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Nurglitch kinda reinforces a point there.

1+1 on paper =2 there is no denying that

now you lay out 1 stone, and before you can add the other stone to the pile a random guy jacks it from you, leaving you with a 1, when you intended to do a 2. Thats how warhammer 40k works.

chance of a outcome can easily be manipulated to any side favor rather its adding a extra dice to roll, or a modifier in the game. So in essence the luck on your graph couldn't be consistent as the chance of a dice roll rather you need a 4+ or a 2+ varies that chance dynamically.

I think what could help you is ask your opponents to write a battle report as well as you. You might find one situation from your prospective completely different from his.

Nurglitch wrote:No, communism is likewise not a great, or even good theory. It's unachievable by a race of super-beings, and incoherent in its theoretical apparatus.

Sorry, pet-peeve for the "Well, it looked good on paper!" crowd. Inevitably anything that looked good on paper but worked badly in practice would have also worked badly in theory if the paper hadn't overlooked relevant details, not made silent assumptions, and not made subtle leaps of logic.

I agree, communism is not that good, even in theory. It puts power into a single group of people (oligarchy) which is never a good idea. I never bought into Communism or Marxism. At best I could say that some concepts of such a form of government may look good on paper, but overall it is not good.

Crom wrote:Did we not all agree that all games are decided mostly by skill and dice rolls can only really make a small impact at best?

Actually, not exactly. My position is that, because events that determine victory are themselves determined by dice, luck is the prime determiner of the game. Skill also makes an impact in that it lets you mess with luck, but as both players get closer in skill level to each other, this impact of messing with luck decreases relative to other factors.

xlightscreen wrote:chance of a outcome can easily be manipulated to any side favor rather its adding a extra dice to roll, or a modifier in the game. So in essence the luck on your graph couldn't be consistent as the chance of a dice roll rather you need a 4+ or a 2+ varies that chance dynamically.

I think we're using different definitions of "luck" here. With the way I'm using this word, I'm talking about the uncontrollable elements of the game (like the die rolls). Yes, you can shorten your odds of success for any given thing, at the cost of lengthening them for something else. This is what skill is.

By calling luck constant, I'm not saying that it's constant FOR THAT DIE ROLL, as the odds of any one thing being successful can be heavily influenced by decisions both players make. What I'm saying is that across the entire game, the die rolls will always fall within a certain band (you can't roll a 13 on 2D6), and that the die rolls themselves are unaffected by player skill (unless you're cheating).

How much luck impacts a game is, of course, determined by the specific of the luck. If I couldn't roll lower than a 6 with every roll I made, then luck would probably be a pretty huge factor that game, for example. In the end, I can't control luck, however,thus it's relative increase to other things the more that the other things are being controlled.

Ailaros wrote:I don't actually know where luck and skill cross, I only theorize that at some point they do. Furthermore, thinking about the lines on the graph may be a bit misleading. Perhaps if you thought of them as really fat lines, or intersecting fields, a more clearer picture could be created.

Ailaros wrote:This comes from the idea that changing odds has diminishing return. Going from a 1:1 chance of something happening to a 2:1 chance is huge. Going from a 100:1 to 101: is not. The same size increase matters less the further you go.

It's actually a truism of controlled variables in general. The more you control for a variable, the harder it is to control for that variable more.

And what are you using to determine that there is no relationship between skill disparity and the degree that luck affects the result of the game? You have made too many assumption that support your theory. I would have to say that Luck is not a constant in terms of its impact on the game when related to disparity in skill.

While this thread was kind of interesting at first, your theory is neither
A) well formulated or
B) reflected of empirical evidence.

We can all agree that where every other variable is equal, luck will be the determining factor.

However, you hypothesize that there is only one factor other than luck, which is skill. Skill is actually an amalgamation of many different things, which in reality are never equal. Since these other variables are not going to be equal, your theory is useless to real-world application. It only tells us what we already know.

