i cant find that simple chart with the expected results, google is not being helpful 
Target lock vs focus vs both on attack dice
Assuming crits are hits:
Standard (1/2)^n
Focus or TL (3/4)^n
TL + Focus (15/16)^n
where n is the number of dice.
Assuming crits are hits:
Standard (1/2)^n
Focus or TL (3/4)^n
TL + Focus (15/16)^n
where n is the number of dice.
NUMBERS! clearly he is a witch and we must burn him!
Assuming crits are hits:
Standard (1/2)^n
Focus or TL (3/4)^n
TL + Focus (15/16)^n
where n is the number of dice.
NUMBERS! clearly he is a witch and we must burn him!
If you strike me down, I shall become more powerful than you can imagine!
Assuming crits are hits:
Standard (1/2)^n
Focus or TL (3/4)^n
TL + Focus (15/16)^n
where n is the number of dice.
NUMBERS! clearly he is a witch and we must burn him!
If you strike me down, I shall become more powerful than you can imagine!
Yes - He becomes a statistic.. 
Now, for the crit-spread:
If you relied purely on rolls or re-rolls, you've got a 25% crit-chance (of overall damage).
If you spent a focus token, you've got a 20% crit-chance (of overall damage).
Of course, these are blind stats: as there's actually a choice in when to spend a focus token, there's a bit of a spread depending on the number of dice you throw.
Focus:
2 dice - 0.25 [kaboom], 1.25 [boom]
3 dice - 0.38 [kaboom], 1.88 [boom]
4 dice - 0.50 [kaboom], 2.50 [boom]
Target Lock:
2 dice - 0.38 [kaboom], 1.13 [boom]
3 dice - 0.56 [kaboom], 1.69 [boom]
4 dice - 0.75 [kaboom], 2.25 [boom]
Focus + Target Lock (assuming you only reroll blanks):
2 dice - 0.31 [kaboom], 1.56 [boom]
3 dice - 0.47 [kaboom], 2.34 [boom]
4 dice - 0.63 [kaboom], 3.13 [boom]
As a late answer, there is a tool showing these figures in Squadron Benchmark:
http://xws-bench.github.io/bench/#proba
The table is computed dynamically, it takes usually 2-3s to fill. For a given number of dice rolled by the attacker (rows) and the defender (columns), the following figures are computed:
- % to hit, taking into account defense roll and focus/rerolls/evades/cloacks
- mean number of hit results remaining after the defense roll
- mean number of criticals results remaining after the defense roll
One of the side effect of focus is to increase the % to land a critical, since there are more hits to cancel before cancelling criticals.
NUMBERS! clearly he is a witch and we must burn him!Assuming crits are hits:
Standard (1/2)^n
Focus or TL (3/4)^n
TL + Focus (15/16)^n
where n is the number of dice.
If you strike me down, I shall become more powerful than you can imagine!
Stop misquoting the films. Space wizards deserve better.
NUMBERS! clearly he is a witch and we must burn him!Assuming crits are hits:
Standard (1/2)^n
Focus or TL (3/4)^n
TL + Focus (15/16)^n
where n is the number of dice.
If you strike me down, I shall become more powerful than you can imagine!
Stop misquoting the films. Space wizards deserve better.
"O Rly?"
-- Obi Wan, captain of the Enterprise
Focus and TL have the same return value on attack dice because attack dice are 50/50 and the focus is 2/8 equivalent to the effect of a reroll.
So which is best? Focus is best if you will also be on the defence that turn where TL is better over successive turns if not being attacked or you have no agility dice to improve.
Also there is the consideration of variance. Focus improves the result only on a single roll whereas TL is the equivalent of 2 rolls (in regards to variance), meaning that variance is statistically better with TL
The other benefit of that reroll is that you can improve a die into a crit whereas focus will only ever return a hit and never a crit.
So which is best? Focus is best if you will also be on the defence that turn where TL is better over successive turns if not being attacked or you have no agility dice to improve.
