Wednesday, January 02, 2013

Blood Bowl: Fan Factor

Sceadeau's league is looking to get started on Saturday which means it's getting down to crunch time as far as finalizing a team to fit under the starting salary cap. I was talking with Robb yesterday about different ways he could pare his team down to 1500 TV. His modified stats right now are 1600 which means he has to purge off 100k worth of stuff. One easy cut is my primary punching bag Lestzh, his level 1 lineman suffering from a smashed hip, a smashed ankle, and a serious concussion. I love beating that guy up and it makes me sad that he might get retired instead of getting straight up killed. That's 50k and he could just light 50k of his cash on hand on fire. But the thing that got me thinking was his 3 fan factor. He could also throw away 90k worth of cash and 1 fan factor in order to keep Lestzh! (Well, really, he should retire Lestzh and spend 50 of that 90k on a replacement but that's not nearly as fun.) But what is that fan factor even worth? My dwarves have 6 fan factor... Is that a good thing? Note that there's no easy way to gain fan factor (you need to win/draw and roll high to gain it) but it's trivial to lose fan factor (concede a match on turn 1!)

First off, what does fan factor actually do other than inflate your team value? Well, at the start of each game you roll 2d6 and add in your fan factor to determine how many of your fans showed up to the game. Your opponent does the same. Then you compare results to work out the FAME rating. If you tie, no one gets any FAME. If you're not tied the higher number gets 1 FAME. Unless they at least double the opponent, in which case they get 2 FAME. The only other use for fan factor is determining whether you gain/lose it at the end of a match and that can be pretty much ignored here. In the long term a winning team will have high fan factor, a losing team will have low fan factor. We don't care about the long term at this point in time. All we care about is if fan factor is worth the salary cap hit for entering the league.

Ok, so the only thing we care about is how fan factor impacts FAME rating. What is FAME rating good for? Well, the first thing it does is it makes you money at the end of the game. You earn 10k per FAME rating. I don't know how useful this is actually going to be. My dwarves could enter the league with 6 fan factor or 60k in cash on hand. It would take 6 FAME cash bonuses to make up the cash on hand I could have had to start with, nevermind the 60k worth of inducements I'm giving up every game by having the fan factor instead of the cash. For some teams this will matter more than others. My halflings make way more money than they could possibly spend, for example, so they really don't need the fan factor or the cash on hand. My dwarves want to save up for a deathroller because they're cool... Maybe the fan factor is a reasonable way to do that. I suspect no. End game cash is nice, but really not worth the cost. What else does FAME do?

FAME also comes into play on 4 of the kick-off results. Two of them are pretty common: cheering fans and brilliant coaching. Each one has you roll a d3 plus your FAME plus your cheerleaders or assistant coaches. High number gets a free re-roll. One of these will come up 5/18ths of the time and you'll probably have 5 kick-offs per game so you're looking at more than a re-roll per game on average being up for grabs. Some of these kick-offs will be so late in the half that the re-roll won't matter, but it's not nothing. On the other hand, my dwarves could trade in 5 fan factor for an actual re-roll in TV and that gives me a re-roll each half with no randomness involved at all. Now, the kick-off re-rolls also have the advantage of denying your opponent the free re-roll which definitely has uses. Let's look at some numbers after a break...



My FAMEMy Free Re-RollHis Free Re-Roll
-211%100%
-133%89%
067%67%
189%33%
2100%11%

Keep in mind that you can impact these results with cheerleaders or assistant coaches. I could take my 6 fan factor, turn it into 2 of each, and still save 20k off my team value. Then even if I give up 2 FAME to my opponent I'm still sitting in the 67% each band, and I'm smiling if it's any other FAME result.

The third kick-off result is throw a rock. 1 in 18 kick-offs will have this result come up, and when it does each player rolls a d6 and adds their FAME. Highest number gets to injure one of the other team's players at random. No armour roll needed. This is only going to come up every 3 games or so. It's likely to have an impact on the game when it does, and no one likes the idea of having a guy die to a rock, so it could be useful to mitigate the damage done... But it's really not going to happen all that often. And even when it does, how will having FAME help you out? Note that on ties someone on each team gets injured.

My FAMEOdds My Guy InjuredOdds His Guy Injured
-283%28%
-172%42%
058%58%
142%72%
228%83%

Going from 0 FAME to 1 FAME means that in 1 of every 18 kick-offs you're shaving 16% off of your chance to get injured and adding 14% to his chance to get injured. This means that you can expect to prevent one injury every 113 kick-offs, or something like every 22 games. So, yeah, it does _something_. But it doesn't do very much! I doubt the league will even have 22 games.

The last kick-off result is pitch invasion. This is the rarest kick-off result (along with get the ref) and only comes up 1 in every 36 kick-offs. What it does is you roll a d6 + FAME for every opposing player. Anyone who gets a 6 gets stunned. So 1 in 6 of your players will get stunned with even or positive FAME, 1 in 3 will get stunned with your opponent being up one, and 1 in 2 will get stunned with your opponent being up two. This sounds like a big deal, and every 7 games when it gets rolled crazy things will happen. Having half your team stunned before you get to go is brutal. That means half your team is going to miss 2 turns which probably gives your opponent an easy score. Assuming it's not right at the end of a half. And while it's probably easy for them to score no permanent injuries are going to result from it. (Well, the rest of your guys might well get surrounded and knocked over...) This is certainly bad news, don't get me wrong, but is probably giving your opponent one free score every 7 games even that big a deal? It's probably not even that bad, since he's still losing 1 in 6 guys too. Many teams only have a couple guys who could realistically go get the ball anyway, and if they get taken out it's not a huge deal. Plus, if you're only 1 FAME off then you're probably looking at losing 4 guys to his 2. For 2 turns. Bad, but not the end of the world.

