G40 League House Rule project

gamerman01

Slight adjustment -
I like this one better

Karl7

Question:

I often ask myself how many wins/losses could you attribute statistically to pure luck. I assume the more games you play the more likely you will reach the statistical averages of rolls over time. But as you do that you will obviously encounter the outlier luck instances. So it seems per X games you play you could safely predict N/X games would be the outlier games where you either get killed or win by luck. Of course strategy would mitigate against luck (but how much?). I assume (I once had a basic understanding of statistics) that the given the relative combat values per number of units generally on the board, the most common roll is about 2.5 chance out of 6? So if the average number of average rolls per game is Z, spread over X games, you would could predict the likely number of outliers that would skew the game?

I was wondering if anyone has run any of the numbers on this.

Am I making any sense here?

boldfresh

@Karl7:

Question:

I often ask myself how many wins/losses could you attribute statistically to pure luck. I assume the more games you play the more likely you will reach the statistical averages of rolls over time. But as you do that you will obviously encounter the outlier luck instances. So it seems per X games you play you could safely predict N/X games would be the outlier games where you either get killed or win by luck. Of course strategy would mitigate against luck (but how much?). I assume (I once had a basic understanding of statistics) that the given the relative combat values per number of units generally on the board, the most common roll is about 2.5 chance out of 6? So if the average number of average rolls per game is Z, spread over X games, you would could predict the likely number of outliers that would skew the game?

I was wondering if anyone has run any of the numbers on this.

Am I making any sense here?

no karl, you are not making any sense at all. :-P

Karl7

ah, man! :-(

gamerman01

2.5 chance out of 6? What?

You can’t mathematically determine exactly how many games you win or lose because of luck, no matter how much you know about statistics. This is because it’s impossible to quantify the exact degree of luck vs. skill in any particular game.

Luck in certain battles is much more important than in others. It is possible to have overall better average luck than your opponent in a game, but yet still be the “unluckier one”. Maybe your opponent got a lucky roll when it really mattered.

Sometimes a lucky hit takes out an enemy battleship. Sometimes, just an extra infantry or two that will get slaughtered on a counter-attack anyway.

The comparative skill levels of the players has a lot to do with how many games are actually won and lost by luck. If you are very close to the same skill level, then luck is much bigger factor in who will win. If you are a lot better than your opponents, you’ll usually beat them whether you’re lucky or not.

JWW keeps saying he’s so surprised that some players can consistently win 80-90% of their games, even though there are so many dice throws.
But some players are just a lot better than most other players, so if a player is in the top 5-10% of players in skill level, we are seeing that those players also only lose about 5-10% of their games. Once in awhile maybe it’s because they screwed up or just actually got out-played. Some of those games, of course, they lost because their luck was so much worse than the other player’s. But we have players who only lose 10-20% of their games, consistently, year after year. This tells me that skill is a much bigger factor than luck in A&A.

Now that said, if two players are of the same exact skill level, dice will decide many if not most of those outcomes.

Two players of the same skill level will each win about half of the games when playing a game with no luck - chess. Why is this?

There are games with a lot of luck and not very much skill involved (Uno, for example?) that a more skilled player can still consistently win at.

I’ve played over a hundred games of chess in the past 2 years with lots of different kids ages 10-16. I never lost a game. Once I blundered and gave up my queen to one of the more skilled 16 year olds, but I recovered, took advantage of his over-confidence and came back to win. You can still lose a game of chess to someone much less skilled than you, but it will very rarely happen if you’re not careless.

I’ve also played dozens of rounds of Uno with young kids - ages 12 and 14. Of course, they win quite a few hands. But I win significantly more than my share, because my experience and skill wins me several hands.

A&A is somewhere in between Uno and Chess on the luck/skill ratio.
I believe it is impossible to quantify how many games you win or lose purely because of luck, for many reasons. One of the big ones is that the players probably have different levels of skill.

