##### Overview:

Two important parts of the game are turnovers and blocking. It is important to realise what the chances are of what you are attempting to do. Blocking comes in two parts: firstly the chances of taking down the other guy whilst remaining standing and the chances that a block will result in a turnover for yourself. Knowing the probabilities and statistics for the blocking side of the game can be vital to success.

So I present the following charts involving the main blocking skills and their odds of success.

- Tackle isn’t listed as you you can just check the columns that exclude the Dodge skill for the defender.
- For Loner, you can look at the Pro rows except you lose a reroll as well.
- For when you have Block vs Wrestle, it is assumed you want to remain standing, if you don’t mind them using their Wrestle, you can treat it as though you have Wrestle yourself.

##### Charts showing the odds of a successful knock down:

One Die Blocks |
||||||

Attacker | Defender | |||||

None | Block | Dodge | Block+Dodge | Wrestle | Wrestle+Dodge | |

None | 33.3% | 33.3% | 16.7% | 16.7% | 33.3% | 16.7% |

Block | 50% | 33.3% | 33.3% | 16.7% | 33.3% | 16.7% |

Wrestle | 50% | 50% | 33.3% | 33.3% | 50% | 33.3% |

Pro | 44.4% | 44.4% | 23.6% | 23.6% | 44.4% | 23.6% |

Pro + Block | 62.5% | 44.4% | 44.4% | 23.6% | 44.4% | 23.6% |

Pro + Wrestle | 62.5% | 62.5% | 44.4% | 44.4% | 62.5% | 44.4% |

None + RR | 55.6% | 55.6% | 30.6% | 30.6% | 55.6% | 30.6% |

Block + RR | 75% | 55.6% | 55.6% | 30.6% | 55.6% | 30.6% |

Wrestle + RR | 75% | 75% | 55.6% | 55.6% | 75% | 55.6% |

Two Dice Blocks |
||||||

Attacker | Defender | |||||

None | Block | Dodge | Block+Dodge | Wrestle | Wrestle+Dodge | |

None | 55.6% | 55.6% | 30.6% | 30.6% | 55.6% | 30.6% |

Block | 75% | 55.6% | 55.6% | 30.6% | 55.6% | 30.6% |

Wrestle | 75% | 75% | 55.6% | 55.6% | 75% | 55.6% |

Pro | 67.9% | 67.9% | 41.2% | 41.2% | 67.9% | 41.2% |

Pro + Block | 84.4% | 67.9% | 67.9% | 41.2% | 67.9% | 41.2% |

Pro + Wrestle | 84.4% | 84.4% | 67.9% | 67.9% | 84.4% | 67.9% |

None + RR | 80.2% | 80.2% | 51.8% | 51.8% | 80.2% | 51.8% |

Block + RR | 93.8% | 80.2% | 80.2% | 51.8% | 80.2% | 51.8% |

Wrestle + RR | 93.8% | 93.8% | 80.2% | 80.2% | 93.8% | 80.2% |

Three Dice Blocks |
||||||

Attacker | Defender | |||||

None | Block | Dodge | Block+Dodge | Wrestle | Wrestle+Dodge | |

None | 70.4% | 70.4% | 42.1% | 42.1% | 70.4% | 42.1% |

Block | 87.5% | 70.4% | 70.4% | 42.1% | 70.4% | 42.1% |

Wrestle | 87.5% | 87.5% | 70.4% | 70.4% | 87.5% | 70.4% |

Pro | 79.9% | 79.9% | 54.3% | 54.3% | 79.9% | 54.3% |

Pro + Block | 93% | 79.9% | 79.9% | 54.3% | 79.9% | 54.3% |

Pro + Wrestle | 93% | 93% | 79.9% | 79.9% | 93% | 79.9% |

None + RR | 91.2% | 91.2% | 66.5% | 66.5% | 91.2% | 66.5% |

Block + RR | 97.6% | 91.2% | 91.2% | 66.5% | 91.2% | 66.5% |

Wrestle + RR | 97.6% | 97.6% | 91.2% | 91.2% | 97.6% | 91.2% |

For using Pro the calculation is 1/3 * (1+(2/3*1/2))=0.44. It is the Pro and Reroll calculations I am the least certain on and if any maths gurus care to jump in and explain it in more detail I am happy to defer, or be corrected if they are wrong. The answers seem to be in the right ball park though, ie Pro should succeed more times than without it but less times than with a Reroll.

