Hey guys! 

What do you think about an additional ranking that factors in luck? 

The luck stats are automatically calculated for each game (as in how much your unit loss count differs from the expectation value). I thought it would be neat to calculate a ranking that factors in these values. After all it is much easier to win a game if you killed 20 units more than you should have. On the other hand, if you are 20 units down and you still win the game you deserve more points, since you obviously played a very good game. 

I haven't thought about the math yet, first I wanted to hear what other people think.

poq

I think there are way too many luck factors beyond dice luck for this to be meaningful. Unfortunate, because it'd be interesting.

The luck of starting first, the luck of a good position on the map, the luck of getting a set with 3 cards at the right moment, ...

I agree, there are many factors of luck involved, even with dice rolls. For example whether you get good rolls early on in the game rather than later when it doesn't matter so much any more. Or if that good/bad set of rolls happens at a crucial moment or not. 

Of course we cannot take all these factors into account. But the pure numbers are there and ready to be analysed. Also, I am not suggesting to replace the present ranking with the luck-adjusted one. I see it more as a scientific analysis. A bit like a team of scientists who analyse football matches (shots taken, passes attempted/received, etc.) to gain knowledge about the season. It does not change the outcome of the season. It does not make the champion any less deserved. It's just interesting.

This is an interesting topic.  I agree there are many form of luck as mentioned before.  As poq says though it would be neat to see something that accounts for luck even if it is not 'official'.  I have noticed that dice luck, at least for WGWF 1 v 1, seems to be the most significant of the varied aspects of luck.  I have graphed my luck versus ranking and there is a strong correlation between the two.  I have also tracking my winning % comparing % with bad luck and % with good luck and there was a substantial difference.  I just found the post and below is a quote showing the large impact of dice luck for me.  Good luck takes my win% from 33% to 85%.  The data is for about 700 games, so I think it is meaningful

Overall Win %     59%

Seat 1 win %     72%

Seat 2 win %     39%

Win % if game luck is positive     85%

Win % if game luck is negative    33%

Win % for seat 1 and pos luck     93%

Win % for seat 2 and neg luck    19%

I think this illustrates the strong impact of luck for Wargear Warfare 1 v 1.  Although all games will be impacted by dice luck, 1 v 1 games are more sensitive to it.  In addition, I think this board is also more sensitive than others to a lucky turn because you can tip the balance of a game in just one turn.  For example, if you win 3 territories on the first round.

Those are interesting numbers SquintGnome. And since you mention two player games in particular, that is a good example for scenarios in which non-dice luck plays an unusually prominent role.

In my experience the above stated non-dice luck factors such as the starting position and turn order are not decisive in 3+ player games. As long as fog is disabled, the gameplay quickly compensates for these initial advantages - given the participating players are reasonably experienced. And the unit placement algorithm should prevent extreme placement advantages. If cards are set to a fixed value even the effect of getting the right cards at the right moment is minimized. 

The bottom line is that there may be a category of scenarios in which all non-dice luck factors are minimized and the dice remain the only significant agent of chance. And in these cases the luck-adjusted ranking would indeed be meaningful.

• 3+ players
• no fog
• fixed card values
• ... ?

This category can be narrowed down even further by leaving out bords which do not meet certain requirements. For example the effect of dice-luck in the opening stages of a game can be limited by the board designer: Take a board where the initial unit count as well as the initial bonus is set to 3 - such as the standard risk board. In this case each player generally has one attack of 5vs3 to capture his first country and card (sometimes you can split up the attacks, but that is not generally possible). Here the outcome of that first attack plays a significant role for the entire game. On a larger board with an initial bonus of let's say 9 these initial attacks are not so significant and are very rarely game deciding. 

I suppose we can think of even more ways to minimize non-dice luck factors.

..then there's the whole issue of the value of the luck ranking itself.   Winning a game after being 20 units down is all but insignificant in a game with thousands of attacks.  ..as opposed to winning with a similar deficit when the game only required a few hundred attacks to win.

There are many threads here addressing the issue; it's been a tough nut to crack because calculating z-scores is brutal on the system; yet rumors that theres a feasible way to create a percentile system have been recently making the rounds.

M57 wrote:

..then there's the whole issue of the value of the luck ranking itself.   Winning a game after being 20 units down is all but insignificant in a game with thousands of attacks.  ..as opposed to winning with a similar deficit when the game only required a few hundred attacks to win.