I agree that 40k is not a superbly tactical simulation, you'll have to stick to archaic hex-and-chit WW2 games for that. I think "tactical" is in fact the wrong word to use for 40k. I prefer "controlling variables". For example you can try to control whether your Land Raider is visible or not, but there is nothing tactically genius or stunning about moving to get a cover save. You can try to control your Ork Boyz reaching the Eldar gunline, but "move forward!" isn't strategically mind-blowing. When I think tactics I think feints, pincer moves, misdirection, flanks, ambushes, etc. but because of all the different units and stats and variables in 40k those overarching tactical/strategic ideas can't actually be executed.
In a totally fabricated scenario where the players are playing exact armies and have exactly perfect tactics, then yes, skill is removed as a factor and the ONLY remaining variable is dice. But that is true of any game with dice (or other ways of simulating randomness). However since such a scenario doesn't occur on a game to game basis, luck does not have the monumental importance you are implying. Why can't such a scenario occur? Player fatigue, mistakes, misjudgements, miscommunication, and every other small error that adds up to change the course of a game.
That is why Chess and other luck-less games are considered by some to be superior to those with random factors: because they are a truer measure of player skill, knowledge, and fortitude.

Dracos wrote:And what are you using to determine that there is no relationship between skill disparity and the degree that luck affects the result of the game?

Actually, I'm claiming that there IS a relationship between skill disparity and the degree that luck affects the game. Its kind of central to the theory

Dracos wrote:We can all agree that where every other variable is equal, luck will be the determining factor.

However, you hypothesize that there is only one factor other than luck, which is skill. Skill is actually an amalgamation of many different things, which in reality are never equal. Since these other variables are not going to be equal, your theory is useless to real-world application. It only tells us what we already know.

bosky wrote:In a totally fabricated scenario where the players are playing exact armies and have exactly perfect tactics, then yes, skill is removed as a factor and the ONLY remaining variable is dice. But that is true of any game with dice (or other ways of simulating randomness). However since such a scenario doesn't occur on a game to game basis, luck does not have the monumental importance you are implying. Why can't such a scenario occur? Player fatigue, mistakes, misjudgements, miscommunication, and every other small error that adds up to change the course of a game.

Man, why is this so confusing to people? What could I say that would end the seemingly endless stream of people that are saying that this theory only works when the players are of exactly equal skill? Seriously, this is come up over a dozen times in this thread.

While this theory is saying that IF the two players are EXACTLY equal, then the ONLY thing that will matter is luck. The theory is also saying that AS the players become UNEQUAL, the skill disparity will matter MORE, relative to the disparity.

Ailaros wrote:
Man, why is this so confusing to people? What could I say that would end the seemingly endless stream of people that are saying that this theory only works when the players are of exactly equal skill? Seriously, this is come up over a dozen times in this thread.

While this theory is saying that IF the two players are EXACTLY equal, then the ONLY thing that will matter is luck. The theory is also saying that AS the players become UNEQUAL, the skill disparity will matter MORE, relative to the disparity.

Probably because the thread is 16 pages and most people are reading your version 2 summary and then replying? That and a lot of people have set views and won't really budge based on forum posts.

Ailaros wrote:Actually, I'm claiming that there IS a relationship between skill disparity and the degree that luck affects the game. Its kind of central to the theory

Your graph says otherwise.

Dracos wrote:

Ailaros wrote:Actually, I'm claiming that there IS a relationship between skill disparity and the degree that luck affects the game. Its kind of central to the theory

Your graph says otherwise.

Well, let's take a look at that graph here



So you see the Y axis? The higher up something on the Y axis, the more that thing determines the outcome of the game. Now, see the X axis? That show skill disparity. The further to the left you are, the more disparate the player's skill levels are.

Now, watch the magic here - You see how the further left you go on the X axis, the higher up the little red skill line goes up compared to the blue one? That means that when skill disparity is really high, the skill element of the game affects the outcome of the game more. Now, look over to the right. Notice how luck and skill are different relative to each other.

I'm pretty certain that this graph shows a relation between luck and skill, and that the purpose is to show how luck and skill affect the game.

Actually that is not true. The graph shows that Luck has value Y given any point on the X axis, meaning that for any given value of disparity in skill, Luck still has the same value Y on the "Determiner of Result" scale. So Y=L for all values X, meaning there is no relationship between Y and X.

edit: One thing to note is that the quote above in my post is questioning skill disparity, and you were talking about skill in your last post. Perhaps that is where your confusion comes from.

bosky wrote:When I think tactics I think feints, pincer moves, misdirection, flanks, ambushes, etc. but because of all the different units and stats and variables in 40k those overarching tactical/strategic ideas can't actually be executed.

..........................

You must play a different version of 40k than me.

