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2019-07-11 04:49:30
rating 5.7


2013-08-24 12:51:34
rating 4.4
2013-06-04 02:48:26
rating 5.6
2013-04-22 03:32:37
rating 5.5
2013-02-27 09:30:14
rating 3.9
2013-02-24 20:15:12
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2012-11-20 08:22:39
rating 4.9
2012-11-09 12:38:32
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2012-09-21 04:54:32
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2012-09-06 04:57:04
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2012-05-11 01:19:46
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2011-06-25 16:07:38
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2011-05-28 17:15:33
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2013-02-27 09:30:14
24 votes, rating 3.9
Examining Luck
So, in my most recent match, I felt like I had bad luck, and my opponent agreed.

I wanted to see whether this was actually the case, and so I looked at 1's, to see who got more, if we got an unexpected amount, if they came on important rolls, how many turnovers were caused by 1's, and whether we got consecutive runs of 1's.

My opponent rolled 345 dice (not including any d8 rolls).
I rolled 283 dice.

My opponent rolled 56 1's. (The expected amount was 57.5 He got almost a completely average number of 1's.)
I rolled 63 1's. (The expected amount was 47.2. I got 33% MORE 1's than expected for the number of dice I rolled.)

For those interested, the standard deviation on number of 1's rolled on 283 dice is 6.3.

This means that in 283 dice rolls, 70% of the time I should have rolled between 41 and 53 1's. 27% of the time I should roll between 34 and 40, or between 54 and 60 1's.

Only TWO percent of the time will someone roll more than 60 1's on 283 dice.

This means, disregarding everything else, I rolled so many 1's, you have a better chance of Double Powing a S3 blodger with a S2 rookie than I had of rolling that many 1's.

From here we can see that, purely on dice rolls alone, I was somewhat unlucky.

The following is all looked at backwards; hopefully tomorrow I will reexamine this in light of HarvestMouse and bigGuy's comments and make it more useful to read.

Now we consider how many key rolls were made, and how many were 1's. (Things that are NOT key rolls include: armour rolls, injury rolls, first skill rolls when the player in question has a re-roll from a skill (such as the first dodge roll for a player with dodge who is not next to a player with tackle), bloodlust with an available victim (bloodlust when every player on the field is a squig counts as an inherently problematic roll, since it requires a team re-roll to avoid a turnover), really stupid rolls, foul appearance rolls (even if failing FA might mean allowing the opponent to score, and so a team re-roll would be used, failing the FA does not inherently cause a turnover), block dice (all skulls are inherently not a problem except the last one if all dice are skulls, or the first skull on -2 or -3 die blocks; so for a 2d block, with 1 skull, that would inherently not be a problem, but a triple skull 3d block would only have 2 that count as inherently not a problem), ttm attempts, right stuff attempts (unless the ball carrier is the one being thrown), bomb checks to see if they hit a player or not, interceptions of bombs, safe throw, etc)

We instead consider how many turnover potential rolls we made (not including multi die blocks, those will be checked seperately).
My opponent made 66 key rolls, resulting in 8 1's; this further resulted in 6 turnovers.
I made 73 key rolls (hurray 3 turns of having 6 squigs and no herders on the pitch!), resulting in 18 1's, which further resulted in 8 turnovers.

My opponent, with 66 key rolls, could expect to get 11 1's, with a standard deviation of 3; so he was lucky, but not crazily lucky to only have 8 1's for those rolls. (About the same as getting a pow or a pow/push or a push on a 1die block.)
My team, with 73 key rolls, could expect to get 12 1's, with a standard deviation of 3. Chances of getting the 18 1's I did are about the same as getting a skull on a 1 die block. Unlucky, but easily predictable.

At this point I would like to consider team re-rolls available, and how that affects turnovers.

