Wednesday, March 13, 2019

The Return of the (Numenorean) King (Or, How Heroic Strength helps Elendil... and your hero, too! ... if they actually win the fight)

So far, we’ve looked at Heroic Strength solely in terms of the benefits it can confer if our hero loses the fight. In part 1, we looked at how Heroic Strength can protect heroes who are swarmed by cavalry models or find a Mordor troll up in their grill, by shrugging off knock-downs, offering us cheeky ways to blunt what monsters usually do well, making us too heavy to hurl and harder to rend, and keeping our all-important mount under our hero’s heroic tushy. And in part 2, we examined how, depending on the opponents we’re facing, Heroic Strength may even provide comparable (or better) protection than Heroic Defense.

All of this should give us some confidence that if we expend Might to call Heroic Strength, there are at least some scenarios (which also happen to be particularly dangerous scenarios) where we’re probably going to see at least some return on our investment even if we lose the duel. Now let’s consider how Heroic Strength can help our hero if he wins the fight.

More maths! More charts! To war!


High Strength Values are Rare Birds

High Strength, more so than any other profile characteristic (other than Wounds and Heroic Stats, like Might, Will, and Fate) comes in a very limited range. Fight Values vary widely, particularly among heroes (F3-F8, with a lot of F5-F6), and even among troops (F2-F5). There’s a lot of variance among Defense values as well (D3-D7 for troops, D4-D8 for heroes), and for Courage (C2-C6), and both Defense and Courage can also be affected by wargear choices as well (Armor/shields and War Horns, respectively). There’s no gear upgrade for Fight Value, unless you count elven-made weapons (which improve your odds of winning fights without actually changing fight values), but the fact that Heroic Strike can improve your Fight Value by D6 (in a world where most models that can strike will reach their maximum fight value on a roll of a 4-5) makes the idea of obtaining a maxed-out FV seem attainable.

Maxed-out Strength is unheard of. Not a single model (yet) has S10, unless you count siege engines (and only a handful of them, or you recklessly charge a gauntleted Gundabad Catapult Troll). Even the mighty Smaug, Calamity of Calamities, tops out at S9. So do the Balrog and Mumakil. Sauron and Beorn only climb to S8 (unless Beorn the bear is handing out death-hugs... watch out for those btw...). S7 is high, even for monsters. Mordor, Isengard, and Gundabad trolls have it, but not eagles (usually), not Fell Beasts (anymore), not even Tiberius’s beloved Wild Warg Chieftain (unless he uses Heroic Strength! I told you, what's not to love?). And most heroes (unless they’re monster heroes) are unlikely to reach even S6, making a hero with S5 is a very special bird (Elendil and Isildur, Dwalin and Dain, the King’s Champion, Azog and Bolg, Uruk-Hai / Morannon / Gundabad / Mahud heroes, at least most of them). So are S5 warriors (Black Guard, half-trolls). But for 85% of all profiles (if not more), you’re looking at a Strength profile of between 2 and 4. Which makes a 33% chance to double (or close to double) your hero's native strength characteristic pretty exceptional.

Related image

Free hugs for all! Who says no?

Unlike Courage (warhorns, drums) and Defense (shields, armor in various forms), there’s also no equipment upgrade you can buy to increase your hero’s Strength (unless you count Piercing Strike weapons, or pseudo-strength gear like 2H weapons, which we’ll talk about momentarily). It’s that rarity that makes Heroic Strength, and its allure of up to +3 Strength, incredibly unique. +3 Strength isn’t a probable outcome, but it’s not exactly a long-shot either (5+, 2/6 results, or 33%). So what does this benefit gain us?

The Basic Benefit: More Likely to Deal (More) Wounds

Thus far, we’ve been focusing exclusively on the gimmick benefits of higher Strength characteristics. No longer.

The primary reason we want high Strength is because if we win a duel, higher strength (usually) means an easier to-wound roll. And wounding your enemies not only conveys tactical advantages (the fewer models your opponent has, the less he can do, and therefore the less we have to worry about), but is always a way to win victory points in any scenario (yes, even in Reconnoitre).

Just to get our bearings, let’s revisit everyone’s most worn page in their rule book: the wound chart!



