between the two is you have to ignore a Zanshin swing landing if you are sitting on 80TP since the time to 100+TP is the same whether you have Ikishoten merited or not.
Edited, Apr 12th 2011 3:33pm by JaxReborn
____________________________Jacs of Leviathan
SAM, MNK, THF, NIN, SCH, DRK, BLU 90
Woodworking 100+3, Synergy 57