I have consistently won over 80% of the A&A games that I have played, for the past several years. :-)
I would estimate that more than half of the games I lost, I got out-played. So I think less than 10% of the games I’ve played, I lost because I had too much bad luck, or bad luck when it counted most. I’ve had many games where I had bad luck at critical times, but was able to recover because I was more skilled/experienced than my opponent, or my opponent got careless. Just like when I screwed up and lost my queen to the 16 year old.

Does that help with the question you often ask yourself, about how many wins/losses you attribute to pure luck?
I think that depends a lot on how skilled a player you are, and the skill of your competition.

gamerman01

While we’re talking about luck, I would also point out that experience tells me that the earlier you are in the game, the more weight the luck has. Of course, because the effects are cumulative throughout the game.

Sometimes players will “grab their side” and moan and groan when they get diced late in a game, maybe because they’re trying to get back in it. But luck in seemingly much smaller battles and with much smaller IPC losses in the first couple rounds can have as much or more influence on the outcome of a game.

I guess I’m just saying that it’s usually hard to say who was luckier in a typical game. As you said, as you throw more and more dice (and there are a lot of dice rolls in an average A&A game), the luck will tend to even out and approach expected averages. Also, situational luck is impossible to exactly quantify.

For example, was it luckier that you failed in your attack on Z106 on G1 (losing a sub and failing to sink a destroyer/transport), or that I failed on my attack on your Japanese destroyer and transport with my American sub on USA3? (These are made up but realistic examples)

Answer: impossible to determine.

Now we all (probably) tend to compare IPC values and ignore which powers were involved, what round it was, etc etc. If you got lucky and shot down my bomber with AA, and I got lucky and took out an extra infantry with my defense somewhere, we tend to compare the bomber that costs 12 and the infantry that costs 3 and think that losing the bomber was a much bigger loss. But it’s not that simple.

Shoot, we’ve all seen where sometimes our bad luck turns out to be good because it causes the other player to do something different than they would have, and it back fires! Or, it just plain distracts them! Or makes them over-confident.

In summary, we can obsess over the role of chance in A&A, but ultimately that sucks the fun out of it for everybody. The good players WILL win most of the time and the bad ones WILL usually lose. Some games of course will be won by the player who didn’t play as well, because he got better luck. Lots of games, if the players are the same skill level (because then luck is the factor that is different).

Jeff28

I was going to guess 10 percent of the time you get diced. But I see Gamerman came to the same conclusion in a few more words.

Tyzoq

@Karl7:

Question:

I often ask myself how many wins/losses could you attribute statistically to pure luck. I assume the more games you play the more likely you will reach the statistical averages of rolls over time. But as you do that you will obviously encounter the outlier luck instances. So it seems per X games you play you could safely predict N/X games would be the outlier games where you either get killed or win by luck. Of course strategy would mitigate against luck (but how much?). I assume (I once had a basic understanding of statistics) that the given the relative combat values per number of units generally on the board, the most common roll is about 2.5 chance out of 6? So if the average number of average rolls per game is Z, spread over X games, you would could predict the likely number of outliers that would skew the game?

I was wondering if anyone has run any of the numbers on this.

Am I making any sense here?

you lost me at N/X, I don’t think N has been defined. I say Jeff and Gamer are about right with 10% but they are both good players and good players are usually better at controlling outliers. Outliers are based on variance (statistically speaking) and I will often choose to make fewer stronger attacks in order to decrease the variance of the outcome (the amount dice will hurt me). Similarly If I feel I am winning a game I may decide not to attack a fleet that I have a 60-70% chance to win against because naval battles have a high variance based on value of units lost. If the battle goes bad and my opponent ends up winning this may hurt more than if I just wait, however; if I’m in a close game with an equally good opponent then I would take the 60-70% chance with good odds to come out ahead in unit value.

gamerman01

@Tyzoq:

Similarly If I feel I am winning a game I may decide not to attack a fleet that I have a 60-70% chance to win against because naval battles have a high variance based on value of units lost. If the battle goes bad and my opponent ends up winning this may hurt more than if I just wait, however; if I’m in a close game with an equally good opponent then I would take the 60-70% chance with good odds to come out ahead in unit value.