The wound chart follows a basic rule (though it took me forever to apply it consistently from memory): if your strength matches your opponent’s defense, you wound them on a roll of a 4+. If your opponent’s defense exceeds your strength by 1 or 2, you roll a 5+. If your opponent’s defense exceeds your strength by 3 or 4, you roll a 6+. If your opponent’s defense exceeds your strength by more than 5, you’re rolling double rolls (6/4, 6/5, 6/6), and if you’re S2 or below, you eventually hit a point where it’s impossible to wound the target.

The system also works in reverse. If you can get your Strength to the point where it is just 4 behind the target's defense (say, S5 vs. D9, instead of S4 vs. D9), you go from wounding on a 6/4 to just a 6 (eliminating random rolls where you can is almost always a good thing). If you can get your Strength to just 2 less than the target's defense (S5 vs. D7, instead of S4 vs. D7), you're now wounding on 5s. If you can draw your Strength even, then you're wounding on 4s, and if your Strength exceeds the target's defense by 2 or more, you go from wounding on a 4+ to wounding on a 3+. Each jump (usually in increments of 2) makes it easier for our models to wound.

As we just discussed, finding ways to improve our strength is relatively hard. Some armies have benefits to strength value (*cough* Rohan *cough*), but most of the time we're left with creative solutions that allow us to pretend we have higher strength than we actually do.

Back when Piercing Strike allowed us to resolve strikes at our Strength + D3, any generic S4 warrior model equipped with a pick or axe had a 33% chance to get up to S7. The cost was potentially severe (if you lose the fight, your defense went down by D3), but if you have the higher fight value, a banner nearby, a supporting friend, a trapped opponent, etc., the potential benefit of that high Strength gamble (S7 wounds D5 and below on 3s, and up to D9 on 5s) was too powerful to ignore.

The new rules (which now cap Piercing Strike at a benefit of just +1 Strength if you win the duel, but retain the D3 Defense loss if you lose) have somewhat rebalanced the calculus. Because adding a single Strength may not increase your to-wound roll at all (improving your strength from an even value to an odd value improves your to-wound chance against models with odd Defense values, but not even), the loss of D3 Defense poses a much higher risk for a benefit that may or may not actually increase your odds of wounding.

The other most common work-around is to use two-handed (2H) weapons, which effectively allow you to wound as if your Strength was at least 2 higher than it actually is (+1 to wound always equates to improving your model’s strength by +2, even though you can sometimes achieve the +1 to wound effect with just +1 strength, depending again on whether your Strength and the target’s Defense are even or odd). But there are limitations. For one, most models that have 2H weapons are paying a premium penalty for that in the form of a -1 to their duel roll (which is a big deal, especially for models that don’t have Might). Models that have Burly (or an equivalent rule) are rare and highly sought-after, but the armies that can field them pay a premium for that as well (this time in points). Burly heroes exist, and are incredibly powerful, especially if they have axes. But there are many named heroes with set war gear who never have the option for either Piercing Strike or a 2H weapon.

"He was twitching because he's got my two-handed Piercing Strike embedded in his head!"

Short of these workarounds (and the ultra-rare magical/special weapon rules, like Anduril or Azog’s “I am the Master”), Heroic Strength is our only way to improve the to-wound roll we need to kill enemy models. Unlike Piercing Strike or 2H weapons, there’s no inherent penalty attached to Heroic Strength. It doesn’t inherently reduce your odds of winning the duel, doesn’t reduce your defense value, and actually may improve your odds of surviving a fight that goes against you in certain circumstances.

In addition, the most probable outcome of Heroic Strength is an increase of 2 or more Strength (3+, 4/6 rolls, 67%) which is always enough to increase our to-wound odds by +1 (unless we're already wounding on a 3+, in which case our S5 hero is pounding D3 mooks... and really, shouldn't your hero be doing something more productive than pounding D3 mooks?). If our hero has even Strength (say, S4), any roll (1+, 6/6 rolls, 100%) will result in at least a +1 to-wound against odd-Defense targets (and vice-versa for heroes with odd Strength attacking even Defense), with a 1-in-3 chance of proccing a +2 to-wound modifier (5+... again, assuming you aren't beating up on D3 mooks...).