[End Post]

Dashofpepper wrote:

bosky wrote:When I think tactics I think feints, pincer moves, misdirection, flanks, ambushes, etc. but because of all the different units and stats and variables in 40k those overarching tactical/strategic ideas can't actually be executed.

..........................

You must play a different version of 40k than me.

[End Post]

He plays the same one you do, it's just harder to hoot and yell like some iteration of 40k's Muhammad Ali when you're able to tell yourself the game isn't some superbly layered series of surprises.

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MikeMcSomething wrote:

Dashofpepper wrote:

bosky wrote:When I think tactics I think feints, pincer moves, misdirection, flanks, ambushes, etc. but because of all the different units and stats and variables in 40k those overarching tactical/strategic ideas can't actually be executed.

..........................

You must play a different version of 40k than me.

[End Post]

He plays the same one you do, it's just harder to hoot and yell like some iteration of 40k's Muhammad Ali when you're able to tell yourself the game isn't some superbly layered series of surprises.

No need to be peevish. But if you don't think that feints, pincer moves, misdirection, flanks, ambushes.....and even psychological warfare are parts of 40k, you must not play the same version I do either.

Nurglitch wrote:

Dracos wrote:Actually that is not true. The graph shows that Luck has value Y given any point on the X axis, meaning that for any given value of disparity in skill, Luck still has the same value Y on the "Determiner of Result" scale. So Y=L for all values X, meaning there is no relationship between Y and X.

Quoted for EMPHASIS.

First off, that's a graph thrown together quickly to illustrate a point, I think, and not one that is meant to be perfect. Hence the lack of markings and values.

Second, I think what you guys are after is an illustration that the effect of luck decreases based on *absolute* skill instead of relative skill. So basically a 3rd axis or a different graph.

Ailaros wrote:Actually, I'm claiming that there IS a relationship between skill disparity and the degree that luck affects the game. Its kind of central to the theory

This is what he claimed. I told him his graph did not say this. He posted the graph as proof of this. I debunked his claim about the graph. That's all.

edit: Oh, and he did it in a rather condescending manner, which was actually funny considering that he was incorrect.

At this point, we're just hashing over exactly how an example graph is displayed.

Here: on the far right of the graph, luck is about 90% of how things are decided. On the far left, luck is about 33%. The Y axis is how much effect skill or luck has. Luck is held constant to reinforce the fact that it's not controlled based on the disparity of the skills.

The "degree that luck affects the game" is not the same as how much of an effect luck has. The former is relative, the latter is absolute. At a certain skill level, luck may have a huge effect, but skill disparity matters more (left side). Or, at a higher absolute skill level, it could have smaller effect but the difference in skills is small enough to matter even less than luck (right side).

He stated the graph shows the former. It does. The graph would perform the way you expect if you convert it so that the Y-axis is "degree of effect". In that case, the sum of blue and red would be a constant (100%). If we did that, the blue line would start low and go higher, again supporting his statement.

Things get a bit mucky when there's a lot of switching back and forth between relative and absolute terms, and there's been a number of people getting it backwards. Ultimately, he made the graph to illustrate exactly the point he's making, and he's not a complete idiot. The illustration may not be perfectly clear, but this discussion would work a lot better if people avoided starting from the assumption that their detractors are completely slowed.

Okay, I have put a little thought into your theory, and how you are replying to people speaking against it, and I think I understand what is going on here.

Basically, I think a lot of people are reading your theory and making the incorrect conclusion that luck is the only determiner in games, while skill quickly means less when you play someone with the same skillset you have.

This is incorrect. All you are stating is that a game involving dice has a luck element that cannot be removed completely from the equation. No one can prove you wrong on this theory because it is a fact (let's just call it a law?). I do not fully understand why this concept needed to be posted. It would be like posting a theory that, "Armies with at least one HQ choice tend to win more games of 40k than those without any HQ", or, "The ability to measure 6" in your turn directly correlates to moving your units correctly".

Regardless of the number of detractors, you can adamantly stand by your theory because regardless of how people challenge your definition of skill, you just fall back on, "Dice are involved, so there is always a luck element."

Now that we have this out of the way, I think you should reconsider your graph. Consider a theoretical, extremely skilled player, A. He sets up to play against another extremely skilled player, B. Skill in this little example will obviously have to cover all aspects, such as listbuilding, decision-making, meta-analysis of the situation, etc.

