What's an AC/CL worth?

[mattgslater]

Oops. 4x3x40k = 480k, not 640k. So to make it a wash, you have to have a team that tends to play a whole extra drive, or both sides have to value a TRR at Extra Training, or you need a Master Chef, or you need to KNOW you're a FF underdog. Any two of those makes it a good idea.

@Smeborg: I think there's value in bucking many trends, where the trend's value is marginal. This is a good example: sometimes, just doing what the other guys aren't is worth it. Certainly when there are too many AC and CL coaches, you can stay lean by just taking none at all.

[mattgslater]

Hmmm... 5x40kx3 is just a little less than 4x40kx4, and both are just a little less than 648k. I think we can peg BCB/CFB at 4. So it's worthwhile to win your AC+CL war if your RR counter value (RRV) times your expected meaningful drives (EMD) > 162k, and then remember that it's 25% better if you're an FF underdog and 25% worse if you're an FF overdog. If you play a bash team or a struggling agility team, with EMD=3, you break even at RRV=54k, or TRRV=108k. TRRV=108k only if you constantly run into Master Chefs, or if you are always inducing Extra Training (or would if you could). You might take them for situational purchases if neither of those applies, and it might be worth it on a team with pricey RRs and money problems, like Necro, Norse, Nurgle or Ogres.

If you play a successful agility team (or if you get turned over on offense over and over, and keep coming back for more), with EMD=4, you break even at RRV=40.5, or TRRV=81k. TRRV=81k if one side pays more than 50k for TRRs and the other doesn't have enough rostered. It's also worth it if you're suffering a lot of casualties and are cash-poor, because that sets TRRV to double cost. So if you're trying to be TV-conscious by saving TRRs on an elf team, you can cover for it by taking an AC and a CL.

Skaven and Vampires seem to benefit more than most on this math, getting a disproportionate number of quick TDs and meaningful drives, with high TRRV (for AG teams) and money management concerns. Also, I've seen a lot of Wood/Dark elf teams with one RR or none at all to take extra positionals. This is a risk/reward thing, and when it goes wrong with early player death the team sometimes takes a long time to recover, and buying enough RRs (at double price) seems like a low priority. I'm not a fan of this tack, but if I did this, you better believe I'd hire an AC and CL.

[Asperon Thorn]

If I wanted a game to be all about number crunching, I'd play 40k...

+1

The last few table top 40k games I have played you could pretty much just compare army lists and then save the time of the actual game.

"Oh, you have this. . let's see my counter is. . but your counter counter. is, and my counter to that. . . but then. .yeah I can't counter that one thing . . .

. . basically roll 6 dice, if you fail 4 armor saves I win, if you make them, you win. . game over."

Asperon Thorn

[mattgslater]

That is so never happening in Blood Bowl; no matter how much number-crunching you do, all it will ever be is one advantage among a possible many. You can reason your way into BB mastery, but to do so you have to be (or make yourself into) a polymath; on top of 40k-esque resource management, BB has actuarial and tactical elements far beyond the level of 40k.

See, for 40k, this kind of analysis is the defining skill in the game. In BB, you can do this to get a leg up. It's like the difference between maintaining your engine and winning the race: if your car isn't running well you won't win, but NASCAR will never break down entirely to tune-ups and engine tinkering.

40k doesn't care about that: the actual "game" itself is just where you prove the theory you went in with. The smoother-running engine wins 90% of the time. In BB, the metagame is just a prelude, one more phase of the action. A 40k army is a program operated by a technician, while a BB team is more like a tool wielded by an artist. A Magic deck is sort of a compromise between the two.

[mattgslater]

Rookie on rookie, BCB/CFC is 3.6. 648k/3.6 = 180k. In 3 drives, you need a TRR value of 120k. In 4 drives, you need a TRR value of 90k. This makes an AC/CL a fair value in Winnings terms, and about inducement quality in TV terms. For most teams, that's not so hot. I think you need more than half your opponent's FF and no more than your opponent's FF+2 or double opponent's FF, in order to be reasonably assured of getting maximum value on one AC/CL.

[mattgslater]

How does it stack up against FF? What I'll do is compare FF0, FF5 and FF10 to FF+2 and an AC/CL for the underdog, and then cover a larger gap just to see if I'm missing something, like maybe 12 vs 7. So...

Note: this comparison is only good for CF/BC. For Throw a Rock, Pitch Invasion and Winnings, FF value is over-and-above. Throw a Rock and Pitch Invasion are 30% as likely as CF/BC; value is highly subjective, but I think it's more like a Wizard than a TRR.

Team A: FF0 vs. Team B: FF2
Average FAME (for B): 734/1296 (+0.57)
Average BC+CF advantage (for B): +2.71
BCB/CFB (A/B): 4.17/3.37.
So at the rookie level, a CL and an AC are worth a little under twice their weight in FF on the average... before considering thrown rocks, pitch invasions and more than 2k per FF per match winnings, at this level. I'd rather have the FF.

