WhiteShark

This is a fair question; I will do my best to give it a fair answer.  Do not percieve any brevity or ommision as any sort of disregard, though.  Instead, forgive it as a sign that I am working from a phone, with just my thumbs, and am a bit "done" with typing this way, having just carried on an extensive but important conversation on a separate matter.   Apologies in advance.
 
The best summation I can offer is to refer back to an earlier point in this thread where- I believe it was our friend Doc Democracy- pointed out that one can roughly tailor things to produce the kinds of combats one desires, from six-turn slugfests to three-punch drops.
 
And he is right.  And it works.  And once you do it, players very quickly adapt to their new constraints- that is, players optimize their builds for the arena in which they play.  Your recourse is to either forbid this (which I have get to see go well in any game under any circumstances), or do the same in order to offer any actual challenge.
 
Take into consideration the bell curve of the attack roll.  Players will optimize their characters here, too, be it additional skill levels, tactical maneuvers, etc.
 
But the best routine adjustment players can hope for is +3 or +4.  More extremes are possible through cunning planning and careful teamwork, setting, bracing, adding skill levels and environmental bonuses, etc, but during a typical combat using loose campaign limits, the best typical adjustment is an additional three or four points on his CV.
 
Your villain likely will have a few of his own tricks, and can likely get two or three points of adjustment of his own; more if you make,it point to not dumb your villains down now and again, and maneuvers and environment, etc are available for your villain as well.
 
With everyone optimized- even just a little-  for their table rules, in my own experience, it is really unusual to get a running (ie, non-surprise) combat where the antagonists have more than four points of CV different, with two or three being the most typical.
 
Looking at the bell curve and the shifts for CV differences, the odds of scoring a hit are quite predictable, and upsets like wild dice rolls- as we know- are less common the more dice you roll.  Our attack roll uses three dice, so upsets are more _possible_, but still not terribly likely.  You can get a pretty solid feel for who gets in the first hit, and who gets in the most hits.  
 
A damage dice pool of what-  twelve to twenty dice?  Is even more consistent than the attack roll.  And of course, you have a very good idea of how many blows it takes to drop each character _because you designed specifically for that_.
 
In absolutes?  No; it is not one hundred percent predictable.  In practical terms, the nature of the bell curve for 3d6 and for pools of large numbers of dice make both "who hits who the most" consistently- not perfectly, but consistently- predictable, and the results of a typical damage pool are easily compared to the targets available.
 
When things like campaign limits or recommendations come into play, players _will_ optimize for them; GMs optimize for them,  and the end result is that, from the meta, it actually becomes _easier_ to predict, but the limits, ultimately, reduce the variables in play.
 
 
When you design those guidelines toward the idea of "drop in X hits," it all becomes that much more consistently predictable.  Again: not perfectly, but more consistently.  In a way it is a help:  I know just what villains to send against them to give them a challenge!" Or "to take the wind out of their sails" or "to give them a quick victory," but again, that is possible because the guidelines have made the outcomes more consistently predictable.
 
Is this always the case?  No; of course it isn't.  In fact, I expec2r several post demonstrating how wild rolls are still possible and how a scenario once went totally opposite the plan because of three or four of them.   I have a handful of these stories myself.   However, they are called wild rolls for a reason, and when I compare my own handful of them against all the time I played under rule-of-X style limits, it just reinforces the increased predictability such guidelines bring. 
 
Even with an unusual amount of wild rolls in a session or two, the longer a given campaign goes on, the more dice get thrown, the more the resolutions averages out to the initial prediction.
 
Is it bad?
 
Inherently?  No; not in any absolute way.  The points made in this thread, such as "design your villain to drop in three hits" and such demonstrate that for the majority of users, it might even be _desirable_.
 
For me--
 
Let me stress:
 
_For me_, I found it _intolerable_.  Because I like wild crazy things to happen?
Well, _yes_, but in fairness, as a general rule, I bristle equally hard at conversations of predestination, so there is a thing you know about me now.  ;).
 
But _for me_, it was a big stab against what I thought Champions with it's unique build and combat and damge resolution systems were providing us.  I felt like I had been somehow cheated (no; of course I hadn2t been cheated, but emotions and logic have different names for a reason.  ).  I had just assumed that campaign regulations were helping, when in fact they were providing me the opposite of what I wanted: a high degree of unpredictability.  Truly crazy stories to tell,   I saw two options:
 
Institute the hit location rules (which I did not want to do) to provide radical damage swings and spice things up, or go play something else.
 
So I did that.
 
I missed HERO, and almost ten years later, I came back, but I havent used limits, caps, regulations, or rule of X -type things since then.  For what it is worth, I have been much happier.  Maybe it _is_ harder, and I don't think most people happy with what they have would want to even consider it, but it works for me and mine, and I am quite tickled to play again.
 
