High FF

[Darkson]

Remember to roll a D6 for each player on the field to determine how many fans are killed. Let the blood flow baby!

Ahh, the got old days of career spectators killed stats.

[Longshot]

If you start with no RR, you will surely loose.
Dont forget than turnover can happen on any '1' so this is 1/6.
None of Elf player have dodge for example (i meant HE).

Great Post H&M (like a clothe store in france )
I never take a big FF....

[Marcus]

Joshua: I wasn't trying to argue the value of FF in tournament play, I was addressing your question of the odds of the FF roll coming into play on the kickoff table. Tournament format was a nice way to show the effect over a fixed number of games where the Gate is not an issue.

As for a league situation - what is your rationale for bulking up your starting team? You're really only looking at one extra positional player, or swapping out 2-3 linemen for positional players. It is a hell of a lot faster to buy in those players after 3-4 games then it is to wait on FF rolls to drift you up to where you could have been had you bought the FF when you started the team.

Furthermore, you're now playing catchup with the other teams who started with a high FF and have been winning games.

The key issue is you can only ever buy FF once, when you create the team, you'll only ever gain more through luck. IMO that's painting yourself into a corner for the benefit of a couple of extra skills on your team for the first 3-4 games.

The question, then, remains is: how advantageous is it to, as you say, bulk up your starting team? The more I've played this game the less I believe that a skilled up starting roster is the be-all and end-all of starting a league team. Raw numbers, Fan Factor and Rerolls have always been the issue for me.

In my experience it's easier to beat a team of 11 positional players than it is to beat a roster of 14, even if those 14 are linemen. No I can't give you a statistical analysis of that I just know how I play. One of the first things I do is check your number of reserves, if it's 0 or 1 I go hunting for the best player on the pitch and clatter them. Repeat until you're men down then play as normal. I don't need to spell out why numerical superiority wins games.

Now, if you wanted to spend that FF money on an extra lineman or two you're in an interesting situation, you've probably exceeded (16 - <positional players>) and now are in the situation where you are going to want to sack players to bring positional players onto the roster. That's more money down the drain that your low FF won't be helping.

My 0.02 euro

[High & Mighty]

If I'm wrong, show me the numbers! H&M posted a very well-thought out post, but at the end of the day, it's just a subjective opinion.

Crunching numbers isn't my strong suit, but until I see some done, my opinion is no more wrong than the opposite viewpoint. I can't see much evidence of that so-called cash crunch that H&M mentions, as Fan Factor should continue to increase until it reaches the same level as the other teams in the league. True, if your FF is low relative to your TR then you will have a harder time coming up with cash, but since you spent more money on your team to begin with, you won't miss it as much as you're buying your players and rerolls and stuff. That analysis doesn't convince me (as eloquent as it is) that you don't end up in the exact same place.

This may be a case of "Be careful what you wish for." There is math underlying what I said above. If you trust me for a second, below is the equation governing all winnings in BB in a generalized case where the opponents fan factor starts and changes throughout the season the same as yours (this just reduces the variables). I don't have time to put up how to get to this but perhaps if I have time I will try to put something up next week.

Code: Select all

$=[3.5+W]-[(Y+C)/25]+F[.31-.0052N]+N[(*-(N*/60))(.052)-s/125]

Where

Code: Select all

$=Game winnings for one game
W=+1 mod for win (so if you win the game this is 1 and it's 0 if you lose)
Y=Total money spent AFTER creation on players and rerolls(base cost)
F=Starting Fan Factor
N=Number of games played
*=Fan factor mods so (1+w+t+k-(1-w))
  where:
     w=Win percentage
     t=Percent of games in which you score 2+ TDs
     k=Percent of games in which you get 2+ casualites
     (1-w)=Percent of games you lose
s=Average number of SPPs you have earned per game (current roster)

IMPORTANT NOTE: You may say the fan factor mod is wrong because it doesn't factor in the -1 mod for your fan factor greater than 10 (and -2 for 20 etc.) Again you'll have to trust me but it's already up there, but since that is simply a factor of starting fan factor, games played, and the lower-case percentages above, it is already factored out...I said trust me.