And, of course, while Heroic Strength doesn’t carry the drawbacks or risks of 2H weapons or Piercing Strike, we can always stack their benefits on top of Heroic Strength if we wish, opening up the extremely rare scenario where we can wound D7 models on 2s and D9 models on 3s (a S5 hero with Burly and a 2H axe/pick calls Heroic Strength, rolling a 5+ to go to S8, then Piercing Strikes with his 2H weapon up to S9, whereupon he goes from wounding a D7 model on 5s (S5 vs. D7) to wounding a D7 model on 2s (S9 wounds D7 on a 3+, the 2H +1 modifier makes that a 2+)... preferably while mounted on a goat or warg).



"Can openers"? Child, please… we call this is a "nutcracker." And yes, it is as painful as it sounds.

If that sounds like overkill to you (if you're trying to get a combo heroic combat slingshot off against a Vault Warden, it's not overkill by the way), don’t worry: any S4 hero who can 2H without penalty (or has sufficient Might to risk the -1 duel penalty) who rolls a 3+ for Heroic Strength is going to have effective S8 (S6 from Strength, plus the +2 Strength equivalent for the 2H weapon), which will wound up to D6 on 3s and D8 on 4s, which is plenty deadly. If that hero happens to have an axe or pick as well, you can extend that up to D7/D9, which most opponents will find utterly incomprehensible (followed closely by terror, and avoidance, and whispers of dread in the hallways to your future opponents in the tournament, all of which are probably conveying tactical advantages to you). Having a hero who can flex to wounding Smaug or the Balrog on 4s if they have to are nice to have lying around. You know, just in case. Again, not bad for a single point of Might, right?

When a Might point isn’t “a” Might point

The other objection to spending Might on Heroic Strength is based on opportunity cost: if you spend that Might point to call Heroic Strength, you won’t have it to add +1 to your duel roll or any to-wound rolls. Might is, after all, a limited resource.

I think the opportunity cost objection is probably the strongest objection to using Heroic Strength. But in fairness, it's also probably the strongest objection to using any heroic action. Because Might is a finite resource (even Aragorn will eventually run out of Might if he spends it recklessly, albeit for just the remainder of the turn), I think it’s helpful to be skeptical any time we’re considering spending Might on something that offers us merely a probability instead of a certainty. If you have higher Fight than your opponent, and roll a “5” in the duel roll, you know exactly what you’re getting if you spend that point of Might (you're winning the combat). Similarly, if you roll a “4” to wound, and you know you wound the target on 5s, you know exactly what you'll get if you spend a point of Might to improve that “4” to a “5” (you’ll deal a wound... or at least strip a Fate point... and potentially a wound and more than one Fate point if your opponent is particularly unlucky).

Heroic Strength doesn’t offer that sort of certainty, at least not on the offensive side, because (a) we don’t know that we'll win the fight (and therefore get to strike at all), and (b) we don’t know how many to-wound dice we’ll roll that are just one short of wounding (i.e., how many "4s" we'll roll when we need "5s" to wound). We also may not necessarily know for certain that our odds of wounding will improve by +1 at all, because not every +1 increase to strength results in a +1 increase to wound (see the wound chart above).We do know that getting +2 strength will get to that +1 to wound, but that’s only a probability (albeit on 4/6 rolls (3+, 66.7% probability), which is a decent chance all things considered).

Having said that, every heroic action (at least in its base form, and virtually all of them in practice, subject to perhaps the very rare corner-case exception) is subject to this same objection, because they ask us to trade a Might point for probabilities rather than certainties. Heroic Strike was one of the most common heroic actions prior to the new rules change, and is still highly valued. It can be game-winning when it works, but it's also an extreme example of trading might for a probability. Because your final Fight Value is improved based on a random D6 roll (meaning there’s a lot of variance), it’s the ultimate “trading Might for a random result” unless (a) you have a starting Fight Value of 9 (in which cases you know, with certainty, that you're going to F10), (b) you have a starting Fight Value of 6 or greater than your opponent (in which case you probably know, with certainty, that you'll out-fight your opponent whatever you roll [or tie your opponent if your opponent as a FV of 4+]), or (c) your opponent has no remaining Might (and thus can't Strike in turn). Plus, once you've improved your fight value by that random result, you still have to actually… you know… win the duel roll? With random dice? Not exactly a model of certainty.

The point of this is not to poo-poo Heroic Strike (that’s coming later ;-) ), but rather to emphasize that most players routinely gamble Might on possibilities rather than certainties; and often repeatedly in a single game or even a single round (contested Heroic Moves, anyone?). It’s fair to ask whether Heroic Strength is more valuable than keeping Might in reserve for the certainty you can get by altering a dice result to win a duel or inflict a wound. But if we’re routinely willing to throw at least 1 Might per round into a probability roll, I think we’d also benefit from looking at just how much Heroic Strength buffs our probability to wound. Because I’m feeling especially thorough, we’ll examine both (and in inverse order, just to mix it up).