He had 8 potentially problematic 1's, and 5 team re-rolls. This resulted in 6 turnovers, which, assuming 2+ checks each time (or mostly 2+ and some 3+) is somewhat more turnovers than expected; but he used several team re-rolls on non turnover events, like preventing an intercepted bomb by re-rolling safe throw, which COULD have been a turnover event.
I had 18 potentially problematic 1's, and 13 team re-rolls. This resulted in 8 turnovers, which, with my mass of 2+ but many 3+ rolls, is almost exactly expected.

Finally, I rolled 9 double 1's.
My opponent rolled 5 double 1's, and a single triple 1.
The number of consecutive 1's is somewhat misleading though, as the majority of them occurred on things like armour/injury checks, or during a bomb sequence.

In the end:
My opponent seemed to have SLIGHTLY above average luck with 1's and re-rolls, but not enough to worry about.
On the other hand, I rolled far more 1's than expected, with a higher rate of 1's for key rolls than expected. I also rolled more consecutive 1's than he did. I think from this, I (and my opponent) are quite justified in saying luck had a significant effect on my game.

This does not take into account the fact that my opponent had an agi 4 big hand stunty player, and many players with two heads (so the vast majority of his rolls required a 2+ if they were important rolls), whereas many of my rolls were 3+, and some were 4+ to avoid turnover. This does not look at armour/injury rolls, where my claw/mb and blockle players ought to have had an advantage over his single tackle (without block) and his few block OR mighty blow players. This also doesn't look at kick off results (with him getting a perfect defense and 2 auto bonus team re-roll results (included above) due to his cheerleaders and assistant coaches, whereas I got a single high kick when I already had a player one square from the ball.)

And it certainly does not take into account that some of the rolls made were done after all the important things were completed; a turnover at that point simply didn't matter.

If anyone has any suggestions on how to further refine this, or expand upon this, in an effort to find a method of 'comparing luck', either between opponent's in a match, or between matches, that would be wonderful.

I expect many, MANY ratings of 1.
Rate this entry
Posted by Reisender on 2013-02-27 09:33:07
if you had called this: examining 1s, all would be fine.
Posted by pythrr on 2013-02-27 09:34:47
Posted by Venetiari on 2013-02-27 09:39:29
Posted by lizvis on 2013-02-27 09:57:37
Posted by the_Sage on 2013-02-27 10:02:08
Rated 5. The title is too broad, but I find this examination of ones much more interesting than most non-quantitative analyses. =)

What I would like to see added to the game statistics is 'number of armor rolls made' and 'number of injury rolls made'. These would carry a lot of information about outcomes.
Posted by Nelphine on 2013-02-27 10:08:57

But the number of armour and injury rolls would be rather misleading in elf ball games. Although I think that combining armour/injury with 1's (and maybe 2's? not sure though.) would be the way to go.
Posted by harvestmouse on 2013-02-27 10:37:22
2 points.

1. Sometimes a 2 or 3 or so are just as bad as a 1.
2. It depends when in the turn (and how important the turn, you do turn over). That last lino dodge out of 3 tackle zones that if it works cool, if not no harm done, is hardly a turn over.

Your studies take neither into account.
Posted by Nelphine on 2013-02-27 10:48:38
@Harvestmouse: I specifically mention that I did not take 1) into account; for my particular game, I also included the fact that since my players had worse stats than his, that I would be more adversely affected by included those other numbers. For instance, I had 8 turnovers just from rolling 1's, whereas I could easily have gotten turnovers from 2's or 3's in several occasions (and on at least one occasion, I did get a turnover from a 2), whereas he probably only had 1 or 2 rolls per turn that could be a turnover on anything except a 1.
As for point 2: You are right in that we both could be taking needless risks (as he ended up doing several times, including at least 1 turnover caused by a 1.) However, overall, the dice should still 'even' out as it were, purely in terms of 1's rolled, even if there might be excessive turnovers due to those risks.

For those interested, the standard deviation on number of 1's rolled on 283 dice is 6.3.

This means that in 283 dice rolls, 70% of the time I should have rolled between 41 and 53 1's. 27% of the time I should roll between 34 and 40, or between 54 and 60 1's.