Now, in the course of the game, A notices that B made a minor mistake. Here is where your graph completely stops working. A, being extremely skilled at exploiting an advantage can use that one mistake to push the game completely in his favour. B, being equal in skill to A, cannot make back the disadvantage A put him into because he then has less opportunity (with fewer models or lacking position) to capitalize on any of A's future mistakes. This is not a ridiculous notion, this is what happens in wargaming. How is this scenario accounted for by your graph? Surely skill played a large role in this scenario, and an individual with much less skill at exploiting a mistakes would have missed a possible opportunity to win the game.

So, what I've learned from the past 3 pages is that I should just take the graph out of the footnotes. All it's doing is confusing people.

Consider it gone.

Fearspect wrote:Now, in the course of the game, A notices that B made a minor mistake. Here is where your graph completely stops working. A, being extremely skilled at exploiting an advantage can use that one mistake to push the game completely in his favour. B, being equal in skill to A, cannot make back the disadvantage A put him into because he then has less opportunity (with fewer models or lacking position) to capitalize on any of A's future mistakes. This is not a ridiculous notion, this is what happens in wargaming. How is this scenario accounted for by your graph? Surely skill played a large role in this scenario, and an individual with much less skill at exploiting a mistakes would have missed a possible opportunity to win the game.

This is part of my theory. Skill matters in relation to the difference in skill level. If one person is better than the other, they will be able to apply more of their combat power in certain ways to play the smartest odds. Call it "capitalizing" if you will, it's still a part of skill.

What the important thing to remember here is that it is the relative skill level between players which is important to this all.

Actually, not exactly. My position is that, because events that determine victory are themselves determined by dice, luck is the prime determiner of the game. Skill also makes an impact in that it lets you mess with luck, but as both players get closer in skill level to each other, this impact of messing with luck decreases relative to other factors.

That is not always the cause though. You can have horrid dice rolls and still win the game, if you are playing missions where objective points are the key focus. Luck is also not a constant, you mitigate bad rolls but utilizing the framework of the rules. I got guys with 5+ armor saves, I put them in cover, I use terrain.


If anything, WHFB is way more reliant on luck than it is skill. For one the winds of magic is pure dice rolls. In 40K you get mission objectives, you get transport vehicles, you get to build an army to a specific tactic. In other gaming systems you don't always get that luxury. I do think one of the best gaming systems I played was the first edition of Warzone. It was based on action points. Every unit had a set number of action points and each action point would allow you to perform 1 action of a unit. Players took turns activating and executing actions 1 unit at a time, so going first wasn't an advantage. So if a unit had 3 action points it could move 3 times, or move once and shoot twice, and so forth.

40K has it's flaws, like any game. However, I would say out of every gaming system I have ever played (all GW games, Warzone, historical, L5R, and others I forget I even played) 40K doesn't live and die by dice rolling. I am sure there are plenty of victory stories floating around to people that had bad dice rolls. The fact that in 40K you can manage odds at dice rolls with so many different things means that it is even less of a risk. If a unit is leadership 10 from a character and that character has war gear that allows for rerolling leadership tests, they are pretty much like 99% never going to fail a leadership test. The only time you might break them would be from an assault that beat them with a high enough combat resolution. Then you have armies like Marines, that have They Shall Know No Fear, which means even if they do break, they will automatically regroup.

I said something like this earlier and I will say it again as far as luck and skill go.

Skill allows a player to give him better opportunities to be 'lucky' and helps mitigate his 'bad luck' or his opponents 'good luck'.

Ailaros wrote:So, what I've learned from the past 3 pages is that I should just take the graph out of the footnotes. All it's doing is confusing people.

I like how instead of admitting that its not saying what you want it to say you are just passing it off like people don't understand.

Ailaros wrote:This is part of my theory. Skill matters in relation to the difference in skill level. If one person is better than the other, they will be able to apply more of their combat power in certain ways to play the smartest odds. Call it "capitalizing" if you will, it's still a part of skill.

What the important thing to remember here is that it is the relative skill level between players which is important to this all.

Anything else there captain obvious?

Crom wrote:That is not always the cause though. You can have horrid dice rolls and still win the game, if you are playing missions where objective points are the key focus. Luck is also not a constant, you mitigate bad rolls but utilizing the framework of the rules.

Both of these points have already been addressed dozens of times in the past 16 pages. I'd go back and read more of the thread.