The two dice block with no skills, you suceed 20 times of the 36 combinations or 20/36 which is the same as 5/9. To work that out mathematically instead of writing out all 36 combinations to find that you do need to find the odds of failing it then subtact that from 1. So one one dice you fail to knock them over on the skull, both down, and the two push results, so 4 of the 6 sides 4/6. You are rolling two dice so multiply them together 16/36 which cancels down to 4/9. 1 – 4/9 = 5/9 = 20/36 = 55.6%.

Your last point regarding Wrestle, it is assumed the aim of the block is to knock the other guy over, typcially you use Wrestle for blitzing the opposing ball carrier. So you knock them over 1/2 the time. It is ignoring the fact that you also go prone, as this isn’t a turnover and is assumed that was your intention. If you didn’t want to go prone, then you just look at the odds as though you didn’t have Wrestle.

Hope that clears it up a bit.

Pro+RR:

= 1/3 -> knock down chance

+ 2/3*1/2*1/3 -> didn’t knocked down * 50%proRRchance*knock down chance

+ (1-1/3-2/3*1/2*1/3)*1/3 -> (didn’t knocked down) * knock down chance

= 3/9 + 1/9 + 5/9*1/3

= 4/9 (knock down with Pro)

+ 5/9*1/3 (didn’t knocked down with Pro * chance to knock down)

= 63,0 %

looks hard but it’s super easy:

You multiply the chance to failing a knock down with the chance of knocking down in the next try and sum it all up.

The chance to fail a knock down is 1- knock down. Like u did all the time with RR: 1-1/3=2/3.

To fail a knockdown with Pro is 1-knock down with pro = 1 – 0.4444 = 0.5555

so you just add +0.5555*1/3 to the term and its done.

Sorry for my bad english, hope you got it nevertheless =)

Fantastic info Coach! Much appreciated. Question for you about the calculations used to determine some of the results. My math skills are far from elite, so bear with me 🙂 Regarding a one die block, I understand the odds of a succesful knock down, while remaining standing, are 2 of 6. However, when Pro is factored for the Att (None for the Def), how do you arrive at 44.4%? Is this due to the 50% chance that Pro will not result in a re-roll? How does this result in 4 of 9 chances of success?

Regarding a two dice block, what calculations are used to arrive at 55.6% success rate for Att/Def using None? Given this % relates to 5 of 9, what constitute the 5 succesful results. Before looking at your chart, I thought a two dice block, with Att/Def None would result in a 66.7% success rate (2/6 + 2/6 ). I do not doubt you have posted the correct % as I have seen these same odds elsewhere. However, I would like to understand what I am doing wrong regarding the calculations.

Finally, given wrestling results in both Att/Def lying prone on the pitch (rather than a Def knock down, while the Att remains standing), shouldn’t the odds be 33.3% the Att will remain standing, while the Def is knocked down. Again, what am I not seeing?

Don’t take any of this as a criticism. I am just trying to resolve a bit of confusion on my end. Again, your post is much appreciated.

Cheers,

J

His odds are right across the board (so far as I’ve seen). The other way to look at 2 die unskilled blocks is that they’re the same as 1 die blocks with rerolls. Basically, if you’re looking for a specific case (knocking someone down) it doesn’t matter if you roll one die and then the other or if you roll both at the same time.

To Jyrmar, you’re running into the problem a lot of people run into with stats, think of it this way, by your logic a three die block would’ve meant 1/3+1/3+1/3 = 100% chance of success, which I’m sure you realize is wrong (As I’m sure you’ve seen a 3 die block fail). You have to check for failure before checking the next in line, so you multiply the odds of failure times the next odds of success for each new roll. So your first die has a 1/3 chance of success, then, if you failed (2/3 of the time) you check your next die which has a 1/3 chance of success. So your odds of success are the two possibilities of success added together 1/3 (the first die roll) + 2/3*1/3 (The second die roll if the first didn’t work) = 55.6%.