None of these things impress me much. But maybe if I look at how often you'll be giving up 2 FAME it'll be more impressive? Looking at some of the teams that might be joining the league there's a range of fan factors from 1 to 10. I can't figure out a reasonable way to summarize things so I think I'm going to look at things from an EV perspective. So, to 2 decimal places, here is your expected FAME result over the long haul when comparing your fan factor (on the left) to your opponent's fan factor (on the top).

012345678910
00.00-0.32-0.61-0.86-1.07-1.24-1.38-1.5-1.59-1.67-1.73
10.320.00-0.30-0.58-0.81-1.01-1.18-1.31-1.43-1.52-1.60
20.610.300.00-0.29-0.54-0.77-0.96-1.12-1.25-1.36-1.45
30.860.580.290.00-0.27-0.51-0.72-0.91-1.06-1.19-1.29
41.070.810.540.270.00-0.25-0.48-0.69-0.87-1.01-1.13
51.241.010.770.510.250.00-0.24-0.46-0.66-0.83-0.97
61.381.180.960.720.480.240.00-0.23-0.45-0.64-0.80
71.501.311.120.910.690.460.230.00-0.23-0.44-0.63
81.591.431.251.060.870.660.450.230.00-0.22-0.43
91.671.521.361.191.010.830.640.440.220.00-0.22
101.731.601.451.291.130.970.800.630.430.220.00

Eh, I don't know how well that turned out. One interesting thing is that the odds of a 2 FAME either way drop as fan factors get big. If my 6 fan factor went up against Robb's 0 fan factor then I'd expect to gain .72 FAME on average. If we both throw away 3 fan factor and spend that cap space in other ways instead then I expect to gain .86 FAME on average. My team comes out ahead on that exchange. This makes me feel like the first few points of fan factor have a reasonable impact on FAME. On the other hand, if I burned away my fan factor to nothing and went up against one of Sceadeau's teams with 10 fan factor there's a very high chance I'm giving up 2 FAME since the average is 1.73. More than 73% of the time he'll get 2 FAME. That's pretty significant!

Or is it? Keep in mind he's giving up 100k worth of stuff in order to have that 10 fan factor. That's 2 full re-rolls each half for my dwarves. And what exactly does he gain? He makes an extra 20k after the match (and therefore will earn that 100k of stuff in 5 games), and he gains about half a re-roll per game, and I lose 7/9ths of a re-roll per game, and I get an extra guy injured by a rock every 15 games, and he saves a guy from injury every 12 games, and every 7 games he likely gets to score a free touchdown from a pitch invasion.

That's assuming he gets the 2 FAME, which is more than 73%. But some of the time he'll only get 1 game, which knocks all those numbers down. Even if it was always 2 FAME I think I'd rather have 2 re-rolls per half than all that other stuff. Going into the league, and considering just the first couple games, I absolutely would rather be on the 0 FAME side than the 10 FAME side. That said, after 6 games he'll have made all that cash back himself. The problem is re-roll costs are doubled so it'll actually take more like 11 games to earn enough money to buy those re-rolls, and even when he does that he'll still be giving up a re-roll's worth of inducement money with the 10 FAME. And teams will have had a chance to narrow that FAME gap, especially if he actually loses early games in the league while waiting for that cash engine to kick in.


I think I'm going to have to mull it over in my head a little bit more, but I'm definitely leaning towards conceding a few games to wreck my fan factor going into the start of the league. It just doesn't feel like the fan factor is worth the TV cost. Certainly not compared to more re-rolls which are a very cost efficient way to spend money before the start of a league! So maybe if my team had enough re-rolls I'd be happier carrying fan factor? 

3 comments:

Duncan said...

Probably not an issue yet, but remember that once you have any 51 SPP players, conceding games to tank stops being a viable option. Each guy at that level has a 50/50 shot of leaving the team in disgust when you concede. Also, I'm not sure how you arrange the games, but there might be an issue of some kind with entering games just to concede - since you're giving away your MVP and money, the opponent is getting a major advantage at no risk, and there may be a rules issue there.

Nick Page said...

The 51 SPP thing is definitely good to know, thanks!

We have a 'feeder league' running with as many pick up games as you want. On Saturday we're each transferring one team into a closed league with only scheduled matches allowed.

So this isn't a long term solution, and whoever I end up scooping to will get a short term advantage for sure, but since they have to be in the open league to play the game they're not in a position to actually use the unfair advantage. If they're transferring in themselves they need to stay under the cap anyway, so at worst I'm helping them catch up to people who had more time to level up.

More likely I'll scoop to a new team of Robb's so he can have a more diverse set of teams to play for fun going forward.

Robb said...

Update on trivial news: Lestzh now also suffers from a broken collerbone. Out of pity/spite for me, he was the MVP that game, and has leveled into the kick skill.