There are many threads here addressing the issue; it's been a tough nut to crack because calculating z-scores is brutal on the system; yet rumors that theres a feasible way to create a percentile system have been recently making the rounds.

Are there any plans in the works to create a luck stat for Simulgear games?

AttilaTheHun wrote:

Are there any plans in the works to create a luck stat for Simulgear games?

No.... I'd need one of our resident mathematicians to help with this.

tom wrote:

AttilaTheHun wrote:

Are there any plans in the works to create a luck stat for Simulgear games?

No.... I'd need one of our resident mathematicians to help with this.

What problems are you running into? I may be able to lend a hand.

Some of the complexity with luck in Simulgear games is illustrated by the following two examples (assume 70% attack dice):

Example 1: You attack 10 units against 7, and only eliminate 6.  On average you would get 7 units (10 times 70%), so your luck here is -1.

Example 2: You attack 7 units against 2, and only eliminate 1.   You "should" much much more often than not get both, so your "luck" is basically also -1 (to be exact, it's more like -0.98 or something like that).  You can't take 7 times 70% for an average of 4.9 units and compare that to what was eliminated since there are only 2 units to attack.

It is much more likely to have 1) occur than 2), so should 2) get a higher weight since it is a much less probability?  If so, how much?  1) and 2) are almost totally separate situations...

It could be something like taking [1 minus the percent chance times the number of defending units] that you can successfully take over a territory when attacking, and if you are successful then that value is added to luck, and if you fail, that value is subtracted from luck.  This could then be added to the more traditional luck, where you look at expected unit loses versus actual.   This isn't perfect I know, but perhaps it'll serve as a good place to start the process.

I'm not mathematician, or a statistician by any stretch, but isn't this the situation where people start using standard deviations?

Wouldn't you want to be x number of deviations from the statistically probable outcome and use that as your luck score? (i think they call these x scores if I remember anything right)

I think the point you make Cona is a good one where you attack 7 versus 2.  Even though you are expected to kill an average of 4.9 units you can never kill more than 2.  I think the way to handle that is to measure the dice "hits" and not the kills.  So in this case if you got 5 hits (5 of the 7 percentile dice were less than or equal to 70%), your luck would be +.1 even though you only got 2 kills.

Cona Chris wrote:

Example 2: You attack 7 units against 2, and only eliminate 1.   You "should" much much more often than not get both, so your "luck" is basically also -1 (to be exact, it's more like -0.98 or something like that).  You can't take 7 times 70% for an average of 4.9 units and compare that to what was eliminated since there are only 2 units to attack.

Why shouldn't you do that? A 70% kill-chance means that every unit has a 70% chance to kill. So if you end up killing only 1 out of 2, that means that 3.9 out of your 4.9 expected kills did not occur. And this fits quite well with our intuition: We will feel very unlucky if 7 units do not win against 2. 

But what happens when both units are killed? I assume the game engine calculates each unit's attack separately. If we consider the attacking unit's perspective, the deviation from the expectation value can be calculated after every attack. Let's keep to the 70%. If a unit makes an attack and kills, you get +0.3 on your luck scale, if it misses, you'll get a -0.7. If we do the math for the example above, we get the following: Let's say the first attacker kills and the 6 following all miss. Then we have 0.3 + 6 x (-0.7) = -3.9, which is the same result as above.

What is counter-intuitive about the second example (7 winning against 2), is that if your first two units make the kill, you actually end up with a luck value of +0.6 although you are well within your expected 4.9 kills. If the game dynamics would work accordingly that would be fine, but I am not sure that is the case. If the rules were such that each unit only had one move, then units that did not succeed in the kill would have to stay behind (one move rule). In this case it would make a big difference if (a) the first two units succeeded or (b) the last two, because the situation on the board would look a lot different in both cases: (a) would mean that all seven attacking units advance to the attacked tile, while (b) means that only two units advance while 5 stay behind. So +0.6 for (a) vs the the -2.9 for (b) would fit our intuition because (a) is a significantly better position than (b). 

I don't think SimulGear is programmed that way though, but I am not entirely sure, I haven't paid close enough attention. If all units advance as long as the battle is won, then the whole range of +0.6 to -2.9 would represent the same situation on the board: Not a very good map. In this case we would require an additional calculation to compensate for the distortion caused by allowing the second move. 

