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I'm looking to introduce an recurring enemy in my new 4e/Ultramodern4 campaign that's an on-going, ruthless opponent. I want this specific opponent to be an exception of the normal 4e pattern of all enemies being reasonable fights; I want to make the enemy overpowered enough to strongly encourage players to deal with him in a non-direct manner without removing it from the table entirely, or artificially limit it (by physically removing access, or some sort of ritual to allow the enemy to escape, etc).

With this in mind, I want to level him outside the normal leveling scheme.

Since the highest official monster level is 36 (and the highest official player level is 30) it seems the answer might be 6, but this is just an educated guess at best.

Mathematically, how much of a level difference can I make a boss compared to the party while still allowing the possibility of direct confrontation?

Note: Most of the party have put considerable effort into optimizing their characters, if that might play in at all.

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    \$\begingroup\$ Must it be a single enemy? Whatever the tipping point, it's bound to be a fight where most attacks against it will miss, so direct confrontation would be very boring. It's much easier to make it unwise to directly confront because it's a large group of enemies with a powerful Elite/Solo as your main guy. \$\endgroup\$ – Erik Jun 21 '16 at 21:04
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An average L30 PC (assuming primary stat at 18, increasing it every 4 levels and a +6 implement/weapon AND the inevitable relevant Expertise feat) will be aiming at about +32 to hit a NaD. L30 monsters will have NaDs ranging from around 42 to 44, generally.

This means I need about a 10 or a 12 on my attack roll to hit. (realistically, it's going to be lower between powers, feats and situational effects, but these are the basic numbers)

A level 36 monster will see defences ranging from 45 to 47. Which means I could be looking at a 13 or 15 to hit.

Having a character with only a 33% chance to hit is not fun for anyone.

Those are all the basic numbers to look at. But you say that your characters will be pretty optimised. So maybe one of them just walks up, casts an SE stun with a -15 to saves and you spend the fight having them whale on what amounts to a rock. Or the creature is stuck fighting the Defender and can only hit on a crit because of stacked defence bonuses.

The short answer is that levels, once the party is at a certain level of optimisation, don't mean that much. A well-built party working together as a team can take on incredible odds. Especially with a good controller or a highly-efficient healer.

Basically, the level of a creature is not what makes it dangerous. It's going to be in what it can do.

Consider the L12 Basilisk. it has an at-will AOE that applies an SE effect that progresses with failed saves from Immobilised, Restrained to permanent petrification. And it can keep applying it so that someone can have three versions of the effect going on at once. it's terrifying. Compare it to a level 16 Archon Waveshaper, who just pushes and slows. One of these is far more dangerous than the other.

Summary: levels will affect the fight, but may serve to only make the fight frustrating. The danger is going to be in what the creature can do.

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Note: Most of the party have put considerable effort into optimizing their characters, if that might play in at all.

While individual character optimization can make a considerable difference in effectiveness, it still pales in comparison to full party optimization (i.e. Radiant Mafia).

Solo fights are often frustrating. If the solo boss is too high a level (with defenses that are too high) then characters end up missing too often and it becomes a drawn out, slow, grindy battle. If the solo boss is too low a level then Team PC can end up quickly debilitating it with status effects (even when the solo monster gets +5 to saves). It is really quite difficult to pick the perfect solo monster to give the party a good (and fun) challenge. Generally, I suggest you avoid such encounters and make sure the boss character has at least some lower level henchmen to get in the way of Team PC.

Mathematically, how much of a level difference can I make a boss compared to the party while still allowing the possibility of direct confrontation?

If you don't want the party challenging the BBEG right away then make it clear (via a NPC) that Team PC cannot defeat the BBEG without first acquiring some sort of McGuffin that limits the BBEG's power. Perhaps the BBEG can, from a position of safety, summon an escalating number of mini-bosses endlessly until Team PC retreats. In that case, Team PC will be forced to find another solution.

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The way I would handle it is not make the boss mechanically difficult (if you decide to stat him at all, nothing says you have to have stats for him), but make him incredibly powerful in other ways. Have him have vast resources, access to powerful magic, high level henchmen (who are statted out, but whose goals aren't to survive, but to do their master's bidding). He should work at making the Players' lives difficult, or circumvent their successes. Nothing makes a character madder than working hard and spending resources to get a result, only to discover that it is what the BBEG wanted all along.

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