Question 1: How much does Heroic Strength improve my probability of wounding?

Before we can assess what Heroic Strength does to our chance of wounding, we need to know something about our odds of wounding generally. We’ve already talked about the wound chart, which gives us the basic benchmarks for figuring out what our models need to roll to wound opposing models by matching our strength against their defense. For the vast majority of models to wound the vast majority of opposing models, we’ll need to roll somewhere between a “3” and a “6,” but in general any “6” we roll to wound will wound.

So let’s start with our odds of rolling a “6.” If our model has a single attack, wounds on the roll of a “6,” and has no rerolls, modifiers, etc., then we have a 1-in-6 chance of wounding our target, or just shy of a 17% of causing a wound. This means we have a 5-in-6 (83%) chance of not dealing a wound, making that outcome far more probable than wounding. In table form, we could chart our current probabilities like this:

Odds of rolling 1+ “6s” with 1 Attack die


1 Attack
No “6”
83.33 %
1+ “6”
16.67 %

Most heroes (and some elite units) have 2 attacks instead of one. The chance of rolling a “6” jumps up quite a bit (nearly double, almost 14 percentage points) if we roll an additional dice (which is why banners cost so many points, why heroes with built-in reroll effects are generally so expensive, and why only a few models have the Bane of Kings/Venom special rules). But notice that even with two attacks, our chance of rolling one or more “6s” is still quite a bit less (31%) than our chance of rolling none (69%): 

Odds of rolling 1+ “6s” with 1 or 2 Attack dice


1 Attack
2 Attacks
No “6”
83.33 %
69.44 %
1+ “6”
16.67 %
30.56 %

Elite heroes generally have 3 attacks. The jump from 2 attacks to 3 again improves our odds of rolling at least 1 “6” (this time by 11.5 percentage points instead of 14), but we are still in a situation where we’re less likely to roll at least one “6” (42%) than we are to roll no “6s” (58%): 

Odds of rolling 1+ “6s” with 1-3 Attack dice


1 Attack
2 Attacks
3 Attacks
No “6”
83.33 %
69.44 %
57.87 %
1+ “6”
16.67 %
30.56 %
42.13 %

Very, very few heroes have four attacks built into their profiles, and most of them are absurdly epic monsters like Sauron or the Balrog (and, for some reason, Dwalin, Champion of Erebor, who is a monster but in a very different way…). Four attacks is where we finally get to the tipping point where rolling a “6” becomes more probable than not rolling any “6s” (hence why it’s marked in green), but only just:

Odds of rolling 1+ “6s” with 1-4 Attack dice 


1 Attack
2 Attacks
3 Attacks
4 Attacks
No “6”
83.33 %
69.44 %
57.87 %
48.23 %
1+ “6”
16.67 %
30.56 %
42.13 %
51.77 %

If we continue to calculate the probabilities, we see the gap widen the more dice we add. At 5 attacks, we have a 60% chance of rolling at least 1 “6”; at 6 attacks, it’s a 66% chance; at 7 attacks, a 72% chance, and at 8 attacks, 76%, or slightly better than 3-in-4: 

Odds of rolling 1+ “6s” with X Attack dice


1 Attack
2 Attacks
3 Attacks
4 Attacks
5 Attacks
6 Attacks
7 Attacks
8 Attacks
No “6”
83.33 %
69.44 %
57.87 %
48.23 %
40.19 %
33.49 %
27.91 %
23.26 %
1+ “6”
16.67 %
30.56 %
42.13 %
51.77 %
59.81 %
66. 51 %
72.09 %
76.74 %

Note: For purposes of this example, I’ve stopped at 8 attack dice (since this is where most heroes will cap out when rolling to wound while mounted), but you could theoretically calculate the odds of as many dice as you like using anydice’s probability calculator [https://anydice.com/program/1401a] (enter the number you want to calculate the probability of rolling in the { } symbols, and set the number of six sided dice you want to roll to “Xd6” where “X” is the number of dice you want to roll).

