What's FF worth?

[mattgslater]

Okay, so the question is: "what is Fan Factor worth?" Is your FF a drag on your team, or is it helping?

We've established that the cost of FF behaves differently for established teams than it does for new teams. New teams consider FF in lieu of "garbage value" that's not leading to an inducement, with starting cash that would probably otherwise go to an Apothecary. Experienced teams consider the value of an Apothecary as 10k inducement value. Teams above the Spiraling Expense threshold add 667 GC per FF point or per point of difference over SE threshold (whichever is less) to the cost.

We've figured out how to calculate the cash value of FF, using two charts, one based on the difference, and one based on the difference to double the opponent's FF. Since opponents' FF varies, it's best to think about mean odds of each level of FAME for FF7, 8, 9, 10 and 11, against FF7, 8, 9, 10 and 11.

@ FF7
FAME 2: 0.05%
1: 25.45
0: 9.18
-1: 63.67
-2: 1.65

@ FF8
FAME 2: 0.14%
1: 34.54
0: 10.11
-1: 54.78
-2: 0.43

@ FF9
FAME 2: 0.29%
1: 44.49
0: 10.43
-1: 44.72
-2: 0.06

@ FF10
FAME 2: 0.60%
1: 54.61
0: 10.11
-1: 34.68
-2: 0

@ FF11
FAME 2: 0.05%
1: 64.26
0: 9.18
-1: 25.49
-2: 0

What's this mean in kickoff table terms? By a funny coincidence (yes, it's a coincidence), the math comes out almost perfectly to: 1/18 of a gained or denied TRR per point of FF (the difference is just a smidgeon over that: FF7 nets 6.96/18, while FF11 nets 11.02/18). The number of RRs per point of FF per game in this case is 10/36 x 1/18 x EMD, or 0.5 plus or minus 0.1. That means one FF point is worth 0.4, 0.5 or 0.6 RR counters, or 0.2, 0.25 or 0.3 TRRs, an inducement value of 20k, 25k or 33k, depending on EMD. Per FF, that's more than double its inducement value. We haven't gotten to the unusual kickoff rolls yet.

Does it cost money?

FF7 vs. FF(7-11) earns 2554 gc/game. 2554/667= 38k gold. If your TV is 40k above the SE threshold, you're not getting money for your FF. If your TV is at least SET+FF, you're burning (667x7)-2554 = 2115 GC per match for your FF.

FF8 earns 3481 per game. The breakeven TV is SET+52k gold. At peak, you're burning (667x8)-3481 = 1855 GC per match.

FF9 earns 4508 per game. The breakeven TV is SET+68k gold. At peak, you're burning (667x9)-4508 = 1495 GC per match.

FF10 earns 5582 per game. The breakeven TV is SET+84k gold. At peak, you're burning 1085 GC per match.

FF11 earns 6639 per game. The breakeven TV is SET+100k gold. At peak, you're burning 695 GC per match.

So in this case, where everybody is FF 7-11, losing-but-staying-around steepens your climb: FF7 costs 1500gc per match compared to FF11, even after including the impact on Spiraling Expenses. And FF pays at least double its inducement value in TRRs alone.

[mattgslater]

So what are Throw a Rock and Pitch Invasion worth?

Pitch Invasion is easier. The value of PI is EMD/216 (1.5%±0.3%) times the number of expected opponents on the pitch, times FAME+1, minus EMD/216 times the number of expected players you have on the pitch, times your opponent's FAME+1, in stuns. A stun is worth a knockdown and a lost action, which does not count to turnover or risk further injury. Obviously, not all stuns are equal in value or impact, but let's not worry about that.

How many players can we expect on the pitch per side? Obviously, not more than 11. I think we should plug in 10 and 11. So that's 1.2%, 1.5%, or 1.8% times 10 or 11, plus that sum times the sum of FAME 1+ plus FAME 2 odds. Assuming slow teams assume 11 players and low EMD and fast teams assume 10 and high EMD, that's a range of 13.2% to 18% of a stun per match on each side. Assuming the true EMD is the average of the two, then we have:

Fast vs Fast: 18%(FAME+1) vs. 18%(FAME+1)
Fast vs Slow: 15%(FAME+1) vs. 16.5%(FAME+2)
Slow vs. Slow: 13.2%(FAME+1) vs. 13.2%(FAME+2)

