The Average Survival (AS) of Heroscape Figures

[Kroc]

Originally Posted by GreenLanturn

Does this value change during the course of the game? Meaning, if Charos has 9 life you wouldn't waste your time, but if he has 1 life he is a great 210 point target.

It definitely scales down. You just take his current life and defense to the table. For example if he has 7 Life left then his AS is 15.5, with only 1 life left his AS is 2.1.

[Kroc]

Originally Posted by Sarpedon

I would only add that most squad units have the benefit of what I would call "replacement survivability". I know that it was beyond the scope of the original post to present this disclaimer in full form so I am doing it know to show how difficult/impossible(?) it is to quantify defensive abilities.

The Deathreavers not only have great (real) survivability at a super low cost, but they save time in order markers too! This is what makes them such a bargain. As one is lost (to a normal attack) another can hop into its place without missing a beat. If the glyph were one of +1/+2 defense, you can see how that would increase their survivability and that of their army.

Further, defensively, they can scatter away from almost all enemy units, whether engaged or not, often leaving the remaining attackers without targets.

And this is EXACTLY why I'm not going to bother with these tables for every single special ability. This is what we call a statistic like attack and range, it doesn't tell you the whole value of a unit.

But, eh hem, I do have to correct a possible error in your post, Sarpedon, it seems like your saying:
a) Deathreaver dies
b) Other deathreaver covers glyph on the scatter.
I thought this at one time, but was corrected. You scatter BEFORE you take any dead deathreavers off of the board. So if one dies you can't just move right onto his space.

Kevin

[Kroc]

Originally Posted by ollie

As with all the lovely stats stuff that gets generated on the site, the first question to ask is: Is this useful in-game or is it just theoretical fun? (Believe me, as a pure mathematician I have nothing whatsoever against theoretical fun.)

Well, ollie, my man, thou are so dissmissive. Like I just said above in the Charos example and as I said in the original post, placement of order markers should be affected by this statistic. AS changes during the game, like last weekend I managed to whipe out 3 of Q9's life in my first attack. Knocking him down from an AS of 15.8 to an AS of 4.2. Quite a blow, ehh?
My opponent lost an order marker because I then whiped out Q9 pretty quickly and he didn't check the table.
Of all the posts I've written on strategy I think this is potentially the one that is most useful. It's only a statistic, but it can be an important one.

Originally Posted by ollie

...In short, tabulations and calculations such as this are interesting in an abstract way and useful once some more situation-specific work is put in. ... How can these numbers be best used?

I think looking over the AS of your army could be very important. I haven't figured it out but you could try to maximize the AS of your 500 point army, then try to win every game on points. I wouldn't want to do that, and wouldn't want to play against someone who has, but that would be interesting.

But outside of tournament preparation, I think these tables do make one important point. They show that we should always augment the defense of already strong units. I didn't realize that before, and I'll definitely be using that in the future.

[ollie]

Originally Posted by Kroc

Well, ollie, my man, thou are so dissmissive.

Sorry for seeming dismissive---that certainly wasn't my intent. My reaction was more "wow, this is really cool, what can we do next".

Like I just said above in the Charos example and as I said in the original post, placement of order markers should be affected by this statistic. AS changes during the game, like last weekend I managed to whipe out 3 of Q9's life in my first attack. Knocking him down from an AS of 15.8 to an AS of 4.2. Quite a blow, ehh?
My opponent lost an order marker because I then whiped out Q9 pretty quickly and he didn't check the table.
Of all the posts I've written on strategy I think this is potentially the one that is most useful. It's only a statistic, but it can be an important one.

I agree with all this---rephrasing my "is this useful in-game" question: Assuming that I'm not going to commit all of this (and the additional Excel file that I haven't looked at yet) to memory, can something useful in-game be extracted?

If I come up against Charos, but haven't memorised the numbers, do I play less than optimally? I'm not sure. A wider context is needed---what alternatives do I have? So, suppose I come up against Stingers and Charos. I can imagine sitting down with these numbers, considering both attack and defence including whatever units I have, to fine-tune decisions and make marginally better decisions. I can't imagine doing this in-game, for two reasons: I won't have memorised the necessary starting data and I won't have the time or mental arithmetic ability to make the necessary calculations even if I knew the data.

Before this is useful in-game I think it needs condensing to rules of thumb (such as my Deathwalker example above or your claim that it's always better to augment the defence of already strong units---see below).

Originally Posted by Kroc

I think looking over the AS of your army could be very important. I haven't figured it out but you could try to maximize the AS of your 500 point army, then try to win every game on points. I wouldn't want to do that, and wouldn't want to play against someone who has, but that would be interesting.

But outside of tournament preparation, I think these tables do make one important point. They show that we should always augment the defense of already strong units. I didn't realize that before, and I'll definitely be using that in the future.

I think you're going beyond what can be deduced from the stats here. There is more to the game than AS. Extreme case: high AS but attack values of 1 across the board. Good army? It's an important part of a bigger picture, but that bigger picture needs consideration.

Again, with the "always augment strong units" rule. I'll go with a "usually augment strong units" rule of thumb, but exceptions based on in-game considerations, or special abilities, or glyphs, or... are not hard to imagine.

Heh, I went all negative again, sorry. As I said at the start, I think this is cool, just not the ending point of the questions it raises.

Originally Posted by Kroc

But, eh hem, I do have to correct a possible error in your post, Sarpedon, it seems like your saying:
a) Deathreaver dies
b) Other deathreaver covers glyph on the scatter.
I thought this at one time, but was corrected. You scatter BEFORE you take any dead deathreavers off of the board. So if one dies you can't just move right onto his space.

