22nd September 2019 at 12:23 pm #3950
Or, which is better: Fan Factor or Coaches/Cheerleaders. (Article by Joemanji, for more wisdom check out his patreon page: https://www.patreon.com/Joemanji )
Ah, the age old question that has been troubling Blood Bowl coaches since the dawn of time, or at least 1993 when Third Edition was released: What shall I do with this 10K I have left over? I have spent many a sleepless night a-pondering and a-wondering whether there is a definitive answer. And now, with the use of bloody numbers and stuff we are going to discover once and for all what that answer is! Are you with me kids? Shall we go on this adventure together? Get ready for some goddamn bloomin light’ mathematics.
Firstly let us just consider the re-rolls. You know the ones, they sometimes come down the chimney at Kick-Off Table Christmas, all wrapped and shiny. Usually for your opponent when he really, really needs them. Let’s brute-force some numbers, working out an an ‘expected re-rolls per kick-off’ for the various options. All against an assumed opponent with no bits or bonuses themselves. These are all just asking whether you yourself get an extra re-roll, and so do include the times both teams get an extra one. Note the gaps, it only makes sense to compare items of the same costs with each other. Obviously three Fan Factor is better than one Cheerleader.
Expected Rerolls per kick-off
Nothing = 0.16771
1 Fan Factor = 0.18980 1 Coach OR Cheerleader = 0.19478
2 Fan Factor = 0.20919 1 Coach AND Cheerleader = 0.22186 1 FF + 1 Coach or Cheerleader = 0.21380
3 Fan Factor = 0.22534 1 of each = 0.23779 2 FF + 1 Coach or Cheerleader = 0.22985 1 FF + 2 of the same = 0.22675
So it seems when considering re-roll gain only, Coaches and Cheerleaders are better than Fan Factor. But this leaves the thorny problem of how to value Pitch Invasion and Throw A Rock. Even if you assume eleven players on each team and work out an expected number of Pitch Invasion stuns per kick-off, how do you compare that to the numbers above? Is it even meaningful given that stuns are worth more or less on different players and in different parts of the pitch? I don’t know, but that’s no excuse not to do some more darn maths. Sums are cool, stay in school!
Firstly for Throw A Rock, assuming three meaningful kick-offs per game, then 1 Fan Factor works out as 0.05 fewer rocks on your players, and 0.05 extra rocks on your opponent’s players. That is per tournament by the way. Oh, but 21/36 of those rocks are stuns. So in terms of players leaving the pitch, the numbers are 0.02 and 0.02.
Finally, I think a nice way to work out the influence of a Pitch Invasion is to consider ‘net stuns’: The number of stuns a team takes less the number the opposing team suffers. I’m going to assume both teams have eleven players, and three kick-offs per game as above. If both teams have no Fan Factor then we can consider the expected net stuns to be zero. The impact of taking 1FF over nothing or an AC/CL is 0.596 net stuns per Pitch Invasion, which works out as 0.298 net stuns per tournament, or an additional net stun once every 3.4 tournaments (or about once every 20 games if you like round numbers).
Interestingly, the influence on Fan Factor on Pitch Invasions is decreasingly non-linear*. So the more FF you take, the less bang you get for your buck:
FF 1 = +0.298 net stuns per tournament FF 2 = +0.564 net stuns per tournament FF 3 = +0.792 net stuns per tournament
As with everything in this blog, the numbers take no account of context. Sometimes you need to score in two turns and stunning just one person from PI swings the game. Sometimes the ball lands deep and you have a slow team, and it doesn’t matter if you stun all eleven opposing players. But at least we have a starting point for discussion.
So a final summary now that we have all the numbers:
By taking a Coach or Cheerleader over a Fan Factor you could expect an extra re-roll once every 6 games.
By taking a Fan Factor over a Coach or Cheerleader you could expect an extra net stun once every 20 games, and an extra rock once every 145 games.
So what did we learn fellow nerds? Did well reach the numerical El Dorado of a definitive answer? Well … it depends. These numbers are somewhat arbitrary, and there is a huge element of personal preference and experience in how you interpret them. How many games do you remember losing to Pitch Invasion or Throw A Rock? How many do you remember losing to not having just one more re-roll? Which do you want to mitigate against most? At least now we are armed with a little extra knowledge to make our choice an informed one.
There are also different considerations to make depending on what team you are using. A slow team like Orcs or Dwarfs is hit much harder by a catastrophic Pitch Invasion than say an elf team might be, but conversely might run out of re-rolls less often than a team relying on multiple dodge rolls per turn.
Personally I don’t think the choice is to worry about only Pitch Invasion / Throw A Rock or only re-rolls. I would want to consider which option increases my win percentage by more over a long stretch of games. If I take the AC/CL and lose 1 game in 100 to a PI but win 2 extra games in that 100 from bonus re-rolls then that seems like a net win. The loss to PI may seem flashier and more memorable when it happens, but it won’t (in my hypothetical example) have made taking the AC/CL the wrong choice.
*This may well be true for AC/CL past the first, I didn’t check. That only matters if you are taking more than three bits and I think that only applies to Amazons, and even then I always prefer at least one Catcher. I’ll leave that investigation to someone else.
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