FF vs Aggregate opponent FF7-11, 1+FAME gain – 1+ FAME loss (net gain) +(net gain for last +1 FF)
FF 7: 1.255 – 1.67 (-0.41)
FF 8: 1.348 – 1.556 (-0.21) +0.2
FF 9: 1.451 – 1.448 (0) +0.2
FF 10: 1.558 – 1.347 (0.21) +0.2
FF 11: 1.664 – 1.255 (0.41) +0.2

So one FF point is worth between 2.6% and 3.6% of a stun per match. That's 28-40 matches on average before it costs you, what, two actions? Two actions tends to mean more for teams that take fewer stuns on account of low EMD. The veteran team should ignore this factor. Before we get to Throw a Rock (which sounds ignorable too, but has (very little) long-term cash value), that FF point is netting almost 400 gold per game above its added SE value and double its inducement value in TRRs.

[mattgslater]

Throw a Rock is 1/18 on the kickoff table. If EMD is baseline (3.24), EMDxTaR = 0.18. There are 36 perms on TaR, each represents 0.5% of an instance per game at baseline EMD. I think we can also ignore EMD variance for TaR, because teams with higher EMD tend to be better prepared to cope with injury than slower/heavier teams that tend to have low EMD. I suspect a majority of teams run below baseline EMD, but for TaR, one has to consider meaningless drives to some extent as well. So let's factor "dead turns" into the injury results and consider all this little silly stuff to balance out, because we already know that marginal tweaks here are too small to matter. So one perm is 0.5% of an injury roll.
FAME +2: 15% to injure, 5% to be injured, net +10%
FAME +1: 13% to injure, 7.5% to be injured, net 5.5%
FAME +0: 10.5% to injure, 10.5% to be injured, net 0%

Hmmm... looks like 0.05 injuries per average FAME point, or one percent of one injury per FF point, citing the math above. An injury on a non-niggling, non-Stunty player is 7/12 of a stun (2 actions), 1/4 of a KO (one drive, plus half the next, a quarter the next...), 1/12 of a BH, etc... let's call it 7/12 of 2 actions, and 5/12 of 8 actions, or 4.5 actions, plus 1/18 of a missed game, 1/36 of a stat loss and 1/36 of a dead player. Assuming half of all stat losses result in termination, that's 1/2400 of a player saved per match, and the same fraction of a player-match saved per match, and 4.5/100 lost actions saved per match, per point of FF. The permanent value is player value/2400, or player cost x 4, divided by 10k. Even for an elf team with median player value 120k, that's 48 gold, not exactly momentous. Still, it adds to the 375 net gold (after SE modifier), to make it a little over 400k gained in gold, and when the 0.045 lost actions are factored into the 0.06 lost actions (.03 stuns) from Pitch Invasion, that's one lost action per ten games per FF point. Negligible? You decide.

So in a perpetual format, where FF ranges from 7-11, one point of FF is worth its cost in both TV and SE terms, plus a "profit" that amounts in the long run to a little over 0.04 on the Winnings roll, between a tenth and a fifth of an Extra Training and 10% of an action per match. If you're below SE threshold, it has the same value except that it nets 0.11 on the Winnings roll instead, a little over 150% more. Clearly, higher FF is better than lower FF, all things considered, in both in-game and metagame terms.

Next, rookies. Then a summary and we're done.

[mattgslater]

For rookie teams, we're going to consider the value of FF 0, 1, 2, 3, 4 and 5 against an opposing FF of 0, 1, 2. This represents teams with up to two wins, one of them taking up to 3 FF. I'll test FF8 against 0, 1 and 2 also, just for giggles.

First, Games to Break Even (GBE) = 10k/winnings gain. Winnings gain = gain on FF+ table, plus gain on F2+ table.

FF1 vs. 0: 1550.
FF1 vs. 1: 1490.
FF1 vs. 2: 1230.

FF2 vs. 0: 1300.
FF2 vs. 1: 1490.
FF2 vs. 2: 1300.

FF3 vs. 0: 1290.
FF3 vs. 1: 1480.
FF3 vs. 2: 1490.

FF4 vs. 0: 1810.
FF4 vs. 1: 1300.
FF4 vs. 2: 1420.

FF5 vs. 0: 1440
FF5 vs. 1: 1060
FF5 vs. 2: 1440

FF8 vs. 0: 600
FF8 vs. 1: 900
FF8 vs. 2: 1500

So if you look at the range of FF as alternative to Treasury (up to 30k), and look out a couple games to where you're giving up about 2/11 of an Apothecary, you're getting 1230-1810 GC per game, or about a seven-game payoff. Given that the FF points will probably live about 10-11 games on average (arbitrary and probably low, but convenient, and besides a GC today is worth more than a GC tomorrow), you've got a 50% eventual payoff for the FF (that is, you pay 10k, and get 15k in Week 1 value before it dies).