I thought that conversation ended the other way round and that Sarpendon's version was the correct one.

Edit. Link.

Edit 2. The important post:

Originally Posted by Grungebob

1) The rat is first killed and removed from the board
2) Then you scatter with 2 other rats

[jotun7]

I like the way mccombju said it. Although the dice has more skulls than shields, it's eaiser to kill than to save. So, normally, even when you have 7-9 defence dice, you would usually get more skulls than defence (or more blanks than shields, depending on which dice you use). I would predict that the averaged figure would last about 3 rounds out on the battle field. But, a very good player would go into the field and die within 3-5 rounds; or if you're lucky: 5-7 rounds.

[ollie]

More thoughts on the always-boost-the-strongest argument.

Originally Posted by Kroc

How to use Defense bonuses: In the augmenting strengths or bolstering weaknesses thread I said that it is always better to bolster weaknesses. This table shows that for defense this is absolutely not true. The benefit of adding one defense dice to a figure is always increasing in the number of defense dice a unit has, and also in the life (the AS in short). So you should always augment the defense of already strong units. For example if you add Finn to Major Q9 you get an AS of 21.4 versus 15.8—he can now survive 5 more attacks. If you add it to a Venoc Viper squad they can not be expected to live longer at all—on average each figure will die in the first attack. (Yes, I know you can’t bolster the VV with Finn, it’s an example.)

[Aside: you mean Thorgrim here.]

You seem to slip seamlessly from "high AS" to "strong". I argue that AS is only half of strong.

When placing Thorgrim's spirit it's strength we want to enhance, not AS. We want to put it in the place that will cause the greatest increase in damage done to our opponent. High AS increases this, but damage done does not solely depend on this. A case can easily be made for putting Thorgrim somewhere that is not optimal in AS. For example, Braxas is a great spot for the spirit. The rate of damage she causes (against most armies) is such that a shorter increased survival time can result in more damage compared with massively increasing the survival time of a unit with less offensive output per turn.

In short, we want to increase expected-total-damage and this can be broken down into expected-damage-per-turn times expected-additional-turns.

Does this make sense, or am I missing some key component of what is going on here?

[mccombju]

Originally Posted by Kroc

And this is EXACTLY why I'm not going to bother with these tables for every single special ability. This is what we call a statistic like attack and range, it doesn't tell you the whole value of a unit.

But, eh hem, I do have to correct a possible error in your post, Sarpedon, it seems like your saying:
a) Deathreaver dies
b) Other deathreaver covers glyph on the scatter.
I thought this at one time, but was corrected. You scatter BEFORE you take any dead deathreavers off of the board. So if one dies you can't just move right onto his space.

Kevin

Wow... I was making the same mistake...

So, what you are saying, Kroc, is that you Scatter after defense dice have been thrown but before wounds are assigned? That is in no way obvious from the wording on the card.

Can anyone provide me with a link to the relevant ruling/discussion? The Book of Deathreavers is lacking this clarification.

Aside: If the above assessment by Kroc is correct, then I don't see why you can't just Scatter away a Deathreaver that was just attacked (i.e. "Last In First Out" would cancel the attack b/c a Deathreaver that is out of range couldn't have been a valid target and the attack "fizzles").

EDIT: I agree with Ollie that Scatter happens contrary to the way that Kroc presented. The official order of events:

Originally Posted by Grungebob

1) The rat is first killed and removed from the board
2) Then you scatter with 2 other rats

[Kroc]

Originally Posted by ollie

More thoughts on the always-boost-the-strongest argument....
[Aside: you mean Thorgrim here.]
You seem to slip seamlessly from "high AS" to "strong". I argue that AS is only half of strong. ...

You're right of course, I want to mention again that AS is only a statistic. Of course there are other things you need to think about when you decide where to put Thorgrimm. (Thanks for the catch, by the way. I'mma going to go edit that right away.)
However I am surprised to realize that probably the best use of Thorgrimm is to put him on Q9. I would have figured that for a waste of time until I did the math.

And about your other point, is this statistic useful if you don't have the table with you? Yea, OK, so you're not THAT much of a math fanatic. If you aren't going to keep them with you then I guess you would just have to memorize them.

BTW, I am SO psyched to know I can remove my rat before scattering. Woo Hoo!

Kevin

[ollie]

Originally Posted by Kroc

However I am surprised to realize that probably the best use of Thorgrimm is to put him on Q9. I would have figured that for a waste of time until I did the math.

A useful distinction to make when making these decisions is, I think, between absolute benefit and relative benefit. Usually absolute benefit is what we care about, but relative benefit seems more natural (to me at least). So, doubling the defence of a one defence figure seems more valuable than the slight increase from seven to eight defence dice. However, as your calculations show, this is not the case.

Perhaps the rule of thumb should be to put Thorgrim on the most expensive figure (assuming the costing is done well, which I think it is, and that you adjust for any wounds taken). Actually, the figure with the highest IGPV is the one to go for.

Originally Posted by Kroc

And about your other point, is this statistic useful if you don't have the table with you? Yea, OK, so you're not THAT much of a math fanatic. If you aren't going to keep them with you then I guess you would just have to memorize them.

Do you allow such tables when you play? That didn't even occur to me, and things make a lot more sense with that bit of information. I'd certainly forbid them at a tournament I was running. (Now I think about it, there was a thread about this a while ago---I'll see if I can dig it up.)

[Sarpedon]

BTW, I am SO psyched to know I can remove my rat before scattering. Woo Hoo!

Kevin[/quote]

Apology accepted! LOL