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As part of my PhD, I'm taking a statistics class, and for this class I need to complete a project that needs to be done quickly from experimental design through data collection and analysis. This needs to be a new study, and cannot have anything to do with my research. So for my project I decided to do something related to 40K.
I've a friend of mine who I play regularly against, usually 40K. And we've always joked that somehow he seems to have trademark good luck (particularly with his Eldar) while I typically show appalling luck. So I decided to test it.
For those interested in the stats, the design is a fully crossed 3-Factor ANOVA. One factor is the player (me and my opponent), another is the dice roll needed (3+, 4+ or 5+ ... other rolls [2+ and 6+] crop up too infrequently to be useful and contested rolls, difficult terrain rolls and leadership tests also don't fit the analysis). The third factor is importance of the dice rolls (high or low, agreed upon by both players at the time of the roll).
As for armies (from memory) - 500 points
My opponent:
Eldar
Autarch (Warp-jump pack, fusion pistol and lots of power weapon attacks)
10 Striking Scorpions (Exarch, power claw, infiltrate & move through cover)
10 Dire Avengers (Exarch, shimmer shield, defend & bladestorm)
10 Dire Avengers (Exarch, shimmer shield, defend & bladestorm)
Me:
Chaos Space Marines
Sorcerer (doombolt, Mark of Slaanesh)
6 Noise Marines (sonic blasters, blastmaster)
6 Noise Marines (sonic blasters)
6 Lesser Daemons
We played 8 games total (multiple games required as replicates - hence the small points size) on a 4x4 board with about 25-30% terrain. Every 3+, 4+ and 5+ roll recorded. Note that the actual outcome of the game is not a factor in the analysis (just how good the dice rolls are), but has been included for your interest.
Game 1: Cleanse
Eldar win, absolute miserable slaughter. None of his units under 1/2 strength.
Game 2: Take & Hold
Edar win, much closer game. Scorpions & autarch dead, handful of avengers survive due to lousy saving throws on my part and the fact that distract makes them such a damn tarpit in combat.
Game 3: Loot
Eldar slaughter (again). Bladestorm is a bitch. Lost an entire squad of marines to one salvo.
Game 4: Annihilation
Eldar eliminate all Chaos forces (seeing a pattern?). Put up a bit of a struggle this game, killing the autarch and reducing all of his squads below half strength.
Game 5: Recon.
Eldar slaughter all Chaos forces.
Game 6: Annihilation
Yep, eldar kill all chaos forces again. Highlight of the game was my sorcerer charging a squad of Dire Avengers (clipping them, only 3 in the kill zone) and being killed outright (see what I mean about my trademark luck?). By this stage I was getting a bit knarly about this, and checked his list as he just seemed to be having his cake and eating it. Yep, about 100 points over. He drops the warp pack and I added in another squad of daemons to compensate.
Game 7: cleanse
Chaos win! Only one squad of daemons and one squad of noise marines left. But all Eldar dead!
Game 8: by this stage we really didn't care too much. I think it was loot again.
Eldar win, but only a handful of Eldar left.
So, 7-1 to the Eldar, but fortunes for the Eldar changed in the last two games when actually forced to engage in a fair fight! Damn those sneaky Eldar...
Now... what's the results of the analysis? My opponent did, indeed, score significantly higher on his dice rolls than me (p=0.001)! Not only that, but he scored significantly better than me when the rolls were important (regardless of what he needed to score).
So there you go. Perfectly justified in claiming that my lousy win record is due to my opponent being luckier than me! (Or maybe I need to have a look at his dice? )
Here are my theories to explain this - this is a freakish result, way beyond anything I would have expected (any other theories welcome - I can use it for my write-up!)
Pure random chance
It's possible there is no pattern and these things have simply cropped up by chance. Well, the analysis has calculated this probability - there is a one in a thousand chance of that. That's a very low chance (well within what's scientifically acceptable as non-random) and completely not what I was expecting! Not only that, but the reason for the study in the first place was anecdotal suggestion that he rolls better than me.
Loaded dice
Not necessarily loaded, but quite possibly uneven in some way. While differences in dice might explain the differences between us, it doesn't explain why he rolls better for important dice rolls.
One possible explanation would be that he has certain "lucky" dice. For regular rolls, he just grabs any old dice. For important rolls he (conciously or unconciously) may prefer to use certain dice. This may not even have anything to do with favourite dice - for example, if his 3 blue dice roll better, if he uses them to distinguish his power weapon attacks, he's consistently going to be using them for important rolls.
Still, there are some dice rolls like scatter dice where we do use the same single dice and he does seem to do better for them. And it doesn't explain Ld tests which require low rolls! Out of those 8 games, he made somewhere between 3-6 leadership tests (morale or pinning) per game. Not one single failure. Unfortunately I didn't record how many exactly, or I could run the numbers on that too...
Rolling technique
I seriously doubt he has a magic technique he's not telling me about, but most wargamers have stupid supersitions about the dice. For example, I tend not to roll dice that have rolled well again - I pick up new dice. Probably stupid, but it is possible something like this could be affecting the dice roll - particularly if there is some non-random likelihood of getting a given roll dependent on the type of dice being rolled.
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