IMPORTANT:Now if you want to skip all the math below and skip right to the point, scroll down to the bold print "So to recap:". Otherwise, keep reading the math explanation below and let your brain hurt.


Now I'm sure that looks like absolutely nothing. but if you break it apart for a second you find (still nothing just kidding):

[3.5+W]=[A]=Base winnings after a game (one d6 plus one for the win)

[(Y+C)/25]=[E]=How much have you spent on players past your starting roster + your current Treasury

F[.31-.0052N]=[C]=Effect of you+your opponent's starting fan factor on earnings, factoring in the effect your starting fan factor has in triggering the negative mods in rolling for fan factor

N[(*-(N*/60))(.052)-s/125]=[D]=the things that grow as games are played, namely fan factor [(*-(N*/60))(.052)] and SPPs [s/125]. The fan factor there may look funny but think of it as if you have played a million games and have perfect probabilities. In that case, the fan factor you earn as play game after game is simply the sum of the modifiers...Again...not important so if it doesn't make sense, take it on faith and here comes the important part.

Simplifying our big equation we get:

$=A-E+C+D

So obviously the money you earn is a factor of what you roll [A] plus the fan factor you started with [C] plus the fan factor you gained along the way [D] minus your growing roster size [E] and the SPPs you gained [last part of D] since this affects team rating.

So hopefully that makes sense. Now the question is, how is this changing as you play more and more games?

[A] is a constant and doesn't change no matter how many games you play.

[E] again is a contant and doesn't change. This may not make much sense but think of this example. You started your Orc roster with 790k in player cost (4 blitzers, 4 BO, 1 thrower, and 2 gobbos). This means to fill out your roster, you need to buy an ogre+2 gobbos+1thrower+1lineman=320k more money. After that, there's no more to spend on players. If someone dies, you are simply replacing them, which is the same as if you kept the same amount of players and threw your money down a hole so it has no effect here. Same logic for rerolls. You bought two rerolls for !20k each once the season started. For team rating purposes, this means you bought a reroll for 60k and threw the other 60k down a hole.

[C] Here's where things get interesting. Notice you've got a larger number (.31) multiplied by a smaller number (.0052) which is dependent on N. This means when you start out your season and N is small (say game 1), you get .31-.0052, which is positive and then is multiplied by the starting fan factor. BUT what happens after you play 60 games? You get .31-.0052(60)=ZERO. This means that at 60 games, your starting fan factor has no effect on your overall earnings, and as you play more games, it actually has a negative effect. The reason for this is because the positive effect of your starting fan factor is slowing being washed away by two things. First by the fact that each fan factor adds one to your team rating and more importantly here, because each fan factor actually increases the negative modifier you have on the fan factor roll once you pass the 10 FF threshold. So we find [C] is increasingly negative.

[D] Now here is where you see the effect of per game growth of your team. Let's say it's game one (so N=1) so you have made no rolls for fan factor and have not accumulated any SPPs. You are left with:

Code: Select all

[(*-0)(.052)-0/125]

which =(*)(.052)

So when you start out, you will start out contributing to your winnings by a factor of .052 times your winnings percentages (1+w+t+k).

Now looking at the equation for [D] again:

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N[(*-(N*/60))(.052)-s/125]=[

We find after 60 games, the equation turns absolutely negative related only to the average SPPs your team earns:

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=60[(0)-s/125]=0-.48s

And in fact, it turns negative before then if your SPPs are too high or your winning percentages are too low. But in general, we find as N gets bigger [D] goes negative.