Another issue is the matter of the defender's kill action. Here again it is important to know how this is implemented in the game engine. Does the defender get his shot for each attacker's shot, regardless of the outcome of the attack? Or is the defender's action only executed if the attacker failed?

For SG I believe for each Attacking Unit a 100 sided (or maybe 101 if 0 is a theoretical possibility) dice is rolled and that number is compared against 'X' (in the above examples that is 70) then a kill of a Defending Unit occurs.  Same thing occurs for the Defending Units (killing the Attacking Units) and that occurs at the "same time" as the Attacking Units.  So I believe all Units actually have a dice rolled, although that information is then summarized in the History log.  See http://www.wargear.net/help/display/FAQ#SGDice

I think there have been some discussions on Luck for SG...I thought it was not too difficult in the math department...but I could be wrong.

The "hits" luck stat would be very straightforward. The mean is given by the percentages of the dice.

However, I think Cona is correct to focus on the outcomes. After all, we count a defender rolling double 6's exactly the same as any other loss of 2 units in turn-based luck stats.

A single battle, like Cona's 7v2 example, can be viewed as a "Bernoulli trial". The mean of a Bernoulli trial is simple enough to calculate. So, we could have an outcomes-based luck stat. The variance/SD is also easy to calculate, so we could also calculate a luck percentile.

My global ranking dropped from just under 100 to now over 300 in weeks because I acquired a taste for two-player realtime games.  

I have done some statistical analysis, but anyone who has played a number of these games doesn't need that to know that luck plays such a large role  in two-player games (particularly on maps like WGWF) that the impact of strategy probably only affects 25% (at best) of these games.    If you think you're a great player and want to be humbled, embark on a run of these types of games.    In my case, the first 40 or so games also coincided with an improbable streak of bad luck.  That luck is finally starting to recover, but if I could remove those games from my ranking, it'd make a huge difference.

So, I am very sympathetic to a feature that would account for luck in the rankings.   At the same time, I recognize the challenges in trying to determine what luck is.  And also, there's a part of me that says if I care this much about rankings, I'm caring too much.

Perhaps a simple and practical solution would be to offer an alternative ranking which does not include 2 player games.   It's really only those games where luck plays such a significant role.  

Even if it didn't become an official feature, it would be interesting to see the impact of ranking without 2 player games.    Also, to test my theory that the impact of strategy in 2 player WGWF  games is 25% at best, it'd be interesting to take the look at the win/loss ratios of the highest globally ranked players and compare it with their win/loss ratios in 2 player WGWF games (presuming they played a statistically significant nmber of games). 

SquintGnome wrote:

This is an interesting topic.  I agree there are many form of luck as mentioned before.  As poq says though it would be neat to see something that accounts for luck even if it is not 'official'.  I have noticed that dice luck, at least for WGWF 1 v 1, seems to be the most significant of the varied aspects of luck.  I have graphed my luck versus ranking and there is a strong correlation between the two.  I have also tracking my winning % comparing % with bad luck and % with good luck and there was a substantial difference.  I just found the post and below is a quote showing the large impact of dice luck for me.  Good luck takes my win% from 33% to 85%.  The data is for about 700 games, so I think it is meaningful

 

Overall Win %     59%

Seat 1 win %     72%

Seat 2 win %     39%

Win % if game luck is positive     85%

Win % if game luck is negative    33%

Win % for seat 1 and pos luck     93%

Win % for seat 2 and neg luck    19%

I think this illustrates the strong impact of luck for Wargear Warfare 1 v 1.  Although all games will be impacted by dice luck, 1 v 1 games are more sensitive to it.  In addition, I think this board is also more sensitive than others to a lucky turn because you can tip the balance of a game in just one turn.  For example, if you win 3 territories on the first round.

poq wrote:

A 70% kill-chance means that every unit has a 70% chance to kill. So if you end up killing only 1 out of 2, that means that 3.9 out of your 4.9 expected kills did not occur. And this fits quite well with our intuition: We will feel very unlucky if 7 units do not win against 2. 

So the luck stat would make no distinction between the following?

7 attacking 5 and only killing 1

7 attacking 2 and only killing 1