It’s easy to get swept away by the positive here (76%! Sign me up!), but the negative is probably more important. Because a dice has six sides, there’s a tendency to think that if we roll six of them, we’ll get at least one of the results we want all the time. The reality is that if we roll six dice, that’s the probable outcome, but it’s not a certainty (it only happens 67% of the time, meaning that in one of every three rolls, it won’t happen). And even if our hero is rolling a whopping eight dice, they will fail to score a single wound in 1 out of every 4 fights if they have to roll a “6” to wound. That’s… incredibly depressing, actually.

What this tells us is that, in general, it’s incredibly hard to wound anything in Middle Earth SBG. Setting aside the fact that you have to win the duel roll to even have a chance to wound (magic, War Beasts, and other auto-damage units excepted, obviously), we then have to roll on a table that is set-up to reduce the probability of wounding if we’re rolling normal amounts of dice (1-4), and can deprive us of wounds even if we’re rolling massive amounts of dice (5+). Which is why anything that improves our odds of wounding (special rules, poison/venom re-rolls, 2H weapons, Piercing Strike, etc.) are rare, expensive, dangerous, or a combination of all three. 

Now let’s see what happens to our probability of dealing at least one wound if we are able to wound on “5s and 6s” instead of just “6s” (in other words, if we improve our odds of wounding by +1): 

Odds of rolling 1+ “5 or 6” with 1 Attack die


1 Attack
No “6”
83.33 %
1+ “6”
16.67 %
No “5” / “6”
66.67 %
1+ “5” / “6”
33.33 %

For one attack models, there’s a predictable improvement (from 1-in-6, or 17%, to 2-in-6, or 33%). We still don’t have better odds of dealing 1 wound (33%) than we do of not (67%), but the gap is definitely smaller. But what happens if we add a second die to the equation?

Odds of rolling 1+ “5 or 6” with 1 or 2 Attack dice


1 Attack
2 Attacks
No “6”
83.33 %
69.44 %
1+ “6”
16.67 %
30.56 %
No “5” / “6”
66.67 %
44.44 %
1+ “5” / “6”
33.33 %
55.56 %

At two dice, we suddenly have a higher chance of wounding on a “5” or “6” (55.56%) than we do of not (44.44%). Again, it’s not a substantially higher chance, but it’s higher. For comparison’s sake, it took us four attacks to get to the point where we were more likely to wound than not on “6s.” And at three attacks, we suddenly have significantly better odds of wounding than not: 

Odds of rolling 1+ “5 or 6” with 1-3 Attack dice


1 Attack
2 Attacks
3 Attacks
No “6”
83.33 %
69.44 %
57.87 %
1+ “6”
16.67 %
30.56 %
42.13 %
No “5” / “6”
66.67 %
44.44 %
29.63 %
1+ “5” / “6”
33.33 %
55.56 %
70.37 %

If we continue to fill out the table, we see steady improvement horizontally: although the biggest jump is from 1 attack to 2 (22 percentage points) and from 2 attacks to 3 (15 percentage points). The jumps taper off after that, and we really start to see diminishing returns on adding additional attack dice once we get to 5 or more attacks: 

Odds of rolling 1+ “5 or 6” with X Attack dice


1 Attack
2 Attacks
3 Attacks
4 Attacks
5 Attacks
6 Attacks
7 Attacks
8 Attacks
No “6”
83.33 %
69.44 %
57.87 %
48.23 %
40.19 %
33.49 %
27.91 %
23.26 %
1+ “6”
16.67 %
30.56 %
42.13 %
51.77 %
59.81 %
66. 51 %
72.09 %
76.74 %
No “5” / “6”
66.67 %
44.44 %
29.63 %
19.75 %
13.17 %
8.78 %
5.85 %
3.90 %
1+ “5” / “6”
33.33 %
55.56 %
70.37 %
80.25 %
86.83 %
91.22 %
94.15 %
96.10 %

Interestingly, the diminishing returns are much less vertically (that is, if we go from needing a roll of just a “6” to a roll of either a “5” or a “6”). For a single attack die, the jump is from 17% to 33% (or 16 percentage points). If we have two attacks (baseline captains), the jump is from 31% to 56% (25 percentage points). At three attacks (elite heroes), our odds of dealing at least one wound jump from 42% to 70% (+28 percentage points). At four attacks (elite-elite heroes, captain-level heroes if they’re mounted and have knocked-down their opponents), it jumps from 52% to 80% (another +28 percentage points). At five attacks, it’s 60% to 87% (+27), at six attacks 67% to 91% (+24), at seven attacks 72% to 94% (+22), and at eight attacks 77% to 96% (+19). In other words, while the advantage of adding more attacks to a to-wound on a 5 or a 6 diminishes rapidly once we get to 3+ attacks, the advantage of changing our to-wound from a “6” to a “5 or 6” is very high throughout (at least through eight attacks… at some point, it will diminish).