This is one of the characteristics of a highly successful A&A player.

I’m thrilled that 2 very successful players have weighed in on the issue.

Could you tell I was enjoying answering that question, Jeff? :-D

I want to reiterate that the roughly 10% of games that the dice steal exists when there a fairly significant disparity in player ability/effectiveness.
I think if you have 2 equally skilled players (so there is little to no skill/experience variance), then the difference in dice luck in a particular game may OFTEN tip the scales (be a deciding factor). So it could be much higher than 10% of games, depending on how good you and your opponents are.

gamerman01

Oh, and that’s exactly what Tyzoq is saying. If you are close to equal skill level (or you perceive that you have a 50/50 chance of winning the game), then you would rationally enter into battles where you have the upper hand, even if it’s small. Then the dice will enter in and will often bless you or screw you.

In other words, the dice will decide a significant percentage of tight games. If most of the games you play are “dog fights” and could go either way, the dice will often decide them. If you are significantly better or significantly worse than your opponent, even with extreme luck to the worse player the outcome will remain unchanged 8-)

gamerman01

Whatever, we have another RESULT!

AA League standings.xls

Karl7

2.5 chance out of 6? What?

sorry if I was being obtuse, I just had a brain fart last night on this. I was just thinking what is average combat value you roll in a game. I would think it would be around 2, given that the most common unit rolled is a infantry on defense. But I figured it might be higher given the prevalence of armor and ftrs.

10% eh? Sounds like that’s probably right. But is it 10% both for wins and loses due to luck or 5% both ways for a 10% total?

gamerman01

@Karl7:

10% eh? Sounds like that’s probably right. But is it 10% both for wins and loses due to luck or 5% both ways for a 10% total?

It varies so much by player, and how stiff your competition is .
With players of equal skill, I think it will be much higher than 10%.
Re-read what I wrote and ponder it a little more… This question you just asked tells me you didn’t understand half of what I tried to say… :-)

gamerman01

@Gamerman01:

I want to reiterate that the roughly 10% of games that the dice steal exists when there a fairly significant disparity in player ability/effectiveness.
I think if you have 2 equally skilled players (so there is little to no skill/experience variance), then the difference in dice luck in a particular game may OFTEN tip the scales (be a deciding factor). So it could be much higher than 10% of games, depending on how good you and your opponents are.

gamerman01

Tyzoq - what was the situation in the game with Fortress? I see you were only in the middle of round 2 - were you winning or losing? Or was it pretty much undecided at that point? I’d like to avoid counting incomplete games in my rankings if nothing was really proved yet…

Thanks

Updated

AA League standings.xls

Tyzoq

I can’t look at it until I get home, but I felt I had a better position having won in sea zones 110, 111, and 106 only losing 2 subs on G1 then on G2 Germany sank the rest of the Royal Navy in the Mediterranean losing only 2 fighters (this was set up by Italy taking territory for Germans to land) … China lost their fighter but did get to build artillery on turn 1… but like you said it was only round 2 anything could happen from there on, Japan was barely even involved in the war yet.

gamerman01

Thanks again

Hmm, I want to award a win and loss when deserved, but yeah, not sure that one went far enough for my purposes. Let me know if you remember more after looking at it, and I’ll consider whatever else you tell me. Sounds like you had a good start going, but maybe too early (for my purposes) to declare a winner or loser.

I hope we haven’t lost Fortress…

Major Major

How many games are lost due to extreme dice?

That is easy, it is exactly 16.66666666666666666666666666666666666666666666666666666666666666666666666666666666666667%
of the time.

I would have written 16 2/3% but I like to envision a vinculum?

Karl7

This question you just asked tells me you didn’t understand half of what I tried to say…

Sorry Gamerman, I was in a rush when I looked through your posts. Good responses though to my semi coherent message. :lol:

gamerman01

I’m glad you liked the responses - it was fun to think about

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