As we figured out earlier, by taking FF2 instead of 20k cash, you're giving up 2/11 of an Apothecary availability to net 5k cash per purchased FF point over time. 2/11 of an Apothecary is 18k inducement value. As a 50% chance per match to be used on a death, it's 9% of a player's value, or about 10k cash, x 5/6. That's less than the 10k profit on the FF. That makes the 2 FF sort of cash-neutral for the 20k saved for Apoth, or maybe a little less, if you think you have a 50% chance to lose a 100k player.

In the next post, I'll look at 18% of an Apothecary availability against the TRR value of FF2 on BC/CF results, then the same for PI/TaR. I can pretty much assure you that unless one or more of my assumptions is just crazy off, you'll rush out and buy 1-2 FF with your "garbage" cash from here on out. That's not what I was expecting, by the way. I thought I was going to come to the conclusion that you should save your cash, but now I don't think so.

[Greyhound]

Matt, even though I have played the game for a little bit now, most of your posts reference acronyms which escape me, making the whole post very hard to read.

I think it limits the audience to a very small crowd of followers who use the same language. It probably also narrow it down to native english speakers from your dialect (American?)

[James_Probert]

Matt, even though I have played the game for a little bit now, most of your posts reference acronyms which escape me, making the whole post very hard to read.

I think it limits the audience to a very small crowd of followers who use the same language. It probably also narrow it down to native english speakers from your dialect (American?)

With all due respect to both you and matt, while matt does occasionally reference acronyms beyond me (particularly his use of american football slang for positioning), in this thread he has used no acronyms he hasn't previously defined in the thread (asides from the obvious GC for Gold Crowns (there, I've defined it!)), which makes this a very readable thread (to me atleast)

EDIT: apologies, he hasn't always defined the acronym as such, but he's alway typed it out in full at least once before using the acronym.

[mattgslater]

Matt, even though I have played the game for a little bit now, most of your posts reference acronyms which escape me, making the whole post very hard to read.

I think it limits the audience to a very small crowd of followers who use the same language. It probably also narrow it down to native english speakers from your dialect (American?)

No sweat. It's not a language barrier: my terms are all in the text. Still, it's rambly and hard to follow. Let me break it down.

If you're at peak TV and those around you are also at peak TV, every point of FF you have is worth 400 gold per game, or 4% of +1 on the Winnings roll, after Spiraling Expenses.

If you're not paying SE, but your FF has hit peak TV range, every point of FF you take is worth 1100 gold per game, or 11% of +1 Winnings.

If your FF has hit peak TV range, the per-point inducement value of the advantage on BC/CF roll is 20k-30k. The value of the advantage on TaR/PI rolls is negligible.

If you have a rookie team, every point of FF you hire gets you ~1400 gc per game, for a seven-game payback. FF2 is a wash to 20k banked in terms of the odds of winning 10k extra times the value of the 0.18 Apothecary-games you lose, if you use your Apoth 5 times out of 9. We haven't yet gotten to the extra RRs, stuns and injuries: those are the gravy.

Predictable conclusion: FF more-than justifies its TV in inducement value alone. Therefore, the more the merrier.

Less predictable conclusion: FF more-than justifies its Spiraling Expenses add in winnings if it is similar to the FFs around it.

Freaky conclusion: The conventional wisdom that you shouldn't start FF on a rookie team only applies if you're bringing a new team into an established format. In a "fresh" format, like a seasonal reset or whatever, you should spend any small remainder cash (up to at least 20k, maybe more) from your starting 1M on FF instead of banking it, particularly if you play a season of 9+ games with a postseason tournament, or are restarting a perpetual format (or even entering a perpetual format against new early competition).

[Greyhound]

No sweat. Let me break it down.

Cheers

If you're at peak TV

How do you define peak TV? is it 1000 for a dwarf but 2500 for chaos for instance?

[mattgslater]

In this case, I mean by "Peak TV" what I should be calling "Peak FF." High enough that you're never/seldom giving up FAME 2, and that your team's climb has reached a state of relative equilibrium. Does that help?

[Greyhound]

cheers... Finally got my head around the concept.

[Coach]

I'm still not convinced that spending the odd 20k at team creation on Fan Factor is worth it.

I'd much rather increase the likelihood that I can afford an Apothecary after the first game, or purchase a new player/re-roll sooner.