Now let’s take it one step further, and see what happens if we can improve our dice roll again, this time by going from “5s and 6s” to “4s, 5s, and 6s.” To avoid tedium, I’ll just present the entire chart: 

Odds of rolling 1+ “3+,” “4+,” “5+,” or “6” with X Attack dice


1 Attack
2 Attacks
3 Attacks
4 Attacks
5 Attacks
6 Attacks
7 Attacks
8 Attacks
No “6”
83.33 %
69.44 %
57.87 %
48.23 %
40.19 %
33.49 %
27.91 %
23.26 %
1+ “6”
16.67 %
30.56 %
42.13 %
51.77 %
59.81 %
66. 51 %
72.09 %
76.74 %
No “5+”
66.67 %
44.44 %
29.63 %
19.75 %
13.17 %
8.78 %
5.85 %
3.90 %
1+ “5+”
33.33 %
55.56 %
70.37 %
80.25 %
86.83 %
91.22 %
94.15 %
96.10 %
No “4+”
50.00 %
25.00 %
12.50 %
6.25 %
3.13 %
1.56 %
0.78 %
0.39 %
1+ “4+”
50.00 %
75.00 %
87.50 %
93.75 %
96.88 %
98.44 %
99.22 %
99.61 %
No “3+”
33.33 %
11.11 %
3.70 %
1.23 %
0.41 %
0.14 %
0.05 %
0.02 %
1+ “3+”
66.67 %
88.96 %
96.30 %
98.77 %
99.59 %
99.86 %
99.95 %
99.98 %

A few things of note:

·        Notice that immediately, we start off with at least a 50% chance to wound on a 4+ (and a 67% chance to wound on a 3+), even at one attack. As you might expect, that +2 baseline improves our odds to wound quite a bit, right from the start (in other words, watch out for those backstabbing Moria Prowlers…)
·        Notice as well that we have diminishing returns (both horizontally and vertically) once we get to 4+ and 3+ to wound, although the vertical gains remain higher than the horizontal ones in both categories. In other words, being able to jump from a “6” to a “5+” is the most valuable jump (in terms of bang for our buck) if we want to improve the ability of our models to wound, and why S4 basic troops feel so much more lethal, especially in packs. Once we make that jump, jumping from a 5+ to wound to a 4+ to wound will not improve our probability to wound as significantly, although…
·        Part of the reason why the 4+ table suffers more from diminishing returns is that as soon as we get to three attacks, we already have nearly a 90% chance of dealing at least one wound, which is almost high enough that we could feel comfortable calling it a certainty (and by the time we get to 5 or 6 attacks, we’re basically there). And if we wound on a 3+ instead of a 4+, we’re knocking on the door of 90% with just two attacks. Not a bad thing at all, particularly if our hero is, say, participating in a combat where another hero has called Heroic Combat. In other words, don’t let the diminishing returns distract you from just how good (i.e., “reliable”) a 4+ or a 3+ to wound is, especially on models with multiple attacks. It’s crazy good.

So what does all this tell us about the probable value of Heroic Strength? At a minimum, it tells us that we have at least a 67% chance (3+, or 4/6 rolls, or a 100% chance if +1 strength would bump us up one tier) of moving our hero’s combat value from its current tier to the next tier tier (wounding on a “6” to wounding on a “5+”; wounding on a “5+” to wounding on a 4+), all the way down to a 3+. That jump has no-brainer value if we’d go from wounding on just 6s to wounding on a 5+ (so S4 against D7 or D8), but still has tremendous value if it pushes us from a 5+ to a 4+ or a 3+ (S4 against D5 or D6).

Once we get to 3+, Strength increases don’t help us any more (making Heroic Strength a better choice against higher defense models), although the +1 to-wound bonus from a two-handed weapon or a special rule like Hatred or Backstabbers, would. So watch out for Mordor’s Goroth if he Heroic Strength’s to S8 with his burly 2H mace if you’re a D6 human and Gothmog is nearby… if you lose the fight, you're already dead.