FF5 vs. FF7
Average FAME (for B): 0.46.
Average BC+CF advantage (for B): 2.24
BCB/CFB (A/B): 4.44/3.6
So here the +2 FF are markedly less valuable and the CL/AC is much better.

FF10 vs. FF12
Average FAME (for B): 0.43.
Average BC+CF advantage (for B): 2.13
BCB/CFB (A/B): 4.52/3.67
See a trend?

FF7 vs. FF12
Average FAME (for B): +0.91 (0.40 per 2 FAME)
Average BC+CF advantage (for B): 4.43 (2.21 per 2 FAME)
BCB/CFB (A/B): 4.77/3.07
So if you're a big underdog, there's potentially even a 20% bonus to the net value of an AC/CL.

But if you're too far off...

FF0 vs. FF8
Average FAME (for B): 1.59 (just under 0.2/FF, a smidge less than the others)
Average BC+CF advantage (for B): 6.74 (1.68/2FF)
BCB/CFB (A/B): 3.78/1.81
Not so hot. The lower-FF team's AC/CL is a better bargain than the other guy's FF investment, I guess.

[mattgslater]

Ah-ha! I can pare it down to a comparison of two numbers!

Factor 1: RR Value: We can simplify the value of a TRR to TRRC x2, unless both teams can be expected to have enough TRRs, then TRRC. As you'll see below, TRRC won't ever be enough. So TRRC x2 it is, with the caveat: "AC/CLs don't pay for themselves if you have enough TRRs think the other side will have enough TRRs, too." Of course, you might just round down on your RR count, if you want an AC/CL. Let's factor that 2 out because a counter is half a TRR, leaving us with TRR value.

Factor 2: Expected Meaningful Drives
I'm assuming 3.24 drives per game, and factoring it into the other side of the equation, now 10k (coach value)/3.24. You'll see why in a minute. This is an arbitrary assumption to make the math easier, and I suspect that most teams will have fewer, while some will have more. Fortunately, 3.24 ± 20% is from 2.6 to 3.9, which nicely sums up the practical range. Moreover, we can break these down by race, much as we can by TRRV. So I've just got a racial multiplier by speed and available strategies.

Factor 3: the Odds
Brilliant Coaching comes up 5/36 of the time, with 9 perms. So BCB implies 5/324. Let's factor this out of the cost of the AC, so now we have 10kx324/(3.24x5), or 10kx20, or 200k.

So now we have targets for BCB. If BCB is this number or higher, winning the AC/CL battle by one is worth it. I'm going to keep it to one decimal place, so the math stays simple. All the above calculations boil down to one number.
Halflings: 75k* x 1 = 75k. 200/75 = 2.7. *With Master Chef; without, 3.33.
Skaven: 60k x 1.2 = 75k. 200/75 = 2.7.
Elves: 50k x 1.2 = 70k. 200/70 = 2.9.
Ogres: 70k x 1 = 70k. 200/70 = 2.9.
Wood Elves: 50k x 1.2 = 70k. 200/70 = 2.9.
Underworld Pact: 70k x .95 = 66.5k. 200/66.5 = 3.0.
Vampires: 70k x .95 = 66.5k. 200/66.5 = 3.0.
High Elves: 50k x 1.15 = 65k. 200/65 = 3.1.
Chaos Pact: 70k x .9 = 63k. 200/63 = 3.2.
Necromantic: 70k x .9 = 63k. 200/63 = 3.2.
Goblins: 60k x 1 = 60k. 200/60 = 3.3.
Chaos Dwarfs: 70k x .85 = 59.5k. 200/59.5 = 3.4.
Undead: 70k x .85 = 59.5k. 200/59.5 = 3.4.
Lizardmen: 60k x .95 = 57k. 200/57 = 3.5.
Khemri: 70k x .8 = 56k. 200/56 = 3.6.
Nurgle: 70k x .8 = 56k. 200/56 = 3.6.
Slann: 50k x 1.1 = 55k. 200/55 = 3.6.
Chaos: 60k x .9 = 54k. 200/54 = 3.7.
Norse: 60k x .9 = 54k. 200/54 = 3.7.
Dark Elves: 50k x 1.05 = 52.5k. 200/52.5 = 3.8.
Orc: 60k x .85 = 51k. 200/51 = 3.9.
Humans: 50k x 1 = 50k. 200/50 = 4.0.
Amazons: 50k x .95 = 47.5k. 200.47.5 = 4.2.
Dwarfs: 50k x .85 = 42.5k 200/42.5 = 4.7.

Finally, BCB. Two calculations: First, subtract your FF from your "target" FF, or a stand-in FF for the team/teams you're competing against. Be aware this number may float. Second, subtract twice the lesser FF from the greater FF (it doesn't matter whose is higher; either way, the second calc has the same effect).

Your net FF: your base BCB
+7 or more: 3
+5 or +6: 3.1
+4: 3.3
+3: 3.5
+2: 3.7
+1: 3.9
+0: 4.1
+1: 4.3
+2: 4.5
+3: 4.7
+4-5: 4.9
+6 or more: 5

Then, 2x lower minus higher (negative number if higher is more than double):
+4 or more: No modifier
+3-+2: -0.1
+1: -0.2
+0: -0.3
-1: -0.4
-2 or -3: -0.5
-4: -0.6
-5: -0.8
-6: -1.0
Less than -6: -1.1, -0.1 per point below, limit -2.