Before anyone thinks I hate on guidelines or limits: I do not.  They have their value.  It is merely that _for me_, they restricted one of the more enjoyable elements of the game.
 
 

Actually, there is a closed-form solution to the problem P(X=R) where R =  the sum of N 6-sided dice.  It's just...pretty messy, as it gets into combinatorics.  Scroll down about halfway to point 6, which gives the form:
https://www.omnicalculator.com/statistics/dice
 
With a larger number of dice, another approach that'd be accurate enough would be to use the normal distribution;  as the number of dice grows, the sum of them gets closer and closer to being normally distributed.  The mean and standard deviation on Nd6 is easy.  The mean is N * 3.5;  the standard deviation is SQRT( [N * (6^2 -1) / 12] )  or SQRT(N*35/12).  Then, Google Sheets has a NORMDIST function:

NORMDIST(R, Mean, SD, Cumulative)
R is the number to roll
Mean and SD are the distribution mean and standard deviation from above
Cumulative is False here, we want the probability of rolling exactly R.  Cumulative would be, I believe, < = to R.  
 
So
=normdist(D6, 3.5*$E$5, sqrt($E$5*35/12), false)
 
Where E5 has my # of dice to roll, then in my test sheet, column D has R values.  
To cross-check?  AnyDice.com has a great calculator that does it exactly.  The differences were small on my 12d6 test;  they'd be somewhat higher on, say, 8d6, and probably excessive if you drop down to something like 6d6.
 
Note that in a loop?  You can save some time by starting the loop at DEF+1.  At DEF or lower, the stun is gonna be 0.  Plus, for a reasonably large number of dice...say, 8 or more...the probability of reaching 5*N is TINY...that's 40+ on 8 dice.  Even 4.5*N, 36, is a pretty extreme outlier...AnyDice says 36+ on 8d6 is only about 6%.  In most cases, what you're looking at isn't how this adds to being KO'd...it's the risk of getting stunned.  But this should be fast enough that you can run the loop from DEF+1 to full max N*6 readily enough.  (Best rolls I EVER saw...11d6.  19 BODY, 58 STUN.  And once, a perfecto on 6 dice...all 6's.  The latter is pretty obviously 1 in 46,656;  the 11d6 roll is about 0.01%, or roughly 1 in 10,000.)
 
A rough gauge for this, tho, might be to say how many strikes before KO, using 4 per die as the average?  That's what I use for my personal estimations.  The low damage rolls, as you note, do nothing.  The VERY high damage rolls, I'll worry about Probability of Being Stunned...which you can also estimate here.  
Given DEF D, and CON C, then it should be
 
1 - (D+C+1, Mean, SD, true)
 
 

I added configuration parameters to the table you provided and rejigged a few things @WhiteShark
 
Everything in column U is used to calculate the values in V3 to AD30.
 
rDEF % - What percentage of your PD should be resistant Mitigation %- The desired amount of damage you want players to mitigate (on average). TTU - The desired TTU you want your defenses to reflect (you may not get this exact number) TTK - The desired TTK you want your defenses to reflect (you may not get this exact number) Min BODY - The minimum amount of BODY you'll allow on the low end Min STUN - The minimum amount of STUN you'll allow on the low end  
Things get weird on the low end so I added in the Min STUN/BODY columns
 
See the screenshot for what it looks like.  Everything is configurable so I hope it is versatile enough for different GMs and styles of play.  Theoretically, you should be able to adjust those parameters and have a more/less lethal game.
 
 

I updated the spreadsheet.  I did some custom scripting so that the values you calculated show up as tooltips for the user.  Now when you edit the DC column the tooltips will automatically update for you.  I think it's unobtrusive this way, people can choose to ignore it and adjust things however they see fit.
 
I ditched the dropdown pickers... they actually didn't allow for editing after the fact which is exactly what I don't want 😁
 
I cut a new version of the sheet at v0.0.3-alpha.

Again, this is super cool.  I already have a few ideas percolating about what to do with this information that may be useful.  I'm thinking something simple like a set of cells that suggest the 'optimal', i.e., calculated value for when someone sets the campaign baseline DC value.  People can safely ignore it that way 😁

Oh no, don't toss it. I'm going to USE it!

Unfortunately, there's no "Rule of Player Competence", which accounts for a lot. 🤣

I was messing around, and I felt that that whole weighting disproportionally favored offense and had been weighted some time ago by myself before certain additions were made to the sheet, like BODY.  The main pivot points remain the most expensive, SPD and DCs are what I try to horsetrade at about a 1:2 ratio.  I'm also rethinking the statement that you should keep things between +/-5% at character creation.  I think doubling it to +/-10% adds much more flexibility for players to get those outliers (Bricks and Speedsters) squeezed into the game.

EGO is at 5% partially because I had 2 points left over 😁 Seriously though, many EGO powers like MC are directly tied to how high your ego is, so I think I think if anything perhaps it is still undervalued.  It really all depends on the campaign and the commonality of psychic powers, also: pushing... it's all very subjective at the end of the day.

