Trencher

Arrow impalement:  (Total: 57 Active Cost, 13 Real Cost) Killing Attack - Hand-To-Hand 1d6-1, +3 Increased STUN Multiplier (+3/4), Damage Over Time, Target's defenses only apply once (9-12 damage increments, damage occurs every Turn, +4) (57 Active Points); OAF (-1), No STR Bonus (-1/2), Required Hands Two-Handed (-1/2), 12 Charges (-1/4), Inaccurate (1/2 OCV; -1/4), Linked (Killing Attack - Ranged; -1/4), Real Weapon (-1/4), Requires A Roll (Attack roll, -1 per 20 Active Points modifier; -1/4) (Real Cost: 13)
 
Lucius Alexander
 
Did the palindromedary eat

I usually simulate it with a -2 limitation. 
 
This came about with the following observation:
An 18 will always miss.  Making a 17- the best hit chance.  If a critical is 1/2 of what you need to hit rounded down, then a critical equals 8-.  An 8- is normal -2.
 
The requires a roll is neat idea and I have used it on martial artists as "finding an opening".  Its a triggered, naked advantage autofire(3) on the punch with requires a roll 11-.  When the villain succeeds on punching a hero, I roll 11-. if successful, the hit is autofire(3). 

As well, abilities that reduce the opponent's DCV become much more powerful. 
 
 
Danger Sense is a flat roll, which is different from the opposed to hit roll.  Really, there should be more granularity on the Danger Sense limitation as well.  This seems like another outgrowth of "when in doubt, discount the limitation heavily"

A -2 limitation is fine and that's what I was going to go with, but the Champions Complete gave it a total of -1 1/2.

Stunning knockdown:  (Total: 54 Active Cost, 10 Real Cost) Change Environment (-1 to  CON Roll, -1 to STR Roll, Stunning), Reduced Endurance (0 END; +1/2) (54 Active Points); OAF (-1), Requires A Roll (Attack roll, -1 per 20 Active Points modifier; Must be made each Phase/use; -3/4), No Range (-1/2), Inaccurate (0 OCV; -1/2), Required Hands Two-Handed (-1/2), Linked (Killing Attack - Hand-To-Hand; -1/2), Can Be Deflected (-1/4), Real Weapon (-1/4) (Real Cost: 10)
 
To be linked to a large hammer. If the attack roll is made by half, roll another attack at -3; if that succeeds, target must roll CON to avoid being stunned and STR to avoid falling down.
 
Lucius Alexander
 
No roll to evade the palindromedary

It's perfectly OK, IMO to "hard-wire" in a critical hit system, either for specific weapons/powers or for specific characters - the PCs and significant NPCs, or whoever.  It could allow for some interesting builds.  It would be a bit strange for one of these hard-wired-crits to do something completely different from the base attack power, but HERO allows it.  The justification for it might be a bit tricky, but that depends on the genre and style you're going for.  Magic can pretty much justify anything.  An exaggerated anime-style, perhaps.
 
The main thing to keep in mind is that making the roll by half is a very rare phenomenon.  So it's worth a pretty big limitation.  Without having to do all the math yourself, you can test it by rolling 3d6 several times.  How many times do you roll 11 or less?  How many times do you roll 5 or less?  etc.

My take on it is, if you look at the Talent builds in 6E1, specifically for Danger Sense, you'll see a limitation "Only if Character Makes Half Roll (-1)". So, I'd use the same value.
 
Lee

I tend to agree with Phil. Based on his observations, I don't even know if I would build this as a power (unless the effects are radically different from the power being used: like Flash adding a Drain or or something like that. 
 
I think you might be better served creating a Critical Hit system for your campaign (as others have alluded to above) and calling it a day:  hit by half?  + X dice of effect, or times 1.x the actual effect.  Roll a natural three?  +Y dice of effect, or times 1.y the actual effect, etc. 
 
Just declare it the way the universe works, at least for main characters.

I'd call it a -2 at least.  The 7- roll is based on the best-case-scenario:  a low-level mook that you can hit on a 14-.  Which is also the case in which the power will be the least useful.  How much extra damage do you need to do to a mook?
 