Only TWO percent of the time will someone roll more than 60 1's on 283 dice.

This means, disregarding everything else, I rolled so many 1's, you have a better chance of Double Powing a S3 blodger with a S2 rookie than I had of rolling that many 1's.
Posted by bigGuy on 2013-02-27 10:53:16
"Of my opponent's 56 1's, 46 of them were inherently not a problem" - so, 10 of them were potential turnovers.
Opponent got 6 turnovers total.

"Of my 63 1's, only 42 of them were inherently not a problem" - so, 21 potential turnover.
You got 8 turnover total.

Looks like you took twice as many risk (100%), and got only 33% more turnovers.

Posted by Nelphine on 2013-02-27 10:58:30
I have also decided I could be more mathematical about the key rolls, and the number of 1's rolled. I should not be giving out information about how many 1's were key rolls; I should be giving information on how many key rolls were 1's. Hopefully tomorrow I can do that.

Of course, I should address HM's point 1) and simply stop looking at 1's, and start looking at successes in general. I could reasonably find an expected value vs actual value, and a standard deviation based on the expected value, and determine the chance of getting at least as many failures (if the luck is thought to be bad) or at least as many successes (if the luck is thought to be good).

However, addressing point 2) will be a little harder, since, while you can tell which move is the 'important' one of a given turn, you can't always tell which of those moves resulted in the potential for the game play over the next several turns, so you can't simply say that some rolls were needless risks.

Any thoughts on quantifying 'important' vs 'needless' rolls in order to address point 2)?
Posted by Nelphine on 2013-02-27 11:00:13
Yeah BigGuy, I've just realized I looked at all of that backwards. I was focusing purely on the ones, and should be focusing on overall success/key rolls, with 1's as simply one result of that. My opponent, with some 60 more dice rolls than me, did in fact make more key rolls than I did, but I didn't actually reflect that whatsoever in my work. My bad.
Posted by SzieberthAdam on 2013-02-27 11:24:13
Luck is even.
Posted by vaclav on 2013-02-27 11:26:51
i got:
- multiple quads in single match
- 15 cas with not stunty team against me on single match
- quad both down/skulls on my bull when he blitzed for 1-ttd
- countles snakes on td zone
- my superstar blodge chaos warior died (apo failed) on -2d blitz without tackle

I just need a scatter td against me , and than I can say that i have seen all...
Its a bit emo i know, but who cares, we are just pixels anyway...
Posted by Nelphine on 2013-02-27 11:37:03
luck is not even. luck evens out.

This is not remotely my unluckiest game. I've had a game where my opponent did so well, it was a 1 in 15000000 chance of occurring. This doesn't come close. Heck, 2 or 3 die rolls the other way, and I could have won this game.

I'm trying to find a way to quantify the luck that existed in a particular game, and this one is simply the first of many I shall examine in my journey.
Posted by Christer on 2013-02-27 11:58:22
In response to this statement:

"Only TWO percent of the time will someone roll more than 60 1's on 283 dice."

Take into consideration that there are roughly 500 matches being played every day, this statement can be rephrased as:

"We expect that 10 people PER DAY will have this kind of bad luck on the site."

Two percent is pretty high.
Posted by Rijssiej on 2013-02-27 12:02:26
Did you automate the counting of the rolls? Or is it just a lot of work? :)
Posted by gjopie on 2013-02-27 12:03:58
Interesting blog, but a genuine question: Does knowing the exact odds of how unlucky you were make you feel better or worse at the end of it all?

Personally, I'm happier writing it off as an unlucky game that will undoubtedly even itself out eventually, and moving on. I'm not sure dwelling on it would make me feel better. If it works for you though, then go for it!
Posted by Nelphine on 2013-02-27 12:33:22
Absolutely. However, I'm trying to see if looking at 1's alone can give any correlation between rolling excessive 1's, or rolling excessive 1's on key rolls, and losing.

If (after I do this 50 times), there is a correlation, then we could say that it might be useful to keep track of this on the game report page.