If you start with zero then any draw or win you are fairly likely to get a Fan Factor increase anyway. If you paid to start with 2 Fan Factor already you just reach the point where getting an increase is more hit and miss sooner. You say that at peak TV (or FF) that it is work 400 income per game, not sure how much that 2FF is worth for those few early games though.

Have you run the numbers on how many games it takes to hit 7 FF based on two teams with the same WDL record when starting with different amounts of FF? I may have missed this if you did.

[mattgslater]

@ Coach: What you're really talking about is the odds that you'll fail an FF roll within a margin of the number of purchased FF before you win a FAME point off that same margin. If we're assuming 7 games for the latter, how do we calculate the former?

Let's take the example of FF1+W vs. FF(0-G), to keep our math easy, where W is Wins and G is Wins plus Losses (L) plus Ties (T). With FF1, you're guaranteed to retain your bonus until after your second win. Let's call that second win W2, and all the games that it takes to get that second win G2. So if you're a .500 coach, that's about 4 games on average. If you're a winner, it's more like 2. If you keep losing, and fall below XFF-4, your pace of winnings will fall off. XFF in a young league tends to track G/2 for each coach, so that takes about 10 games with no more than 2 wins, probably enough to hit payback anyway. That said, coaches who hit SE without keeping up on FF get a bad deal for their FF in SE terms.

Once you've hit those two wins, assuming you haven't taken the loser track described above, you have a chance of failing an FF roll on further non-tie games. Since you only bought one FF, we're only going to talk about the chance of winning or losing by a margin of one. Since the LCM of the ranges involved in losing and winning is 216, we're going to talk in terms of 216ths.

The format will be: FF: perms to lose on a win, perms to lose on a loss, percentage to lose assuming .45/.1./.45, average number of games to get there from FF1, cumulative chance to fail to get there assuming that number of games and no failures, and cumulative chance to fail assuming you win out.
2: 0, 0, 0%, 2, 0%, 0%
3: 1, 6, 3%, 4, 0%, 0%
4: 3, 12, 6%, 7, 9%, 0.5%
5: 6, 18, 10%, 9, 19.5%, 1.5%
6: 10, 24, 14%, 11, 35%, 4.5%

So you have better than an 80% chance of near-certain payback if you're winning some and losing some, and a 2/3 chance of averaging a 50% payback. That's actually low, because at that level you have a lot of chances to lose by more than one and thus get to an easier target, and I didn't account for that. If you're winning them all, you're 95.5% to make it almost there. After that, you have 15 perms to fail after winning on FF7, and 30 after losing, 21 and 36 at FF8, 25 and 30 at FF9, 27 and 24 at FF10, 27 and 18 at FF11, 25 and 12 at FF12, 21 and 6 at FF 13, and 15, 10, 6, 3, or 1 at higher FF. At no point do the odds of losing that one FF point because you had it ever exceed 1/6 on a loss and 1/8 on a win, and usually they're much, much lower. Since the payoff hits 1/7 of the time, it's happy gravy.

If we can extrapolate from the math on the first page (yes, lazy), you get about .1 Apoth/match per 10k banked, in addition to the 10k later, guaranteed. Is that .1 Apoth worth more than the savings? I think it depends on what kind of damage you take in match 2, doesn't it? That 0.1 Apothecary has no chance of saving an irreplaceable player in match 2, because nobody has had a chance of getting irreplaceable. Let's assume an average match yields 2 cas against, or 1/2 dead/retired (all 61+, half of all 51-58, on Cas table, = 1/4). Each Apoth use saves 3/4 of that player, or 3/8 of a dead/retired player, worth an average of 80k, so 30k. So that 0.1 Apoth saves you 3k in player value. Add that to the 10k you spent, and the payoff is now about 10 games, breakeven if you're a winner or loser, and not quite if you're average. The payoff for the Apoth is (probably) faster, but it doesn't come with re-rolls; in effect, you're "renting" the fraction of a TRR for the "interest" on your 10k.

[Coach]

Not sure you have answered what I was asking, the terms and numbers you keep throwing around isn't really that easy to read.

Team A has FF2 to start Team B has FF0

If they both draw their first game then Team A has a pretty good chance of a FF increase, Team B has a 100% chance.

They then both win their second game, Team A has a near 100% chance of an increase Team B still has 100% chance.

Both win their 3rd game, Team A still has a high chance of increase, Team B will still be at 100%

Then they both lose their 4th game, Team A has a higher chance of losing a FF at this point, though there isn't much it it. If they both drew, then A has a higher chance of it going down than B, ergo B has a higher chance of it going up as well.

