Rolling Thunder Forums

So, we finally tidied up the stats analysis me and Daigaro were working on.

Note – yes, there may be errors, and yes, this is pretty primitive analysis based on “dice” rolled and the 26000+ (?) games recorded by BBM to generate expected results etc. Also, apologies for not being able to work out how to decently format the lists/tables (note: if you have any specific questions i.e. specific stats you can ask them, or you can PM Daigaro your email and he can send you the spreadsheet).


Enough intro, onto the stuff:

Expected League Positions – NJ statistically coach of the season
(NB: I mostly did the top half until the method, which Daigaro did)

Based on expected points per game for the league’s teams, adjusted for overall chance and TV, we calculated the following statistically expected league table.

Amazon.....16
Elf............14
Khem........13
Orc...........13
Chaos.......12
Uwd..........12
Halfing........9
Goblin........8
Ogre..........7

(note: the points total is less useful as a guide than the actual positions in the table, which is why we’ve not included points in the below: )

The real final table for comparison:

Chaos
Elf
Khemri
Amazon
Orcs
Uwd
Halfling
Ogre
Goblin

This clearly shows NJ is the coach of the season, massively overperforming. Apologies Ident.

You’ll note that beside the Chaos and Amazon, the actual positions and the predicted positions are very close. Everyone except Chaos and Amazon basically performed according to the statistical expectations of their team.

The Effects of Chance

We worked out the total chance, that is to say, the cumulative chance of 1d6, 2d6, and block dice, weighted for importance (i.e. if you rolled more block dice, your overall chance of block dice has more input on your overall chance) to develop a League Table of Chance. A 1 represents completely fair/average dice.

Team......... CHANCE
Elf......... 1.011074
Halfling......... 1.005566
Golbin......... 0.997611
Chaos......... 0.997139
Khem......... 0.992549
Amazon......... 0.989796
Uwd......... 0.988257
Ogre......... 0.984606
Orc ......... 0.975837

The Orcs had by far the worst luck, actually managing to get 2.4% worse dice than they should have. If you wanted, you could run this through a statistical test to see if the difference between the Orcs’ luck and a value of 1 is statistically significant. I started, but don’t have time.

Here we can see the Expected League Table along with a column showing the points lost or gained due to chance

Team......... Expected Points... Diff due to chance
Amazon......... 15.54......... -0.16
Elf......... 13.93......... 0.15
Khem......... 13.25......... -0.10
Orc......... 12.93......... -0.32
Chaos......... 12.03......... -0.03
Uwd......... 11.63......... -0.14
Halfing......... 8.63......... 0.05
Goblin......... 7.84......... -0.02
Ogre......... 7.43......... -0.12

This suggests that if the Orcs’ negative chance had been reversed to an equally strong positive trend, they could in theory have finished a place higher. You can’t really say they would have gained two thirds of a point though, but you can see it can make a difference over a season.


WOT WE DID

DICE – Whacked all the dice rolled by each team in every match into one big spreadsheet to analyse Nuffle’s Blessing over the course of the season. Used BBmanager and stuck to the breakdowns we all know and love; 1d6, 2D6 & Block Dice. Compared what you would expect to roll from the grand total of rolls Vs what was actually rolled (like BBM).

Disclaimer – We know there are lots of things this doesn’t take into account; ‘critical moments’, how skills affected rolls, what number rolled is deemed successful/failure for the task it was done for, etc. What it is to show is purely what dice were rolled against what you’d expect to get; and using a broad outline of:

D6
1-3 = unlucky/bad/negative/Angry-nuffle; 4-6 = Lucky/good/positive/happy Nuffle
2D6
<7 = unlucky/bad/negative/Angry-nuffle; >7 = Lucky/good/positive/happy Nuffle
Block Dice
Skull, both down = bad; Pushes = meh = POW/Push, POW = Good (based on the BAD having the possibility to case turnovers, again, see disclaimer for skill references, etc).

Hope that makes sense. If not, tough. We may be able to offer some further explanation, but much of this was set up a couple of months ago, and then filled in when the season ended.

Each team has their own graphs to show how they did compared to what expected. Then, at the end there are 3 Super Dooper sheets that have:

1) A cumulative graph with everyone’s dice on so it’s easy to compare, and also see how many dice you threw compared to others
2) A messy looking graph that is used to work out….
3) A cumulative graph of trendlines; the gradients of which demonstrate a team’s inclination towards good or bad dice; and the steepness shows comparatively HOW lucky/unlucky you were to the other teams.
• E.g. 1D6 – the majority of teams have pretty gentle nega-trendlines, but one team (the Carrions) threw a disproportionate amount of high numbers as opposed to low numbers.

Again hope that makes sense, and if not, tough.