I just cut a version called v0.0.1-alpha of the spreadsheet this morning...
I reweighted the base percentages on the baseline table I think they're tighter and a little better, I dunno... you tell me I added some general statistics to the document I added a chart for people who like visuals (like me) The closer the character is to 0 the closer they are to the Rule of X The first character on the sheet is now used to run calculations on the subsequent characters I added the TTU and TTK columns to the character entries TTU is "Time To Unconscious" and it uses your STUN calc from the table you added TTK is "Time To Kill" and it uses the killing damage calc I did a pass through the 400 and 225-point characters we have on hand while messing around.  225pt has some egregious outliers like a 94 velocity on the Cheetah and 0 stats on the egoist.  I added the "Standard Deviation" entry to the stats to try and shine a light on datasets with potential issues.  These types of characters definitely will skew the calculations and one needs to be careful.  The living brain things could be a very deadly fight for the players unless your campaign includes psychics to the point of it being common for Mental Defense, I wouldn't recommend pitting a group of egoists against a group of unprepared (low ego, no MD) players.
 

You are in my headspace!  That is indeed the question I am asking myself.  I set up the campaign for specific things. If they want a toe to toe fight, I want it over in a turn or thereabouts.  Simply working down stats is not interesting.
 
If they go for a more interesting, rolling fight, then that can be fun over a few combat turns as they seek a situation to achieve a KO blow.
 
I do it three times to reflect offensive versus offensive, offensive versus defensive and defensive versus defensive.
 
I reckon I know enough to sort out a spreadsheet but it would be even more useful to be able to upload an hdc file and test it three ways at the click of a button.  😁😇

@Doc Democracy I think your method looks useful, and I don't think it would be hard at all to encode that in a spreadsheet. You said that you run the strawman fight three times for each character, but I'm not sure I see the point in that. Speak not the averages for themselves? E.g., if the offense strawman does an average of 8.5 STUN per attack (50% hit chance * 17 STUN average), then you know that he will KO his opponent after 4.7 (opponent STUN of 40 / 8.5 STUN) attacks on average.
 
I'm of a similar mind, but I'm curious how short is short to you. If you had two perfectly well-rounded characters fighting against each other, how many hits do you think it should take for one to down the other? What about two offense-focused combatants? I realize that you said you picked the numbers off the top of your head, but supposing I placed two of your offense strawmen against each other, one would KO the other after 2.3 hits / 3.6 attacks—so in reality, four attacks. That seems high to me for two characters that are supposed to be offensively oriented.

That's actually the key thing I'm considering right now: what average hits to KO etc. should the baseline values promote? Unfortunately I think this may vary based on setting assumptions. For example, I'm a big fan of guns being deadly, so in my military sci-fi game, I want to keep that average pretty low. Even more so, if two glass cannons went toe to toe, I'd want them to be nearly, perhaps actually, taking each other out with one of their (very powerful) average hits.

P.S.: if you'd like to learn very basic coding, spreadsheets are a fine way to start. There is a lot of easy to understand documentation out there and generally it's only as complex as using some math functions and possibly a few if statements. I'm not a coding expert by any means but encoding this sort of math on a spreadsheet is pretty simple once you get the hang of it.
 
@sentry0 would you prefer that we henceforth continued discussion here or in the file thread? I see that it is possible to upload files in both places, so I don't mind either way. I'm going to ponder the average attacks/hits to KO/dying question some more today before I personally make another revision.

I want to reiterate that in my original post I said that I liked the way it was handled in 5th better than the Rule of X which was essentially campaign norms based on starting point levels.  The title of this thread is the "Vagaries of the rule of X" not "I love the rule of x"
 
The point of the exercise for me is to see if I can make a working Rule of X and see how well my first batch of 6th edition characters do.
 
I have been tweaking the weights in my spreadsheet and things are pretty different now both the speedster and brick show up above 10% which I think is fair.  The 17 die attack the brick has was questionable when I built him but I figured I would let it slide because it has Extra time and increased endurance costs.  Nothing the Rule of X would catch mind you but the new tweaks to weighting call it out pretty clearly as a culprit for his inflated +%.
 
I always pivot damage dice on SPEED and DCV in my games.  The lower you go under the average SPEED and the lower your DCV  the more defenses and damage I allow you to have, within reason obviously.  The inverse is true for characters with high SPEED and DCV.  It's simple and part art and part science but it allows for that spread so characters don't feel so homogenized.  I don't think I'm unique here either, I learned this from my Champions mentor and I'd wager that others do exactly the same thing.
 
I actually fully agree with you on the notion of the Rule of X being handwavy BS, especially the way it's spelled out in the official rules.  I still want to take a run at this and see how far I can take it without needing a degree in Math.
 
I guess I just like a challenge