So how many games with the same record for both teams before team B will likely catch up with team A?

The cost of the Apothecary isn't just defined on irreplaceable players, but you lose an expensive player and you are probably far worse off than you would have been if you saved the 20k. Surely losing a 100k player in the second match far outweighs the extra 400 (which seems insignificant) you get from having the FF at the start?

[mattgslater]

The cost of the Apothecary isn't just defined on irreplaceable players, but you lose an expensive player and you are probably far worse off than you would have been if you saved the 20k. Surely losing a 100k player in the second match far outweighs the extra 400 (which seems insignificant) you get from having the FF at the start?

Yeah, sure, if you lose a 100k player in the second match with 30k-40k in the bank, you'll be kicking yourself for buying the two FF to pay back 2800 gold per match (against the 20k you put out, no less). Now, you're not going to average value 100k per player in match 2. I used 80k. 0.18 Apoth/matches, times 50% to use, times 75% to work, equals 0.0675. Multiply by 80k, and you get 5,400 gold, so the basic cost of the 2FF vs. 2RR is 25,400 gold, effectively payable after match 2 or 3 (when you have an Apoth either way and relative TV bears consideration). That's an 9 game payback at 1/7 payback per game on 20k. What are the odds of paying off 30k in 9 games?

Let's assume you're always 2 FF ahead of your opponent, and you play one win and one loss at each FF point. In this case, your winnings bonus for FF2 is 2,210, plus your F2+ gain.

Format:
Your FF vs opponent's FF: Winnings/expected 2-game winnings/total: Chance of not failing by 1-2 on win/loss: aggregate.
2 vs 0: 2850/5700/5700: 100%/100%
3 vs 1: 2970/5940/11,640: 99%/97%: 97%
4 vs 2: 2900/5800/17,440: 98%/92%: 87%
5 vs 3: 2720/5440/22,880: 96%/86%: 72%
6 vs 4 (one match): 2850, totaling 25,630. So that's a 9-match payoff at .500 vs. all .500, with 72% odds. Even on the other 28%, most of it still includes a gain at half rate (after all, the chances of failing within the purchased FF margin fall by more than half after the first failure, when the margin falls from +2 to +1). And failures mostly come at the end on that chart: more than half of all failures are in the last two games, leaving the payback at 11 games or less. Of the others, the odds of failure with no margin before payback are too low to consider, though it might take several games.

This scenario is sort of a good-case scenario, but not a best-case one. If FF on the opposing side gets high enough that FAME 2 is nigh-impossible (not just rare), you'll make less. But if you're facing FFs equal to or better than your own sometimes, or if you're playing FF0 at FF5, say, you get a huge advantage, netting 3250 per game. (That's sort of a sweet spot.)

That's only the metagame aspect: money and death/retirement. It doesn't account for the other impacts of that 0.18 Apo/match or the 2FF, like lost actions/zones on further drives prevented by the Apoth, crippling-but-not-career-ending injuries Apothed successfully, lost bench and value over replacement/JM on missed matches, or BC/CF/TaR/PI results. If you consider 10+ games of FF per FF point, then you have 10x the value of the FF on a TaR/PI vs. 0.18x the value of the Apothecary on in-game (and next-game) impacts. Is one Apothecary worth 55.56+ games' worth of potential FF impact on TaR/PI? I'm not doing that math; whatever the remainder is is too small to consider. That leaves the FF impact on RR counters and the nine-game payback as the sole survivors. Is the interest on your 25,000 gold worth the added portion of a TRR?

Also, it must be stressed that format is critical. If you're going into an established perpetual league with a new teams and expect to play as a big underdog against veteran opposition, spare cash spent on FF doesn't pay off in any way, and you'll also take more casualties, and need your Apothecary faster. It only works if you're among equals. If you're going into a non-progression format with non-Stunties, you never want to bank anything, and you should compare FF to AC/CL.

[Greyhound]

Tangent alert: What is FF worth in a resurrection tourney?

2 cases:
CASE A: the tourney rules allow you to spend your money on skills, so 2FF is worth a single skill.
CASE B: the tourney rules allow you to spend your money only on staff/players, so 2FF should be compared to the cheerleader/coach option.

Once you removed the $$$ value of FF, are still worth it? It's hard to balance or weigh the impact of a skill but I think an extra Block on your team is probably making Case A redundant and you'd go for the skill rather than the FF (unless it's 1FF I guess)