Dracos wrote:

Ailaros wrote:So, what I've learned from the past 3 pages is that I should just take the graph out of the footnotes. All it's doing is confusing people.

I like how instead of admitting that its not saying what you want it to say you are just passing it off like people don't understand.

I've been bending over backwards to try and help people understand what I'm trying to say. There have been some people that have disagreed, but have been positive contributors. Their opinions and ideas were much appreciated, and helped make the theory better. There have also been some people who misread things and then make statements saying that I'm saying something I'm not. Some of these people, like yourself, form the opinion that this must be wrong, la la la, I'm not listening.

I'm just getting tired of people who come on and spend several pages hoping to convince me of something by sheer weight of assertion while making snide comments at me personally. I do actually feel kind of foolish for not just ignoring you outright this whole time, but I was operating in good faith that you actually wanted to contribute something to the conversation other than just persistent derisiveness.

Lesson learned. I'll just return to ignoring commenters until they start saying things that are relevant.

Both of these points have already been addressed dozens of times in the past 16 pages. I'd go back and read more of the thread.

I have read, and I still disagree that luck has that large of an impact.

@Ailaros

OK let me jump at your side a bit.

I believe you have the point concerning this:

You divide 40k into 2 parts

1. skill
2. luck

no further definition needed.

given that skill is exactly equal, then luck MUST be the decisive factor.
This is simple and logical.

You can also say:



But what do you consider decisive?

lets have the following calculation:



This is why I think luck impact will be reduced if the skill raises, but of course as the difference in skill between the opposing players decreases the luck impact increases.

Crom wrote:

Both of these points have already been addressed dozens of times in the past 16 pages. I'd go back and read more of the thread.

I have read, and I still disagree that luck has that large of an impact.

Why? To me, I have read the theory (both 1 and 2), and agree with most of Ailaros is saying. It's fine if you don't agree, but tell us why you don't agree.

I can say that I don't believe the sun is the reason for the Earth's heat, but unless I argue my point some no-one is going to believe me.

TheRedArmy wrote:

Crom wrote:

Both of these points have already been addressed dozens of times in the past 16 pages. I'd go back and read more of the thread.

I have read, and I still disagree that luck has that large of an impact.

Why? To me, I have read the theory (both 1 and 2), and agree with most of Ailaros is saying. It's fine if you don't agree, but tell us why you don't agree.

I can say that I don't believe the sun is the reason for the Earth's heat, but unless I argue my point some no-one is going to believe me.

My whole point is, that yes luck does matter in 40K, but only to a certain extent. Out of every war gaming system I have played, 40K seems to have more opportunities to control/mitigate bad dice rolls. There are plenty of war gear and configurations you can do to mitigate it down to a very small issue. Twink linked weapons, war gear that allows rerolls, and cover saves all help mitigate what would normally be determined by bad dice rolls. Your actions make a much larger impact on a win than dice rolls do. There are also so many things you can do that do not involve dice rolls to win a game.

If two players are equal skill/experience that doesn't mean they won't make a mistake, or be baited into making a mistake. You capitalize more of mistakes than you do dice rolls. Plus with 5th edition being a mission based game more so than total annihilation (depending on the mission) means you can win by hold objectives, and even if you have bad dice rolls.

In other gaming systems, like WHFB for example, whole turns can rely on dice rolls. The Winds of Magic in the Magic Phase can really kill an army if you roll crap for the amount of power dice. Especially when your strategy or army's strength is in magic.

I think dice rolls do have an impact, but I think if you put yourself in a situation in 40K where dice rolls matter to the extent of costing you the game you probably either took a large risk, or played your tactics wrong. Sometimes you do have to take a risk, because your opponent can put you in a situation where you need to take a risk, so it is not like it doesn't happen. Also Luck is never a constant, you can have both good and bad luck in the same game.

Crom wrote:My whole point is, that yes luck does matter in 40K, but only to a certain extent. Out of every war gaming system I have played, 40K seems to have more opportunities to control/mitigate bad dice rolls. There are plenty of war gear and configurations you can do to mitigate it down to a very small issue. Twink linked weapons, war gear that allows rerolls, and cover saves all help mitigate what would normally be determined by bad dice rolls. Your actions make a much larger impact on a win than dice rolls do. There are also so many things you can do that do not involve dice rolls to win a game.

