Justification for always having a 9 Fan Factor

Posted By: Zombie  - Dead Man Walking 
Posts: 2483 Posted At: (1/13/2002 4:23:20 pm) 

Reply:
Ok, those who are tired of hearing this, you can hit the "back" button now, 
though there's a lot of new stuff in here that you might like to hear anyway.

In 3rd ed, there was no question that 9FF was a must. 
Each extra point of FF basically gave you an extra 2.33k per game for the rest
 of your team's existance. Well, not that long actually, but only until you 
can expect to hit the 75k crowd no matter what. Still, that's quite a long time.

Now with the new edition, it's a little less obvious, but i think it's still 
worth it. With the new winnings table, 1 extra FF gives you 1.75k per game, 
and not even forever either. Since you get -1 on your FF roll for every 10 FF now, 
being higher in FF sometimes means not going up or even going down, and when that 
happens because of your extra FF, it has just been canceled permanently.  

For the sake of discussion, let's assume that when you win, you always get +2 on 
your FF roll, not withstanding the possible -1 (i.e. +1 for winning and +1 for either 
TDs or CAS). Let's also assume that you always get +0 when losing (-1 for losing and 
+1 for either TDs or CAS). That's just to make calculations easier. Let's also assume 
that you win 50% of your games and lose the rest (i.e. no draws). For the sake of 
simplicity, we'll assume no bonuses for playoffs either.  

With these assumptions, here are your chances of going up or down in FF:  
Result . . . . . 10FF . . . . . up . . . . . down 
win . . . . . . . -0 . . . . . . 3/6 . . . . . 1/6 
win . . . . . . . -1 . . . . . . 2/6 . . . . . 1/6 
win . . . . . . . -2 . . . . . . 1/6 . . . . . 1/6 
lose . . . .. . . -0 . . . . . . 1/6 . . . . . 1/6 
lose . . . .. . . -1 . . . . . . 1/6 . . . . . 2/6 
lose . . . .. . . -2 . . . . . . 1/6 . . . . . 3/6  

When between 1 and 9 FF, your chance of going up is 1/3; your chance of staying
 the same is 1/2; and your chance of going down is 1/6. When between 10 and 19 FF, 
your chance of going up is 1/4; your chance of staying the same is 1/2; and your 
chance of going down is 1/4.  On average, someone starting with 9FF will spend x 
games at 10FF (where that +1FF you started with actually gives you -1 on your roll) 
before getting to 12FF, at which point it's unlikely to make a difference anymore. 

In each of those games spent at 10FF, there's a 1/3 chance that the extra FF gives 
you -1FF (i.e. either by keeping you from going up or by making you go down), effectively 
canceling your extra starting FF from then on. Now that number x is what we're looking for, 
in order to know how many games you can expect to keep that +1FF advantage. And that's where 
i ran into a wall...  You see, i didn't know that fact until i wrote this, but looking at the 
table above, it appears that once you get at 10FF and above, your chance of going down is as 
good as your chance of going up. Of course, that's assuming a 50% win percentage and no 
playoff bonuses. This means that a team would be expected to remain at 10FF for a while. 
Even once you reach 12FF, your chance of going back to 10FF is pretty good (in fact, it's 
100% if we're talking very long term, as in infinity). Since your team is expected to be 
stuck at 10FF a lot of the time, it shouldn't take long before that 1/3 chance occurs and 
you lose your extra FF.  It will probably take around 6 games if you keep fluctuating at 
9 to 11FF for a few games, since you'll be at 10FF about half the time and the event occurs 
1/3 times. However, if you're lucky enough to reach 12FF without it occuring, you could 
easily wait a good 20 games or more before it occurs. You can make the calculations if 
you want, but it's getting pretty complex here.  

Let's make it 10 games on average, which i think is a pretty good approximation. 
That's 10 games from the moment you first reach 10FF. If you start at 9FF, it takes 
on average about 5 games before you get to 10FF (remember, even when you win, you can 
still go down, which will make it a lot longer). That's a total of 15 games where you 
get your bonus for the extra FF you started with before you can expect to lose it. Now 
if we multiply that by 1.75k per game, we get a grand total of 26k. This means that each 
point of FF gives you around 26k before it dies out. Since the extra FF cost you 10k, you've 
made 16k profit.  Now, granted, that's not much, but with the limited cash input in the new 
edition, i'll take anything i can get.  

Now i hear you say, "yeah but starting with less FF means better players and more chance of 
winning". This is an argument i've answered numerous times in the past and in great detail. 
To sum it up, i'll just mention the main points of my argumentation here and you can go 
through it on your own at your leisure.  1. Starting with an extra 10k worth in positional 
players doesn't increase your chances of winning significantly. You could easily have won 
even without it and you could easily lose even with it.  2. The extra FF also increases your 
chances of winning by helping you on the kickoff events. This factor must be subtracted from 
the one above, which was already pretty slim.  3. The extra 10k which you spent in FF will 
return to you in less than 6 games on average. Hence, any advantage you might have obtained 
from spending that 10k elsewhere can only be expected to last for 6 games. After 6 games, the 
advantage goes the other way since you'll have more money in your treasury, thus more to 
spend on players.  

To sum up this gigantic post, extra FF gives you significantly less money than it did in 
3rd ed, but since your money needs are significantly greater now, i'd say that the impact 
of the extra FF is almost as big as it once was.  Thanks for reading all this and good day!   

Zombie