7th Ed. Leadership and Cold Blooded Odds

[Caneghem]

EDIT: Below are the correct numbers, thanks to IronShark for illuminating the error.

IronShark
Ld 2 - 7.4%
Ld 3 - 19.9%
Ld 4 - 35.6%
Ld 5 - 52.3%
Ld 6 - 68.1%
Ld 7- 80.6%
Ld 8 - 89.4%
Ld 9 - 94.9%

So I was kind of bored... ok really bored... and decided to figure out how much cold-blooded really boosts chances of passing leadership tests. I think mostly we'll be interested in seeing Ld 6 through 9, so those are the ones I calculated. Figures are %chance of passing/%chance of passing with cold blooded.

Ld 6 - 41.7% / 57.8%
Ld 7 - 58.3% / 74.5%
Ld 8 - 72.2% / 86.1%
Ld 9 - 83.3% / 93.5%

Ld 7 is a flying leap beyond Ld 6, as it goes almost to 3/4 chance of passing. Pack those musos on your skink units for the many rally tests they will be rolling.

Also makes you rethink stubborn Ld 6 stegs... even with a reroll from a BSB, you only pass 82.2% of the time. Not bad, but not even as good as a single Ld 8 test.

Oh and the odds someone breaking the temple guard unit are a whopping 0.42% assuming your Slann is giving them a reroll.

So yeah, cold-blooded is awesome.. that is all!

 

[strewart]

Hmm that is indeed interesting, cool. Definitely a massive difference between ld 6 and 7.

About the steg, you also need to remember it has to lose combat before it needs to test. But yes, even with stubborn ld 6 isn't great.

 

[hellbreaker]

well... that's a good round-up, I might even concider musicians in the bigger skink units(very rare) so that they don't flee off the table.

 

[Corbechev]

Hmm that is indeed interesting, cool. Definitely a massive difference between ld 6 and 7.

About the steg, you also need to remember it has to lose combat before it needs to test. But yes, even with stubborn ld 6 isn't great.

Yeah, I also like to run my important stegadon close to my general to feed off of the higher LD.

 

[strewart]

Remember if it borrows the generals leadership, it loses stubborn... You would have to pick it depending on how much you lost combat by, it would sometimes be better to go with the general's and other times better to stick with 6 and stubborn.

 

[Corbechev]

Remember if it borrows the generals leadership, it loses stubborn... You would have to pick it depending on how much you lost combat by, it would sometimes be better to go with the general's and other times better to stick with 6 and stubborn.

Oh wow, I had no idea of that rule...

So, does that mean that the Temple Guard is testing on their leadership and not the Slann's for stubborn?

 

[Caneghem]

Remember if it borrows the generals leadership, it loses stubborn... You would have to pick it depending on how much you lost combat by, it would sometimes be better to go with the general's and other times better to stick with 6 and stubborn.

Oh wow, I had no idea of that rule...

So, does that mean that the Temple Guard is testing on their leadership and not the Slann's for stubborn?

Stubborn is strange in that it is shared by an entire unit so long as one model in the unit is stubborn (hence the adding of stegadons to Saurus to make them stubborn). So this means the Temple Guard make the Slann stubborn, and the unit can test on the Slann's Ld 9, since he is now the highest Ld model with stubborn within the unit. That's my understanding of it anyhow. Basically, use the highest Ld from within the unit for stubborn.

 

[Craken]

Canehem, you are wrong in this one check page 78 of your rule book it gives a nice description of characters in units with stuborn.

 

[Caneghem]

Canehem, you are wrong in this one check page 78 of your rule book it gives a nice description of characters in units with stuborn.

Ah, so then Temple Guard get Stubborn at Ld 8? Sorry, don't have my book on me.

What then happens if you have a Ld 8 Skink Chief (say he has the item that gives +1 Ld)? This one I have always wondered about.. the steg is the stubborn one not the rider.. is it always Ld 6 stubborn regardless of the skink Ld on top?

 

[Craken]

This works a little different because the Steg is then concidered a mount, thus he then follows the rules on page 79 (the next page ^_^ ). Which states that if either one has Stubborn and some others then the whole combined unit does. So a skink chief with the Helm would give the unit a Unmodifiable Ld test of 8. Which is pretty awesome.

 

[strewart]

Remember if it borrows the generals leadership, it loses stubborn... You would have to pick it depending on how much you lost combat by, it would sometimes be better to go with the general's and other times better to stick with 6 and stubborn.

Oh wow, I had no idea of that rule...

So, does that mean that the Temple Guard is testing on their leadership and not the Slann's for stubborn?

Yeah definitely. Again you get to choose the higher leadership, or the unmodified leadership, depending on what is going to suit you better. Page references are given by others above.

 

[IronShark]

Ld 6 - 41.7% / 57.8%
Ld 7 - 58.3% / 74.5%
Ld 8 - 72.2% / 86.1%
Ld 9 - 83.3% / 93.5%

Those aren't the numbers I got. For cold blooded, I got:
Ld 2 - 7.4%
Ld 3 - 19.9%
Ld 4 - 35.6%
Ld 5 - 52.3%
Ld 6 - 68.1%
Ld 7- 80.6%
Ld 8 - 89.4%
Ld 9 - 94.9%

How did you arrive at your numbers? I don't know of an easy formula for the calculation, so I used a program to generate the 216 possible results of tossing 3 dice, and determined the results from there (eg, 16 of 216 possible results will result in a 2). I've double checked mine, and it seems to all add up.