SO TO RECAP:

[A]=constant
[E]=constant
[C]=increasingly negative
[D]=increasingly negative

Which means we have:

Code: Select all

$=[constant]-[constant]+[increasingly negative]+[increasingly negative]

Or more simply:

$=Constant minus an increasingly negative number

So your $ are getting negative the more games you play irregardless of:
1) What roster you started with
2) What fan factor your started with
3) Whether you win every game you ever play and score 2 Tds and 2 Casualties in each of those games

So at that point you're thinking that it now makes no difference what you do since it all goes to naught in the end. Well, fortunately no one plays infinite games and therein lies the solution to which I referred in my first post. If you constrain the big equation, you'll get the perfect starting roster and team development plan, but I won't bother to put that here since no one will really be interested in the perfect team set-up .

But I will make one last generalization. Imagine you did as good as you possibly could:

1) you won all your games with 2 TDs and 2 casualites to max the ff mod
2) only ever got 15 SPPs in a game (2 tds, 2 cas, 1 mvp)
3) spent 500k on players and rerolls after the start of the season (this isn't a perfect, but it's just an assumption made here to ease the math)

You find the big equation becomes:

Code: Select all

$=2.5+F[.31-.0052N]+N[.08-.003N]

Most importanly, notice that in the perfect case, your earnings in the long run are only determined by how many games you play and what fan factor you started with, so any argument about how you can make it up later is not true.

So in this perfect world, after 24 games, the last part of the equation becomes negative so after 24 games, your own team's natural (and because of our assumptions perfect) growth reduces your earning potential. And after 60 games, your teams starting Fan Factor becomes a negative drag on your earnings.

Plug N=24 into the equation above and you find in the perfect world after 24 games, you are making 29k per game in winnings if you started with FF=1 and 44k if you started with FF=9.

Overall, you find that if you start with FF=9, after 47 games, you will have no more income and if you start with FF=1, after 45 games you will have no more income. This may make you think starting fan factor doesn't matter after all since it only makes a difference of two games as to when the money cuts off, but don't forget that all along, you were earning more money from your starting fan factor since it doesn't become a negative factor until you have played 60 games (but since you have no more money after 47 games, it really makes no difference).

So if anyone is still reading , starting fan factor will give you income for two more total games before running out of income but before then, it will give you more money in every game (in the perfect world..if you don't win all your games, accumulate more SPPs than 15 per game or don;t score 2 TDs and 2 casualties in every game these constraints will cut in sooner).

[DoubleSkulls]

Wow. A nice piece of work. So 9FF it is then.

Ian

[Mestari]

H&M: I like the way you express your opinions.

Given your assumptions, I see nothing wrong in your argument.

However, when you stated your conclusions on your first post you fail to recognise the fact that one of the assumptions has to go at that point.

Namely the assumption that no player dies, no player retires and thus your TR will keep growing. That assumption leads to faulty conclusions.

My comments to your conclusions in your post 1:

High & Mighty wrote:
6) So if you want to grow forever, slow and steady wins the race. Get 14/15 player roster, which will bring your TR to about TR128 on a cash basis, with a couple extra rerolls in there, a TR of 150. At that point, spend all the money you have on wizards and freebooting and keep to the 2/2/1 SPP game and you can grow forever since you are moving south-east on the winnings table...BUT...if you start with too low a FF, you can not get to that TR 150 before the negative mods hit in. This also assumes you can win games with your roster which will likely have less skills than everyone else to start out with because they are all racking up the SPPs and getting more skills than you in the early going. If you don't win, it's all futile. If you roll poorly on the FF table, it's all futile. If you roll high on the winnings table, who cares since you are just blowing the money anyway.

7) Perhaps most interesting, you've got a coordination game. If every team in the league plays by these rules, all the teams can increase forever. But if you've got some teams racking up the players and SPPs early and dominating, they are going to destroy those teams playing for long-term growth in the early stages and those teams will never get going. Meanwhile the successful teams, the ones that went for early fast growth will get stuck but will have already destroyed the competition.