Understanding the value of jumping a wound tier (or two, which we can sometimes do on the roll of a 5 or 6 on our Heroic Strength check) reveals a significant portion of the value we get from Heroic Stength (which, it turns out, is usually good-to-massive). But we’re not quite all the way there, because we still don’t know if increasing our probabilities in this way is a more efficient use of our Might than saving it to actually change to-wound rolls that we know have to be changed.Which brings us to…

Question 2: Does the probability of wounding with Heroic Strength outweigh the certainty of wounding if I save that Might point to modify a wound roll?

We’re actually going to hold off on that question for now. In part because this is already incredibly long, in part because I still haven’t found a great way to measure the difference in probabilities, in part because we have to delve quite a bit more into opportunity costs to do it (which is both inherently complex and requires us to know something about the probability of other things), and in part because suspense keeps life interesting. 

But don’t worry, The Lord of the Rings has tons of important stuff buried in appendices… along with some not-so-important stuff...

(Fingers crossed.)



4 comments:

  1. Very interesting write up (as usual) - though I do think one thing does bear mentioning (hence my objection to Heroic Strength in my original post): most characters who have Heroic Strength are Strength 4-7. S4 heroes only wound D7-8 models on 6s, S5 heroes only wound D8-9 models on 6s, and S6 models only wound D9-10 models on 6s. Since most warriors and heroes can't get to D7+ (unless you're striking a "bunker captain" with heavy armor and shield), most of the time you begin the calculation wounding on 5s - and while spending the Might point on Heroic Strength will improve this to wounding on 4s, you need to get more than one roll of a 4 in order for the Heroic Strength to be worth it. Unless, like was mentioned in the previous two posts, you are paying the Might point for the peace-of-mind bonus that comes (and that has definite value).

    One thing that hasn't been mentioned yet (not sure if you'll be getting to it in your next post or not) is the potential that calling Heroic Strength has on what your opponent calls - if he's worried about getting crushed by Elendil, will that force him to spend a Might point to counter-call some other heroic action? In my mind, that might have a bigger impact than the functional bonus to-wound.

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    1. You've anticipated the next section. :) To foreshadow just a little, Heroic Strength is definitely less efficient if you relatively iffy odds that only one die (or less) is likely to be improved (put differently, the efficiency scales upwards the more attack dice you're rolling, because the more attack dice you roll, the greater the odds of rolling 2+ dice that are one under your target).

      The psychological component is definitely something to consider. You could achieve it both ways: either by losing the fight but withstanding a charge knock-down, either on foot or mounted (which I imagine would be very unnerving), or by winning the fight and dispatching out a high defense model or hero with ease. Preferably by going through the to-wound progression out loud, as if to yourself:

      "You're D9, right? Okay, I'm S5. Which means I need 6s to wound you. But I rolled a +3 on Heroic Strength, so now I'm S8, so sixes become fives. Plus the Piercing Strike, which makes me S9 to your S9, so fives become fours. Plus this two-handed weapon, so fours become threes. Plus I hate dwarves and you're a dwarf, so threes become twos. Plus we're ancient enemies, so I re-roll ones. Let me see... four attacks on the charge, knocking you down, means eight dice on 2s, rerolling 1s, right?"

      *blank stare*

      "Yes..."

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  2. I'm still unconvinced this is anything more than a niche, situational heroic action, but what I did get out of your great number crunching prowess is that my Khand chariots will have a 55.56% chance of killing most enemies it will probably face. :D

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  3. Glad to help ;-) On it’s own, it probably is more gimmicky, unless you have a big hero with 4+ to-wound dice in against another big model, and you’re already willing to blow all your Might if necessary (then I think it’s more value, since it basically mights all your dice if your new Strength characteristic gets you into a lower wound tier). It’s far more valuable if you can combo it with another hero who calls a heroic action, because then you’re getting two uses out of it instead of one (which means it almost always procs once, and usually more than once).

    The chariots seem good value for just 30 points, with 10” move, Monstrous Charge, the trample, and the 5+ in the way (since Khand are so fragile). And against cavalry models, you probably have a much higher chance to wound something since you roll a total of four wounding dice (2 on the rider, 2 on the mount). Plus running over horses has to feel incredibly fulfilling ;-)

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