Hopefully that’s a little clearer, this kind of thing is easier to explain by showing someone… I should know, I’m a stastician and I have to explain these kinds of things all the time.

So for Pro, it’s 1/3 + 1/2*2/3*1/3. You add in the extra half because there’s only a 50% chance you get to check the second die.

Coach and Sneezeguard,

Thank you very much… terrific explanations about the math involved. Definitely clears things up. The odds charts on this site are incredibly helpful as no one wants to have to manually calculate the odds before each play. But, it is nice to know the formulas involved. I have seen a few threads on the official site that could certainly benefit from this sort of information!

I have not played BB since the mid 90’s due to lack of interest on the part of friends. For whatever reason, I never gave FUMBBL a shot. I always thought the mix of American football (with a sprinkling of futbol rules/concepts), the Warhammer fantasy universe and sports management features made for a fantastic gaming concept. And even my wife finds the “Did you know…” blurbs absolutely hilarious.

I was thrilled to discover GW gave Cyanide the green light to develop BB, as I played Chaos League a bit and enjoyed it. The articles, tips and suggestions on this site are incredibly useful in bringing noobs up to speed on basic/advanced strategy. And, I definitely count myself as a noob once again trying to understand all the subtleties involved in making my elves less squishy and more effective against the hordes of dwarves, orces, and other wretched scum on the other side of the pitch.

Thank you for this website and your kind responses above! Anything I can do to contribute, please let me know. Looking forward to your “how to use it and who should select it” article about the Leap skill. Still not totally clear if tackle zones ever factor into the leap agility roll or if the roll is an unmodified agility check, regardless of the square the Wardancer is leaping into… anyway, thanks again mates!

Cheers,

J

The title of the first set of tables seems a bt misleading?

“Charts showing the odds of a successful knock down whilst remaining standing yourself”

I would asume that by “remaining standing yourself” you mean actually not having a turnover or attacker not being knocked down? i.e. when the attacker uses wrestle after a both down result then both players are down (as opposed to the table title) but no turnover ensues. Nevertheless the “attacker using wrestle” situation seems to have been counted as good in those tables, correct?

Hmm there does seem to be some contradiction there from that. You are correct in saying that the odds for the attacker having wrestle have counted yourself going prone as good. I’ll clear that up later, thanks for pointing it out.

No probs.

For me the table is stating the odds of having the opponent player down (including a wrestle skill use) without a turnover; from that point of view the tables are quite correct and maybe just the title may need to be changed a little. Using wrestle could indeed be a desired result so no conflict in the odds.

Here’s a way to see the 1 dice Pro row as x in x chances of success (it is 8 in 18 instead of 4 in 9):

The 18 possibilites are as follows; 3 possibilities for the first block roll multiplied by 2 possibilities for the Pro roll multiplied by 3 possibilities for the second block roll. We are counting only the successful possibilities; these consist of possibilities where the first block roll succeeds, and where the first block roll fails but both the Pro roll and the second block roll succeed. There are 6 possibilites where the first block roll succeeds (success or failure on the pro roll [even though you wouldn’t actually roll it!] and success and push and failure on the second block roll). There is 1 possibility along the branch where the first roll is a push (pro roll and second block roll both succeed) and 1 possibility where the first roll is a failure (again, pro roll and second block both succeed). That is a total of 6+1+1=8 possible ways to succeed out of 18 possible permutations of the 3 dice rolls. 8/18=.44444 repeating.

(Someone may quibble that it doesn’t matter whether or not the two sorts of failure, push and attacker down, are different, and that these odds would be the same if the block die had 2 stars and 4 skulls. This is true but I was trying to give names to the different branches of the possibilities tree).

Any chance you could include a -2d block chart?

Look on Page 2!

Please correct me if I am wrong, but I believe you have a typo in the first table “One Die Blocks,” the “Dodge” column, and the “None + RR” row says 36.6%, and should be 30.6%.

Thanks, I’ve updated the table.

Needs tackle on the tables

If you read the blurb before the actual tables it explains why Tackle isn’t listed.

Great post (and site) Coach.

One thing I’d like to see and I don’t think you covered are the odds of a blocking turnover with the defender still standing. It’s simple enough on a 1-die block, but gets complicated for the mathematically challenged beyond that.