TL improves chances to crit, and disappears if your target dies. Those are the big differences. The fact that you keep the TL is less important if you actually shoot. Of course, if you know you're not going to get a shot, then by all means use TL. But if you do have a shot, the odds of not using TL are small. 12% for 3 dice, 6% for 4 dice. Are you really that sure that you're going to shoot the same target next round? Is the ship you're attacking able to survive until you shoot it this round? Are you sure that you're not better off with a focus that you might need for defense? Those are the questions you need to put to yourself when you choose TL over focus.
Also there is the consideration of variance. Focus improves the result only on a single roll whereas TL is the equivalent of 2 rolls (in regards to variance), meaning that variance is statistically better with TL
The other benefit of that reroll is that you can improve a die into a crit whereas focus will only ever return a hit and never a crit.
Ah... no? Variance is dead-on the same. The illusion is that you're rolling twice, so you can't be unlucky twice, but it's not true.
[Ninja'ed by chilligan, but I think there's some value to posting anyway.]
Also there is the consideration of variance. Focus improves the result only on a single roll whereas TL is the equivalent of 2 rolls (in regards to variance), meaning that variance is statistically better with TL
The other benefit of that reroll is that you can improve a die into a crit whereas focus will only ever return a hit and never a crit.
7am with poor sleep and no coffee isn't the best state of mind in which to consider the calculus of random variables, but I don't think this is true.
First, an increase in variance (as you'd get if you simply rolled more dice) isn't the same as "better variance". Especially in tournament X-wing, there's a good argument that increased variance (or at least an increased coefficient of variance) is actually worse.
Second, I don't think target lock actually increases or decreases variance relative to focus. The easiest way to understand why is by looking at each die by itself: target lock changes the a priori distribution of results, and if you know how the distribution has changed, you can still model the overall result of the attack roll as the sum of the original number of attack dice. That alone says the variance shouldn't change much.
And since variance isn't a terribly meaningful concept for ordinal data, we have to transform each die into a binary result (success or failure rather than blank/focus/hit/crit) to actually compute variance--and as soon as we do that, the difference in distributions between focus and target lock vanishes. So the variance should be he same.
Assuming crits are hits:
Standard (1/2)^n
Focus or TL (3/4)^n
TL + Focus (15/16)^n
where n is the number of dice.
NUMBERS! clearly he is a witch and we must burn him!
Wait -- are you implying he weighs the same as a duck?
On 8/10/2015 at 9:47 AM, chilligan said:Assuming crits are hits:
Standard (1/2)^n
Focus or TL (3/4)^n
TL + Focus (15/16)^n
where n is the number of dice.
I just pulled this out of archives on a google search, however I believe all the ^ should be *(multiplied by the number of dice, not raised to the power). 2 red dice example. .5^2 or .5*.5 equals .25 which is less than 1 die odds. however .5*2 is equal to 1. It should be
Standard (1/2)*n
Focus or TL (3/4)*n
TL+Focus (15/16)*n
Thank you for calculating the fractions though, it was nice to find this.
On 2017-9-21 at 6:34 PM, SkyCooper said:
I just pulled this out of archives on a google search, however I believe all the ^ should be *(multiplied by the number of dice, not raised to the power). 2 red dice example. .5^2 or .5*.5 equals .25 which is less than 1 die odds. however .5*2 is equal to 1. It should be
Standard (1/2)*n
Focus or TL (3/4)*n
TL+Focus (15/16)*n
Thank you for calculating the fractions though, it was nice to find this.
It was a typo from a long time ago, in a galaxy far far away.
You have forgotten about the most important aspect of red dice.
Whenever you pick a TL, you'll have a lot of eyes and reroll into eyes
Whenever you pick Focus, you'll get no eyes
So no matter what... you're screwed. Unless you have got both.
10 minutes ago, Schu81 said:You have forgotten about the most important aspect of red dice.
Whenever you pick a TL, you'll have a lot of eyes and reroll into eyes
Whenever you pick Focus, you'll get no eyes
So no matter what... you're screwed. Unless you have got both.
Blanks. I get lots of blanks. Otherwise, you're correct.
^ came to post that website. Is amazing.
Never tell me the odds!
On 8/30/2015 at 6:27 AM, chilligan said:
"O Rly?"
-- Obi Wan, captain of the Enterprise
Rly
-- Han Starwalker, Bounty Hunter