So if you're going into a perpetual league (opp FF 8?) with a rookie Skaven team, then you're comparing 2.7 (for Skaven) to 5-1.3, or 3.7. Yeah, go ahead and take an AC. If you have a dominant Orc team in the same format, with FF 11, you're comparing 3.9 racial target to 3.5 BCB, not worth it.

[mattgslater]

So, the equation is:

The Target
Halflings w/MC: 2.7.
Skaven: 2.7.
Elves: 2.9.
Ogres: 2.9.
Wood Elves: 2.9.
Underworld Pact: 3.0.
Vampires: 3.0.
High Elves: 3.1.
Chaos Pact: 3.2.
Necromantic: 3.2.
Goblins: 3.3.
Halflings w/o MC: 3.3.
Chaos Dwarfs: 3.4.
Undead: 3.4.
Lizardmen: 3.5.
Khemri: 3.6.
Nurgle: 3.6.
Slann: 3.6.
Chaos: 3.7.
Norse: 3.7.
Dark Elves: 3.8.
Orcs: 3.9.
Humans: 4.0.
Amazons: 4.2.
Dwarfs: 4.7.

Compared to...
Your net FF: your base comparison
(yes, this table smooths it out a bit, but it sure is easy)
+7 or more: 3.0.
+6: 3.1
+5: 3.2
+4: 3.3
+3: 3.5
+2: 3.7
+1: 3.9
+0: 4.1
-1: 4.3
-2: 4.5
-3: 4.7
-4: 4.8
-5: 4.9
-6 or more: 5.0.

Then, double the lower FF, and subtract from that the higher FF+4. If 2x lower is equal to or greater than the higher FF+4, you can ignore the odds of FAME 2 (it might be possible, just very unlikely). If add 0.1 times the (negative) difference up to 20 (or -2.0). So FF3 vs. FF8 is (3x2) – (8+4) = -6, so add -0.6.

So:
0 vs 0 FF gets you a 3.7 (4.1 - 0.4).
0 vs 8 FF: 3.8 (5.0-1.2)
8 vs 0 FF: 1.8 (3.0-1.2)
8 vs 4 FF: 2.9 (3.3-0.4)
8 vs 8 FF: 4.1 (4.1-0)
2 vs 8 FF: 4.2 (5.0-0.8)
5 vs 8 FF: 4.5 (4.7-0.2)
6 vs 8 FF: 4.5 (4.5-0)
7 vs 8 FF: 4.3
10 vs 8 FF: 3.7
12 vs 8 FF: 3.3
8 vs 12 FF: 4.8

I think this means that you get good bang for your buck on one or two ACs playing a low-FF team with expensive TRRs or a tendency to play more than three drives, if you don't have all the TRRs you want. And if you know you're going to be able to do it on one or two ACs, it may even be a significantly better fractional deal than that one last reroll... if you're in the top half of the above list, or if for coaches of your race you overvalue TRRs or play shorter drives. If you have your money thing worked out and don't need to keep earning, you may be best off trimming your FF to six or seven and hiring an AC and CL to maximize your chances of winning BC/CF rolls. I'm loath to do that, personally, as I consider an unusably-high FF to be a badge of honor. Besides, it pays for itself in SE anyway, right?

I don't think it's ever wise to play the escalation game; it's highly unlikely that 3x AC is worth 30k over none. So it's a game of 0, 1 or 2 ACs and CLs, for an investment of up to 40k. If your math ever tells you to take three, either stay at two or fire them all.

[mattgslater]

All the math boils down to this, I think.

1) Halflings? Stop here: Up to 3 each AC/CLs are categorically worth it.

2) Don't take any AC/CLs if:
a) You have the highest TV in your league.
b) You're Dwarfs.
c) You have all the TRRs you want, with no desire to cut any. If you're on the fence, or even just "thinking about it, but not seriously," keep reading.

3) Otherwise, take 1-2 AC/CLs if:
a) You pay 70k for a TRR
b) You play relatively high-scoring games (for or against); that is, you regularly score 3, or regularly score in losses, or regularly give up TDs in wins.
c) You desperately need a TRR, but you have so many things to buy before you can get it....

4) If none of the above, it's a judgment call.

When in doubt, AC/CLs are better if:
a) You have at least a few FF points (about half the league average, give or take),
b) You're routinely a FF underdog,
c) You love your defense, especially if your team has good ball skills and MA,
d) You doubt your offense, especially if your team has good AV and damage skills,
e) You have a 1TTD mechanism,
f) You pay 60k for a TRR,
g) You see a lot of Master Chefs not on Halfling teams.

AC/CLs are worse if:
a) You have no quick scoring game (passing or speedster),
b) You never face 1TTDs,
c) Your FF is more than double that of some of your credible opponents,
d) Your FF is well under half the league average,
e) You pay 50k for a TRR.