A lot of work.

I'm trying to learn how to play better. I want to know if, when I feel like it's bad luck, it IS bad luck; or if I played poorly.
Also, my luck has seemed to be like this for 4 of the last 5 games. Since I'm a mathematician, I want to prove to myself I'm not just bad, although that is a distinct possibility.

One thing I've noticed, when my opponent is wasting me (I was down to 3 players), I GFI a LOT. 17 times in the first half of this game to be exact, which is FAR more than I realized. Interestingly, I still only made 5 more potential turnover rolls than my opponent, and I had 6 re-rolls that half to cover my craziness, whereas he only had 3.

However, he only rolled 1's, 1/9 of the time on his turnover rolls; I rolled 1's 1/5 of the time. I needed every last re-roll I could get, and it wasn't enough. He could afford to spend re-rolls on non turnover rolls and still not worry.
Posted by Nelphine on 2013-02-27 12:39:11
I also want to say, that just posting # of armour and # of injury rolls (perhaps sustained per player) would probably make a big difference like the sage suggested.

In this game, in the first half, my team broke armour 4 times, 3 of which were stuns. My opponent broke armour 12 times, 3 of which were stuns.

Even without knowing number of stuns vs other injuries, 4 vs 12 is rather telling.
Posted by Strider84 on 2013-02-27 13:05:16
If you want some useful answers you'll need to categorize every dice roll into different categories. % no turnover, % get what you plan for this turn done, % overachieve (not depending tries to steal the ball, kick off results, casualties, then you can calculate what your estimation should be for those moves and whether you over or underachieved. Of course this still only gives a broad estimation, but thatshow i usually estimate whether my opponent is allowed to whine or not :-)
Posted by the_Sage on 2013-02-27 13:08:32
No, because the number of armor rolls and injury rolls (and the ratio thereof) is very driving to most games.

Sure, they're less likely to be important than the number of ones/snakes in an elfballing match, but to analyze those well, you'd need to identify the important ones. The advantage of 'armor rolls made' and 'injury rolls made' is that it's very informative as a purely objective measure, much more so than number of blocks.

For instance, if you play against zons without tackle, a high number of blocks tends to result in a low number of armor rolls.

If you play against norse, and your number of armor rolls is high but your number of injury rolls is low, you know what happened.
Posted by the_Sage on 2013-02-27 13:22:58
@ Christer, Vaclav, etc.

This is not about saying the dice/RNG don't work, or about complaining that this was a very bad game. This is a scientist's interest in the numbers behind success and failure, and the perception thereof.

If we could get a quantitative measure of 'you have made N critical rolls, and succeeded in X of them. That is in the Yth percentile of luck.', I would find that very informative. Especially from a meta-analytic point of view, I would be most interested in the games where I won despite bad luck (according to stats), or lost despite good luck (according to stats). Those should be the most interesting game to examine to learn about your own coaching, and that of others. (Although I also suspect that games with a blitz! or with OTTDs feature into this category a lot)
Posted by Nelphine on 2013-02-27 13:39:30
Completed my edit of converting to number of key rolls (potential turnovers) made, and comparing to numbers of 1's rolled.

I realize this is not close to being finished, as I should actually convert to key rolls:failures at those key rolls, instead of simply 1's.

Turns out I made a few errors (generalizing all right stuff rolls to be turnover potentials, etc) so both my opponent and I had less 1's on our key rolls than originally mentioned.

Also turns out that due to late half turns in both halves where I went crazy (a million GFI's in the first half, and 3 turns of 6 squigs making bloodlust rolls with 0 gobbos in the second half), I made a lot more key rolls than I realized. Still my opponent and I both made a comparable number of key rolls, and he rolled 1's on them less than half as often as I did; and while I could fail a lot (27 of 73) of my key rolls on dice other than 1's, the majority of his key rolls (55 of the 66 he made) would only fail on a 1, so concentrating on just 1's still gives some merit for this particular game.
Posted by jamesfarrell129 on 2013-02-27 13:46:48
Too many words! But stats-based, which I like, so rated 6.