This is especially interesting to evaluate for a “block-heavy” team, such as norse for example, when evaluating your chances of dodging out of a hairy tackle zone vs. staying and letting the risk of dodging vs. blocking vs. turning the ball over to the opposing team.

Thank you Wiseman, the only way you will have a turnover and leave the opponent standing is if you rolled a Skull, or a Skull and Both down against an opponent with Block (and you don’t have Block or Wrestle). So you just use the Block or Wrestle (second row) numbers for that.

what does RR stand for in the chart?

It stands for Reroll, so it is the odds if you take into account using a team reroll when doing the block. Note that you may not necessarily need to use the reroll as you might get the result you need first time.

One die + Pro

Knockdown = (72+24)/216

1st Die

2/6 4/6

success branch

3/6 3/6

Reroll granted No Reroll

branch

2/6 4/6

success failure

Chance 72/216 24/216 48/216 72/216

Knockdown = (72+24)/216 = 44.4%

Probability trees are an easier way of calculating the odds

I was looking at the benefit of putting Piling On onto my Troll Slayer who has Mighty Blow & Guard.

The background stats for this analysis are drawn from:

http://fluff.bloodbowlleague.com/?p=cp&cpid=6#16

Please go there for more details.

Piling On is difficult to analyse because there are two possible times that Piling On can be taken. I’ll approximate by saying that half of the time the Piling on is worth it to get armor break (high AV or high value targets) and half of the time it is worth it to get better injury roll only after armor break (not as good target), but you stay standing on no armor break. I’ll ignore cases when you don’t want to use it at all because you need assists or tackle zones.

The following table shows the ratio of probability of Stun, KO or casualty with Mighty Blow versus probability with MB and Piling On used half of the time for each roll type:

Table 1: MB vs MB + Average PO AV and PO Injury

Av Stun KO Casualty

10 0.93 1.91 1.90

9 0.86 1.84 1.83

8 0.78 1.76 1.75

7 0.69 1.67 1.66

6 0.60 1.58 1.58

5 0.53 1.52 1.51

This looks better in a spreadsheet if copy-paste is your thing. The chance of stun goes down because the chance of KO or Cas goes up.

Observations:

1. Mighty blow is always a better skill by a long margin because Piling On hardly ever more than doubles your chance of a good outcome. MB has the best modifiers, except for very high armor targets when you use PO to break armor and the overall odds are so poor in such cases you can’t count on them for SPPs.

2. PO is less useful for lower armor targets (only ~70% boost to good outcome), and since these are when you’ll actually get most of your cas SPPs, PO looks even less useful.

So, is PO a worthwhile skill? Let’s say I’m going with Tackle or MV on my Troll Slayer.

FYI, the odds of good outcomes with MB only are shown in Table 2.

Table 2: Mighty Blow only odds

Av Penetrate Stun KO Casualty

10 16.7% 8.3% 4.6% 3.7%

9 27.8% 13.4% 7.9% 6.5%

8 41.7% 19.7% 12.0% 10.0%

7 58.3% 27.1% 16.9% 14.4%

6 72.2% 32.4% 21.3% 18.5%

5 83.3% 36.6% 24.9% 21.9%

Observations for players with MB:

1. Odds of getting SPPs (Cas) for AV 9+ are not worth worrying about.

2. Even soft targets (AV 7) are pretty hard to keep down (KO+Cas ~31%), showing the emphasis of the game on ball handling. Considering that you had to roll 31% for a two dice block on a blodger with a blocker, tackle is good to push you to a 56% chance of putting down a blodger. That’s an 80% increase in your chance of starting the injury roll process, plus the benefit in your tackle zones.

Conclusions:

1. Piling On is a dodgy skill at best. With the penalty of loosing assists and tackle zones, it’s a no-brainer to avoid unless you have to maximize benefit from Dauntless Stormvermin vs Big Guys, but your odds still aren’t good.

2. I haven’t shown the calcs, but Mighty Blow gives double or better chances of casualty for 7+AV targets and that’s a lot better than you get from PO.

3. Casualties are a tough way to get SPPs, but you already knew that 🙂

what about the odds with frenzy?

It increases the odds of a successful knock down and of a turn over.