RESULTS - THE DICE

General nega-trend across all dice and all teams – skewed towards low numbers and bad block dice – suggesting lots of ‘What could have been…’

Also see what you’d expect in terms of number of dice rolled relevant to race; I.e. the Stunty teams all rolled a lot of D6s and fewer block dice, whereas the bashy teams threw a lot of block dice and few 1D6. Main thing that means is that we’re all savvy enough coaches to understand our teams and how to play them. Well done to us

I don’t think the dice made a difference to the final league standings overall, HOWEVER, the teams that did best (Cangurus and Outcasts) did perhaps have the better dice overall which has gotta help a bit (la’s editor’s note: Chaos didn’t have that good overall dice). NJ’s position at the top was also reinforced by the sheer amount of block dice he threw; over 100 more than the next best blocker (the Ducklingz); possibly coupled with his higher than expected number of POW/Pushes and POWs rolled.

I could do a break-down of each time; but I’ve spent too long on this as it is, and it’s much more fun to figure it out yourself.

I will say that the Ducklingz had by far the worst of the blocking dice; and as this was the ladz’ main ‘strength’ – think this impacted on my season.

Some stats highlights.

Khemri had the best d6 – a massive 1.075
Underworld had the worst at 0.97

Elves had the best 2d6 with 1.04
Goblin had the worst with 0.98

Goblin had the best block dice, with 1.02
Orcs had the worse, with 0.96


Ogres rolled the most d6, 843, compared to the Khemri’s 182.

Chaos rolled the most 2d6, 401. Halfling rolled the least, 201.

Chaos also rolled the most block dice, 797! Amazon only rolled 417.

Nice presentation of David Bowie & Percy's hard work there La.

We did spend maybe a little too much time doing this, but I found it highly rewarding.

We basically figure theres 3 key factors to winning Blood Bowl matches - 1) Dice 2) relationship of you team race & value to that of your opponent 3) Coaching ability.

We can kinda analyse the first two, and then the third purely by process of elimination.

So yeah, NJ's coaching ability shone through last season with him totally over-performing.

And it seems to be continuing this season so far....

Percy recommends Oranje mushrooms with purple spots when tackling statistics; PirlOrc recommends NO mushrooms when tackling Elves. Let's hope he listens...

Hmmm.


Final proof there are "Lies Damned Lies, and statistics"

Glad I didn't have to physically roll all those dice. I would have RSI.....

lawastooshort wrote:Ogres rolled the most d6, 843

Whilst I'm not surprised I have rolled the most, I didn't realise I averaged 105.5 D6 rolls a game. That's insane. I don't suppose you have measured it by roll type, eg dodge, GFI, etc.
Thinking about it, given every ogre needed to roll bonehead before doing anything, 105.5 seems not so silly after all, especially when I got up to having 6 ogres.
Did I also roll the most dice overall?

Khemri had the best d6 – a massive 1.075

E.g. 1D6 – the majority of teams have pretty gentle nega-trendlines, but one team (the Carrions) threw a disproportionate amount of high numbers as opposed to low numbers.

Yeah seems pretty accurate...

The number of 1's and 6's rolled would be interesting too, as rolling them can skew a match as they are always a pass/fail. Also, do you have access to the "Chance" rating from BB manager?

Nice to see me second bottom of the luck chart, but man, those poor Orcs! And I assume that's without the mass of injuries they had at the hands of the Ogres (as I was rolling the dice).

Looking at the table of chance, also seems to show that most of us were unlucky overall.

"Expected league table due to chance" is probably the most spurious chart though. I think there are just too many variables to come up with a formula for how chance affects your final points total. The chart at the moment weights the dice too lightly I feel - ie it cannot result in a team moving up or down except if they were already equal with the other team beforehand.

Gandalf wrote:Did I also roll the most dice overall?

The number of 1's and 6's rolled would be interesting too, as rolling them can skew a match as they are always a pass/fail. Also, do you have access to the "Chance" rating from BB manager

I can have a look tomorrow. Don't have the "Chance" rating, though, no.

Gandalf wrote:"Expected league table due to chance" is probably the most spurious chart though. I think there are just too many variables to come up with a formula for how chance affects your final points total. The chart at the moment weights the dice too lightly I feel - ie it cannot result in a team moving up or down except if they were already equal with the other team beforehand.

Yeah, I haven't worked out a better way yet of taking the expected results and or chance and applying it to something that comes out with a more realistic result pointswise, But you can see that the expected results table (which takes into account chance) looks pretty similar to what happen positionswise. I might come up with a better way, but I don't really have the time to put my mind to it at the moment.

A possible refinement (and I'm not an expert in this so it may not be) would be to tune the D6 break value to each team. Say take the team's average needed roll to pick up in 1 TZ and select good vs bad by pass/fail.

In other words AG 4 teams would be 3> bad 3+ good.

Ag 3 would be 4 and AG 2 would be 5.

This represents the fact that I can roll all the 3s I like, it'll do me no good whereas for an elf that's more than enough.

You might also see if there's a correlation between average stats and dice rolls. Do the ST teams roll more block dice like we'd assume? The Ogres will be the outlier in this case due to the bonehead rolls but the rest should make sense.

lawastooshort wrote:Yeah, I haven't worked out a better way yet of taking the expected results and or chance and applying it to something that comes out with a more realistic result pointswise, But you can see that the expected results table (which takes into account chance) looks pretty similar to what happen positionswise. I might come up with a better way, but I don't really have the time to put my mind to it at the moment.