In the "average" case, you hit on 11-, which means the power works on 5-.  11- is 62.5%.  5- is 4,6%.  This means the power works once for every 13.5 normal hits.  That could be about a -12 limitation.  The power loses about 92.6% of its effectiveness in this average case.  If the normal to hit roll is even lower, then the power activates even less often.
 
Assuming a correlation between how hard an enemy is to hit and how hard an enemy is to put down, then this power becomes more likely to work, the less it is needed, and less likely to work the more it is needed.

It reminds me of Pathfinder where you would threaten a critical and have to confirm it with a second roll.  Sounds interesting, you'll have to let us know how it works out for you.

I disagree.  That would make it more expensive than just having the extra damage all the time.

I personally think this sounds more like a standard Trigger advantage with the trigger being a critical hit.

I second this but I caution you to beware of Higher OCV concepts and OCV/Skills thru XP as they will warp the cost structure. Or you can have the value of the Limitation change with each individuals maximum OCV.

This looks like a 'Requires a Roll" situation. Complicating it, it's a little variable. As GM, I would look at the best chance of having the power activate and use that as the roll. Quickly based on what you said, "If they needed 14 or less to hit it would activate if they rolled seven or less and so on", I would go with it activating on a 7 or less. If I'm reading the Champions Complete chart correctly, it looks like that turns into a -1 1/2 limitation.

I wanted to find the worst Christmas song and this is it. Paul McCartney and Mariah Carey can't compre to this. * Days of Christmas by Destiny's Child
 
This is a cultish sort of record but both the vocalists are annoying but proof that even South Africa can produce rubbish
 

Personally I find these more irritating
 
 

One annoying because it is trying to be deliberately annoying
 
Annoying on the basis of pretentiousness
 

This is a record that can inspire violence. The original is good but this cover version is just awful. It is the Ooh, Aah that does it
 
I would apologise for this but I reckon you ought to know how dreadful some people's taste is. Again a No 1 record. The video makes it worse.
 

First off, anything with an accordion.
 
Whew, that's outta the way.
 
Hmm, hard to nominate one, but let's start with The Lady in Red by Chris De Burgh.  An annoying, droning pop ballad played constantly in the 80s.  Sung in a whiny, strained voice that sounds like nails on a chalkboard.
 
 

Right now I’m listening to Buckaroo Banzai as I surf the net and I got to thinking that the ‘80’s might have been Hollywood’s last gasp at creating true heroes until the recent surge of Superhero movies. 
   Well, neurons started misfiring and I started to imagine an American “League of Extraordinary Gentlemen”.  So far I’ve got Buckaroo leading Remo Williams, Meteor Man, Buffy (the original) vampire slayer and an American (Highlander style) immortal.  
   The only criteria’s would be original movie characters from the ‘80’s (So no Batman or Greatest American Hero) and no dark or “anti” heroes. (So no Professional or Hackers)   Anybody have any candidates?

This is just one man's opinion, and you could disagree with me. After watching "The Last Jedi", my expectations were lowered. In my opinion, TLJ was worse than "Revenge of the Sith". RotS is a bad movie, just not as episodes 1 & 2. Overall, the fun parts outnumbered the non-fun parts. I wish it was as good as Avengers: Endgame, but that did not happen. I disagree with the movie critics, and I give a slight recommendation for others to watch this movie.

You had one job! 
 

Well I bowed out of four color, and much prefer tailored  worlds.  As a creative, I find tight limits is often a stimulus for creativity.  Kitchen sink worlds tend to breed a lack of originality.

Whiz Kid: Hyper kinetic thief and prankster, Whiz Kid seems to dance back and fourth across the hero/villain line as quickly as he does everything else. And for the same reason: lulz. This poster boy for reckless irresponsible youth is up for almost anything to slake his thirst for thrills and amusement. He's not violent, however, and doesn't try to kill or greatly injure his opponents (or the authorities) instead using his speed, agility and wicked but childish sense of humor to escape, evade and harass them instead. His juvenile attitude is understandable as Whiz Kids is actually 11 yrs old. His hyped up metabolism has him the build and development of a boy several years older.  Whiz kid is a frequent friendly rival/partner of the young Speedster heroine Velocity. To be clear, she is NOT his girlfriend. She is his friend who is a girl. 
 

Renaissance Smug arrogant super scientist who decided, in his magnanimous wisdom to bestow his gifts on the world of lesser beings.  A misguided hero/potential villain