I think it makes it a 44.4 chance of knockdown with two 1 die blocks

66.6 chance with block

83.3 with block + reroll

turnover chances on a 1 die frenzy are

44% no other skills

22.3% with block

I think 4.66% with block + reroll

it gets more complex beacuse the number of dice can change for the second roll

hi Coach,

I think there is an error on “Chance for Turnover” table… Wrestle / Block + RR with 3D block…

to fail you need six skulls…

1/6 * 1/6 * 1/6 * 1/6 * 1/6 * 1/6 = 0.00214% which is significantly higher than 0.00002%

why is there no statistics for juggernaut?

For Juggernaut it doesn’t change the odds of getting a knock down on any single block as it just changes a result into a pushback. The only time it makes a difference is if you have Frenzy which is nearly the same as just using a reroll for a second attempt at the block. There are instances where the second block will use a different number of block dice from the first one but I chose not to complicate the tables even further.

When considering it from the point of view of not suffering a turnover, it’s just the same as having Block (assuming you are blitzing and thus able to use it) so you can use those numbers for having Block the same as having Juggernaut.

Juggernaut cancels wrestle on the blitz vastly increasing your odds at bringing a player down for 33% per die with tackle & block to 50% with tackle, block and Juggernaut! Its an essential skill for dedicated player hunters!

Yea, if the guy has Frenzy. I would personally use Juggernaut for a dedicated crowd surfer and 1-turn pusher 🙂

For that I would prefer a STR bonus plus frenzy.

I ALMOST had a catcher developed into this. He was such a beast and he struck fear into my opponents near the sidelines.

Is Pro use always optimizing for knockdown (and not for “avoid turnover”)?

There are going to be times you aren’t willing to risk re-rolling a mere push (because it could change to a turnover), but *would* use a Pro-reroll to avoid turnover. Those obviously lead to different chances of “success”, and especially makes me wonder if the “chance of Turnover” table at the end is done differently from the “chance of knockdown” tables.

Either way, it seems like a note would be useful (in the text lines before the charts).

To be honest it’s so long since I published these I can’t remember exactly. Though you are right there are times you would use Pro when you wouldn’t use a reroll (I used to take it after Guard and Mighty Blow on Chaos Dwarf Blockers for those times I just rolled pushes etc.). Personally speaking though I would never rely on Pro to avoid a turnover if I had a reroll available (well maybe in extreme circumstances) but then I’m not someone who ever really takes Pro on many players apart from Big Guys who can’t use team rerolls due to their Loner skill. I usually think there is a more preferable skill to choose instead of Pro, for instance on Chaos Dwarf Blockers now, you can get Stand Firm on a normal roll when under old rules you couldn’t.

Hi Coach and thank you for sharing the knowledge,

I am wondering about the odds of succes on 2 dice against block with reroll and taking into account the different skills as you did on the 1st page. By success I basically mean when the defenser would loose the ball as it is the most common situation when rolling the red dices may be the smartest move or not. Would you have that laying around on your desktop ? or know a good adress ?

Again thanx for your time, and may the Roll be with you.

Hi Trapeziste, thanks for your comment. You can just use the table on page 2 for those odds, you just have to change the way you look at it.

For two dice against, the odds for knocking the ball loose is either 11.1% if you need to knock them over and you have no skills, or 21% with a reroll.

If you just need a pushback then it is 44.4% or 69.1% with a reroll.

If you need to knock them down and you have Block / Wrestle and they don’t then 25% or 43.8% with a reroll.

If you just need a pushback and you have Block / Wrestle then 69.4% or 90.7% with a reroll.

Just out of interest for teams, such as dwarves, who rely on a blocking game to generate spp; has anyone worked out the average number of blocks in a round/ game.

I assume the receiving round would have 4 automatic blocks, assuming 3 linemen and a blitz

I also assume it would vary depending upon the team played i.e. elves will dodge away.

A rough idea would be interesting though.. don’t you think?

First of all, great tables!!

I make an script to calculate all the odds ( im working with wrestle and stand firm in this moments), including odds of failing and moving, with frenzy and with rerolls too.

Can u check that my maths are correct? mathsbowl.blogspot.com

Thanks to all and continue working with this!!