JackassRampant
Joined: Feb 26, 2011
|
 Posted:
Aug 26, 2023 - 03:55 |
 
|
Okay, so there was an exchange a few months ago about Dedicated Fans, and I did some crunching and came up with some stuff on the value of each DF point.
F = Dedicated Fans score.
S = Touchdowns scored.
D = Delta between two hypothetical F states.
D0 = Delta between two hypothetical starting F states.
DN = Anticipated delta between two hypothetical starting F states after N matches (D1, D2, D3, etc).
T = Tie rate, expressed as a fraction or decimal.
Alright, so every Dedicated Fan to start with, up to five, in addition to the free one:
* Reduces your starting budget by 10k gold;
* Reduces your starting TV by 10k gold;
* Increases your starting Dedicated Fans score (D0) by +1, from a base of 1.
After each match, you score 5k gold in Treasury for each Dedicated Fan on your team or your opponents, plus (4±2) 5k gold increments, plus 2 more 5k increments per TD scored (we'll call that S, since we're using T and D already). Since 4±2 averages 4, and a break-even team will trend to a DF score of 4, we can do some mental shorthand to say that your team will over time earn (8+2S+F) 5k increments per match. S kind of tracks win rates, but very imperfectly.
Also, after the match, your F score increases by 1 if you win, on a (7-F)/6 chance. If you lose, there is a (F-1)/6 chance your F decreases by 1. Observe that D has a D/6 chance of diminishing by 1 after each win or loss. But there is no chance of D diminishing on a tie.
As it works out, the formula for this is:
D(N+1) = DN x (5+T)/6, or
DN = D0 x ((5+T)/6)^N
Observe that W:L doesn't matter. Also, D is D: there's no difference between F1 vs F4 and F3 vs F6, fans are fungible.
Now, another funny thing, if you look around, you will see that T is almost never that far off of 0.2. Additionally, money means less as the season wears on, so even if T is an unconscionably high average of 0.3, more gold later on doesn't mean as much and the compounding orders of magnitude still don't make the difference between 5.2 and 5.3 all that significant: every 5% of tie rate (which is a lot) is less than a 1% increase on the base. So T, it's a legit part of the formula, but it doesn't really matter. 5+T is 5.2, we're not doing rocket science.
So that leaves us with a progression that I plugged into Excel. I could post it if it mattered, but the easy takeaway is that you break even after 2.067 matches, you make a 100% gold profit (so 20k earnings) after about 5 or 6 matches (again, precision is folly), and you average 200% (30k earnings) after 11 matches or so, by which point you can't expect noise not to have taken over even if D=5 and you're considering F6 vs F1, and money isn't all that valuable anyway by then. It's better than that, because it comes in incrementally, and a dollar today is better than a dollar tomorrow. It's worse than that in comparison to starting cash, though, not only because a dollar today and all, but also because starting cash can hit the margins between worse and better starting players (not something you can do with Treasury, where you have to pay the whole thing, and also doesn't apply to starting reserves), and then there's the RR cost double thing.
So now we have: Each purchased DF:
* Reduces your starting budget by 10k gold;
* Reduces your starting TV by 10k gold;
* Increases your starting Dedicated Fans score (D0) by +1, from a base of 1.
* Pays off incrementally to treasury, reaching 10k at 2+ matches, 20k at 5-6 matches, and 30k at 11+ matches before it becomes irrelevant to consideration.
Just wanted to throw that out there, see if y'all can tear it apart and make further inferences. |
_________________
Lude enixe, obliviscatur timor. |
|
Storr
Joined: Mar 25, 2020
|
| Posted:
Aug 26, 2023 - 19:30 |
|
So since one rarely purchases something after game one, and each DF breaks even after 2 games and pays off more afterwards, one should always buy DF with spare money from team building even in short competitions like RRR. And one could even think about making small sacrifices in team building (except on rerolls) if the team starts without DF otherwise.
At least that's what I'd conclude from this.
Thanks for the work, JR! |
|
|
JackassRampant
Joined: Feb 26, 2011
|
| Posted:
Aug 26, 2023 - 21:56 |
|
Yeah. That's about right. |
_________________
Lude enixe, obliviscatur timor. |
|
JackassRampant
Joined: Feb 26, 2011
|
| Posted:
Aug 26, 2023 - 22:48 |
|
Things that make starting Dedicated Fans better:
* You have leftover cash after buying your team of choice: this makes it a no-brainer, but the others are all just contributory.
* You have all your re-rolls and enough players to work with.
* Marginal inducement value could pay big dividends in your format (say, if Bomber and Cindy are running wild).
* Your players are fragile, especially if they are expensive.
* You want to take random skills, particularly on more durable and cheaper players.
* Your season, including postseason, involves at least 10 relevant games.
* You are prone to scoring ties (this is minor, bordering on trivial).
Things that make Dedicated Fans worse:
* Your players are tough and expensive.
* Your starting players have good starting skills from primary categories.
* You need all your starting cash to bring your team up to the point of diminishing returns.
* The marginal value would let you buy a desired Re-Roll.
Rosters that get more value from Dedicated Fans: Amazons, Humans, Chaos Chosen, Elven Union, Lineman-driven High Elves.
Rosters that get less value from Dedicated Fans: Dwarfs, Chaos Dwarfs, Ogres, Nurgle, positional-driven Dark Elves.
Rosters that get less but should do it anyway: Snotlings. |
_________________
Lude enixe, obliviscatur timor. |
|
JackassRampant
Joined: Feb 26, 2011
|
| Posted:
Aug 27, 2023 - 02:22 |
|
Another way to look at it ...
If you never tie, then for any two given DF states, ∆D=D/6, or a 16.67% attrition rate.
If you always tie, then for any two given DF states, ∆D=0, or a 0% attrition rate.
In fact, for T=0.2, ∆D is (13/90)D, or 13.33%. For T=0.25, it's (7/48)D, or 12.5%.
So, your net DF attrition rate is one sixth of one percent per (W+L)%, or if you prefer, 16.6667% minus one sixth of one percent per T% (same number). So if you tie 4% of your games (not likely), you'll suffer 16% DF attrition per match, compounded each match. If you tie 10% (also not likely), you'll lose 15% of D per match.
16% ties: 14% attrition.
19% ties: 13.5% attrition.
22% ties: 13% attrition.
25% ties: 12.5% attrition.
28% ties: 12% attrition. |
_________________
Lude enixe, obliviscatur timor. |
|
Gridironman
Joined: Mar 18, 2022
|
| Posted:
Aug 28, 2023 - 05:37 |
|
I always try to max out my dedicated fans and 3 RRs at the expense of an apothecary if need be. |
_________________
An Amorican Nuffler that bashed in his youth. |
|
|
|
| |
Gnomes are trash
Search