Definitely too much effort to make it better methinks!

@Rav. firstly Ogres are essentially a ST team!

Secondly, "Ag 3 would be 4 and AG 2 would be 5." I think the majority of my rolls would be 2+ as I do so many dodges into space. If you were to do this analysis I maintain you'd have to group it by roll type at least, so as to take out kick off rolls, GFI's, boneheads and the like. Another nice thing would be failed team re-rolls (call it "frustration factor" :p).

It's tricky, you can spend forever and a day analysing it, but your results will still be so-so. You can guess as to how crucial a pick-up was, for example, but there are still so many variables around that that aren't easily measured.... where on the pitch was it? Where was the closest opposition player? (eg I rarely re-roll failed pickups if no-one is in attendance) Or the time my entire ogre front line failed me giving Rav the freedom of the pitch, that was worth 1TD, you can't measure that.

Given the perfect end goal is impossible, I'm impressed you've even gone to as much effort as you have already. Well done sirs.

Gandalf wrote:It's tricky, you can spend forever and a day analysing it, but your results will still be so-so. You can guess as to how crucial a pick-up was, for example, but there are still so many variables around that that aren't easily measured.... where on the pitch was it? Where was the closest opposition player? (eg I rarely re-roll failed pickups if no-one is in attendance) Or the time my entire ogre front line failed me giving Rav the freedom of the pitch, that was worth 1TD, you can't measure that.

Yes, it's impossible to measure the importance of a roll with these stats... Also, they could conceivably be broken into roll types - dodges, passes, etc - but it would be an unreasonable amount of time, I think.

Gandalf wrote:Given the perfect end goal is impossible

Yes - impossible enough to almost make this pointless But it is interesting seeing how on average teams do against each other, and also the amount of dice rolled and certain levels of chance.

Yeah, we knew we couldn't come up with a formula to win a blood bowl match, it's all hindsight anyway, plus the sheer unpredictability of the game is one of it's draws

I think we just wanted to look at a) If all the 'I had bad dice' claims actually make any difference overall - like, you'd expect them to EVENTUALLY even out anyway (And I had also wondered if the game weighted anything to make things 'interesting' at crucial moments, but Rav cleared this up) and b) Looking at the teams/races your own team/race would be playing against to look at the paper/scissors/rock factor.

I think we just got carried away with THEN seeing if we could use these variables to look at coaching ability - if you had the shittest dice, and were more likely to lose against all the teams in your league (and you had evidence) BUT you managed to win it, then you'd have some pretty fine 'Science Icing' to put on your cake

My main motivation was to see if I was just playing badly/sulking/looking for excuses always blaming the dice.

Do the ST teams roll more block dice like we'd assume?

Yes Rav, the graphs show that nicely; the 'bash' teams all rolled considerably more block dice, but fewest 1D6 and the stunty/AG teams vice versa.

I've just realised I can attach files to posts, so I'll do that when I'm at work tomorrow. Then you'll be able to see you own team's breakdowns (I'll first have to get David Bowie's permission, I'm sure he'll be fine with it).

Well done sirs.

Cheers Gandalf

It's a really nice set of stats (although I must admit you lost me a bit in the middle there ).

Thanks for all the hard work that you did whilst being paid to do something else gents

And here's the lovely spreadsheet for anyone who wants to see it....

Oh, no it's not... xlsx isn't allowed apparently. I cant save as as a .odf because non of the graphs work then, and they're the pretty bits.

Email at dphingley@gmail.com if you want a copy and I'll mail you one

DaigaroOgami wrote:And here's the lovely spreadsheet for anyone who wants to see it....

Oh, no it's not... xlsx isn't allowed apparently. I cant save as as a .odf because non of the graphs work then, and they're the pretty bits.

Email at dphingley@gmail.com if you want a copy and I'll mail you one

ODS wouldn't have worked either :p

Can you try uploading the xlsx again now? I've fiddled with some settings.

Think it may have worked?

It did. Huzzah.

Team Shrek rolled the most dice, with a wrist-aching 1,946. Next are Chaos with 1,849. Surprisingly, Amazon are last with 1,294.

Ogres has the worst D6 rolls, with a rating of 97.4%. To rub it in some more, Ogre's most rolled number was 1 and least rolled number was 6! (I tried putting the chance of that many 1's into my calculator, but it rolled over and died. 843! is a hard sum)

My two worst games for D6 were against the Goblins (which I remember the dice screwing me over on) and the Elves (which I remember as being a very close match with my defeat only sealed on the last turn). Also, the elf game I had 7 sixes in 96 D6 rolls, 1 and 3 were my most rolled numbers, and it was my worst block dice of the competition. So those two games are good examples of how the dice don't tell you everything.

Quick look at Chaos block dice, given so much of their team has block it was quite favourable. POW, POW/push and both down accounted for 51.4% of block dice - not way above 50% but enough to make a difference I would say.

"Luck opponent had" would be another factor that could be built into the model perhaps, to give a simple "did luck affect the outcome" rating.