So, Ld 6 has a pretty solid, but not completely reliable, chance of passing with cold blooded. It's really close to 2 out of 3.

 

[Caneghem]

Ld 6 - 41.7% / 57.8%
Ld 7 - 58.3% / 74.5%
Ld 8 - 72.2% / 86.1%
Ld 9 - 83.3% / 93.5%

Those aren't the numbers I got. For cold blooded, I got:
Ld 2 - 7.4%
Ld 3 - 19.9%
Ld 4 - 35.6%
Ld 5 - 52.3%
Ld 6 - 68.1%
Ld 7- 80.6%
Ld 8 - 89.4%
Ld 9 - 94.9%

How did you arrive at your numbers? I don't know of an easy formula for the calculation, so I used a program to generate the 216 possible results of tossing 3 dice, and determined the results from there (eg, 16 of 216 possible results will result in a 2). I've double checked mine, and it seems to all add up.

So, Ld 6 has a pretty solid, but not completely reliable, chance of passing with cold blooded. It's really close to 2 out of 3.

I wound up calculating it based on just "the first" of the three dice... maybe I can give an idea of what I mean. I wrote down 1 through 6, then for each of the outcomes of the "first" die, I figured out how many combos of the other two dice resulted in success. These can be quickly determined by figuring out how many of the combos will result in failure, and subtracting them. It's not a formula, but you can picture it easily enough.

EDIT: Doh, the previous set = FAIL. I totally forgot to count the ones where you drop the "first" number. So the real set would look like this...

5 - 27 pass (5 more gone) EDIT: this was wrong as 4-4 is totally fine so only 4 chances disappear.
6 - 20 pass (7 more gone) EDIT: wrong again 3-3, 3-4, 3-5, 3-6, 6-3, 5-3, 4-3 only two of these are bad, not 7!

So for Ld 8, it would look like...
1 - 36 pass (you'll pass no matter what)
2 - 36 pass (see above)
3 - 35 pass (if you roll two 6's, you will be at a 9, so one possibility goes away)
4 - 32 pass (3 more chances gone, 5-6, 6-5, 5-5. All of those rolls will force you to take a 5.)
5 - 28 (this is correct)
6 - 26 pass (this is correct)

This yields 193/216 or 89.4%. Gee, looks like you got the correct numbers there IronShark! Thank you for showing me the light, now I can finally do a cold-blooded option in my damage calculator.

 

[Caneghem]

EDIT: I fail at math.

 

[strewart]

Caeghem, my statistics are a bit rusty and I am not completely sure where you went wrong.... But I think you have considered too many possibilities. In the ld 8 example with 6 as the first dice:

So for Ld 8, it would look like...
1 - 36 pass (you'll pass no matter what)
2 - 36 pass (see above)
3 - 35 pass (if you roll two 6's, you will be at a 9, so one possibility goes away)
4 - 32 pass (3 more chances gone, 5-6, 6-5, 5-5. All of those rolls will force you to take a 5.)
5 - 27 pass (5 more gone)
6 - 20 pass (7 more gone)

Lets expand it a bit.

The first 6 rolled is the one removed, because it will be highest, even if it is equal highest. So for ld 8 on 2 dice, you could get anywhere between 2 and 12 on 36 rolls, right? Here are all the possibilities:

___1___2___3___4___5___6
1__2___3___4___5___6___7
2__3___4___5___6___7___8
3__4___5___6___7___8___9
4__5___6___7___8___9___10
5__6___7___8___9___10__11
6__7___8___9___10__11__12

You can see that there are 10 results that equal greater than 8, so actually 26 out of 36 will pass if the first roll is a 6. You must have made a mistake in your numbers somewhere.

Anyway, I put this on excel since I also could not figure out a quick formula to work it out considering the highest dice must be removed. See if this method makes sense to you:

I drew up 3 columns, the first repeated 1-6 over and over for one dice, the second had 36 1's, followed by 36 2's etc. and the third had 6 1's, 6 2's etc. This accounted for all 216 possibilities. The next column summed all the results, so I had a leadership roll if 3 dice were used. I then used the MAX function so the maximum number in each row was displayed, eg:

roll:------max
1 2 1-----2
1 4 5-----5

The next column obviously was the sum of the first 3 dice minus the max column. I now had a column with the actual leadership rolls given the highest dice removed. In the next columns, I used an IF logic function for leadership 5-10, so for the first IF the roll is equal or less than 5, put 1, if greater put 0. Repeat that for other leadership values. It was then a simple matter of summing the IF columns, successful leadership rolls were 1 thus I got the number of successful rolls for each leadership value. Now I just divide that by the total possibilities (216) for the percentage. A slightly faster way of IronShark's method. I got:

ld5 ld6 ld7 ld8 ld9 ld10
52.31481481 68.05555556 80.55555556 89.35185185 94.90740741 98.14814815


Uff.... What a head f*ck

 

[Caneghem]

Yep strewart, I was removing too many possibilities from the 5 and 6 in my example, because I forgot to take out ones that drop the "first" number.

IronShark's numbers are correct, but I still like my method for solving better than counting through all the possibilities!

So yeah, cold-blooded is even BETTER than I thought.

 

[hellbreaker]

Please tell me that I understood that?

Math hammer... hard... *shoots himself*

 

[Azactoth]

Iron shark's resaults are true... I calculate them with excel and I found the same resaults too...

 

[Aranigej]

Thanks for the calculations guys! Gives us all a good picture of our odds with the scaly ones.

 

[Enginseer]

The current numbers are correct guys. (I've done the calculations also)