Actually, the dice are everything. Yes, 40K gives several opportunities to help turn the luck in your favor. That doesn't mean it goes away. 3 Broadsides with Markerlight support (twin-linked BS5 shots) will almost certainly hit with all their attacks, but that doesn't mean they do. I can still miss with all of them. Despite setting up Markerlights and Broadsides for an ideal shot, I still miss. There's nothing to be done about it either, I just rolled bad. I don't see my actions, despite putting me in a good situation, doing much to make up for that Broadside missing.

If two players are equal skill/experience that doesn't mean they won't make a mistake, or be baited into making a mistake. You capitalize more of mistakes than you do dice rolls. Plus with 5th edition being a mission based game more so than total annihilation (depending on the mission) means you can win by hold objectives, and even if you have bad dice rolls.

Except that if you rolled poorly, it's likely that either your units are dead (you can't control), their units are not dead (they can contest), or more likely, some combination of both. The only action in an objective match that could not be determined by dice is moving onto an objective out of terrain with no enemies around, granting you control. That's skill, but it's either an action your opponent anticipated (if closely skilled) or didn't (if large differences in skill are present). Either way, it's accounted for in the theory. If that's the reason you won the game, you skill overcame the luck. If not, then the luck still has a large factor, since the other objectives are likely being contested or controlled by the opponent, and you need to roll some dice to destroy/remove those units from those objectives.

I think dice rolls do have an impact, but I think if you put yourself in a situation in 40K where dice rolls matter to the extent of costing you the game you probably either took a large risk, or played your tactics wrong. Sometimes you do have to take a risk, because your opponent can put you in a situation where you need to take a risk, so it is not like it doesn't happen. Also Luck is never a constant, you can have both good and bad luck in the same game.

I don't get where this idea of a game coming down to a few rolls means it was a bad game on your part. I just consider it an even match then. If, on turn 7, I've put myself in a position to win and I only need a few rolls to work in order for me to win, I consider that game a well-fought game, regardless of the mistakes I may have made. If I haven't been swept off the table by 7, I obviously did something right, and if I still have a chance to win, I'd say I did a fair bit right.

And yeah, sometimes luck is nice to you (like when the Tau beat my Sisters in CC - nice to my opponent), or bad to you (like when 2 Eldar Jetbikes with fortune and 4+ invulnerable saves die to dangerous terrain, of all things). But in the end the dice affect everything of real consequence in the game. I don't shoot without dice, I don't wound without dice, you don't save without dice. You move into cover, which is an act of skill. Whether or not the cover saves you from my guns is a matter of luck. No matter how skilled you are, you have to roll to succeed at almost anything. And if the dice don't feel like working with you, you'll fail at things you should succeed at (like penetrating armor 12 within Melta range - happened to me about 5 times in 3 turns, and about 12 shots). When you're good enough to overcome bad luck, the skill difference is large. If not, the skill difference is less. This is the basis of the theory.

I don't get where this idea of a game coming down to a few rolls means it was a bad game on your part. I just consider it an even match then. If, on turn 7, I've put myself in a position to win and I only need a few rolls to work in order for me to win, I consider that game a well-fought game, regardless of the mistakes I may have made. If I haven't been swept off the table by 7, I obviously did something right, and if I still have a chance to win, I'd say I did a fair bit right.

Yes, this is a well fought game. But you are referring to a described situation, where you lose due to a few rolls, which is very bad playing. Why does the opponent need only some bad rolls on your part to win?

And yeah, sometimes luck is nice to you (like when the Tau beat my Sisters in CC - nice to my opponent), or bad to you (like when 2 Eldar Jetbikes with fortune and 4+ invulnerable saves die to dangerous terrain, of all things). But in the end the dice affect everything of real consequence in the game. I don't shoot without dice, I don't wound without dice, you don't save without dice. You move into cover, which is an act of skill. Whether or not the cover saves you from my guns is a matter of luck. No matter how skilled you are, you have to roll to succeed at almost anything. And if the dice don't feel like working with you, you'll fail at things you should succeed at (like penetrating armor 12 within Melta range - happened to me about 5 times in 3 turns, and about 12 shots). When you're good enough to overcome bad luck, the skill difference is large. If not, the skill difference is less. This is the basis of the theory.

Yes, this is of course correct.
But still, luck does not get more important the more skilled you are. The theory makes one suggest that (although this is not, what the theory is saying as I understand it), but It gets less important. That is the problem with the theory.