To get a full picture, you need to check all your actions over the match, and determine the % chance of pass/fail.

Also, you'd need to take into account the 'critical' actions, over the unnecessary ones like end-of-turn blocks etc. I'd much rather have a double-skull on a block thrown at the end of a turn, when its not important and I'm just using up player actions, rather than when hitting a ball-carrier.

Finally... add some graphs! :-)
Posted by Nelphine on 2013-02-27 13:58:02
As another note, about this game in particular, I think, having looked over the data a little more, that one of the biggest things about the match had nothing to do with the 1's rolled at all.

Rather, in the first half, 10 of the 12 bomb attacks on my players (which needed a 4+ to affect my player), and 8 of the 18 bomb attacks in the second half, hit my players.

Those first half bombs also broke armour far more often than expected; and in the second half, 3 of the 8 hits were on Fluffy, my legendary Squig Hopper, and all 3 broke armour.

So 2 things: The bombs performed FAR better than normal, allowing the usually slow horrors to completely dominate the pitch, and, I set up in a fashion that totally allowed those bombs to work.

Based on the results, the damage done to my team, and my lack of ability to even pretend to control the pitch, I think underestimating the horror bombers is what truly did me in in the end, even though only 1 had pass, and 2 had wild animal. (Of the 11 4+ wild animal checks, 8 of them passed, and at least half of those were bomb attempts.)

Blaming it on 1's, while semi-reasonable, is still no excuse for not being better prepared for a horror team of '2+ everything to do with the ball, including ttm, right stuff, pick ups, and dodges' + 'dream team perfect bombers'.

Live and learn.
Posted by BlizzBirne on 2013-02-27 17:15:27
long, but interesting - so i read it through. congrats on that. ;-P

if i was to assess "luck" and "bad playing decisions" i think i would categorize each action (both mine and my opponents) and their potential results into three categories

A: bad result for me (turnover, loss of player, score against me etc.)
B: neutral (no immediately good or bad consequence for me like failed armor roll, irrelevant turnover of actions after the main turn moves or so)
C: good result for me (opponent player off the field, score for me, succeeded pass, handover etc.).

Every action-result is associated with a certain statistical expectation value so that for a combined amount of actions per result category you should be able to derive the average expectation value based on the actions. the expectation value of your own actions will tell you something about your coaching decisions. comparing the expectation value for good, neutral and bad results with the real distribution will tell you something about the luck component.

well. also that might have its gaps. it's just what i would do if i REALLY had a lot of time to invest here. ;-P
Posted by happygrue on 2013-02-27 18:51:19
This topic has already been put forward by Kalimar. If really interested in debating it, moving over the the thread is a good idea:

Posted by Nelphine on 2013-02-27 20:53:54
But HappyGrue, that topic largely fell by the wayside. I'm doing this in my own blog, so that I can continue to update and modify it, and always know precisely where it is.

The plan is to do this for at least 10 games, using the same team, and see what kind of results or trends emerge.
Posted by strikereternal on 2013-02-27 21:10:15
Expected a typical whinepost about luck but this is a pretty decent starting point. Analyzing 1s in and of themselves is quite a simplistic way to go about it as others have mentioned.

I'd love to do some studies of my own but unfortunately, as far as I can tell, there's no easy way to pull a log of actions and dice rolls from a replay, which is the main thing holding me up.
Posted by strikereternal on 2013-02-27 21:11:50
Note that the goal in such a study would not be to evaluate the fumbbl RNG (I have 99.99% confidence in its correctness) but to try to establish some metrics and evaluation systems for "luck" and performance in Blood Bowl games. Basically what the_Sage is talking about above.
Posted by neoliminal on 2013-02-28 00:56:06
It would be cool to have a post game analysis which took the die rolls and figured out just how much deviation they were from standard... In other words just how "Lucky" or "Unlucky" the coach was that game.