I reply:

The problem with your conclusions revolves around your TR growth assumption. Even though you are on the right track with wanting coaches to keep their TR on a certain level, some obvious conclusions available from understanding the oscillating nature of TR are omitted in your post:

In your model the TR increases slightly all the time, starting from your rather low ideal value of about 150, finally resulting in "being stuck".

When adding in the possibility of the TR going down (death, voluntary retirement) we end up with a completely different ideal system, where no team gets stuck:

Model of TR development:
Phase 1: Development: Team is growing - income is good, players develop, TR grows. There may be some sudden set-backs in form of fatalities etc. but the main trend is a growing team.

Phase 2: Plateau: At a certain point, development gets slower - income is getting scarce, TR is inflating, lots of handicap is given to weaker teams but the team is not advancing much because there is a long way to go to the next skill roll for most of the players. This state can last for some time.

Phase 3: Downfall: At some point TR goes down, unavoidably. Money is not sufficient to replace those casualties, the stars get severe aging results and are retired etc. The team cohesion is broken, games are being lost as the TR is still too high compared to the teams ability. Casualties can extend this drop quite dramatically.

Phase 4: Recovery: TR drop stops at some point - casualties and stars have been replaced as income has returned to better levels, TR is cleared of excess bloat and the team is able to turn the direction of TR change. At this point the team returns back to Phase 1.

Now, a clever coach manages the team so that he attempts to balance just below the Plateau phase: he retires players and spends money. This way he attempts to sustain the highest possible competitive ability without making his team go over the top. He manages to sustain a small income that is enough to replace the casualties and retirements. He aims to keep his TR at a constant level, but the actual result is that he goes through the same cycle as the other teams, only that his downfalls and recoveries will oscillate with a smaller amplitude.
The teams that ambitiously and stupidly aim to get as bloated as possible will fall down a lot more violently. Our clever coach thus manages to keep his team constantly competitive while the fool tries to make a big team and finds himself in falling a lot below his would-be-equals.
Our clever coach also retains one option not available to the others: by keeping his TR at a suitable level, he is able to (when necessary) inflate his team - for example for the most important games, and afterwards drop back to the more stable level in a more controlled fashion.

So the main difference to your conclusion is that there is no spo... poverty trap. If the TR increases too much, the team will get into a downfall (eventually). But the teams (if the coach keeps playing) will recover and make a new rise.

Now in this system, the high FF is not 100% necessary, but naturally it's recommended as it is one factor in determining what is the critical TR level before the team enters the plateau phase that inevitably leads to the downfall. I claim that the clever and lucky coach could get away with a lower FF - by keeping his TR low enough, and by increasing his FF over time in order to lift the level of TR that can be sustained in a stable fashion. And the better starting roster can help there.

What is the target TR then? At what level should one start keeping the TR stable? There is not a single answer, but the answers depend most notably on these factors:
1)Coaching ability (absolute and compared to other coaches)
2)Overall TR level of the league
3)Team race
4)FF (own and others)
5)and a few others.

The phase-system above is a rather hastily written one, but it certainly portrays the real-life scenario (where we accept the nature of TR development) better and serves as a good approximation of how teams develop in the limiting end of the TR spectrum.

[Joshua Dyal]

Thanks, H&M for the analysis. I think you left off the cyclical nature of TRs, though, which Mestari already covered much more eloquently than I will be able to.

[High & Mighty]

However, when you stated your conclusions on your first post you fail to recognise the fact that one of the assumptions has to go at that point.

Namely the assumption that no player dies, no player retires and thus your TR will keep growing. That assumption leads to faulty conclusions.

Even though you are on the right track with wanting coaches to keep their TR on a certain level, some obvious conclusions available from understanding the oscillating nature of TR are omitted in your post:

When adding in the possibility of the TR going down (death, voluntary retirement) we end up with a completely different ideal system, where no team gets stuck:

I like your model of development very much and there is "wiggle room" for what you describe. I also WANT to beleive it's true very much. My problem is that unless it happens in the model, I've got no proof. The problem is that retiring and dead players are factored into the equation which is totally dynamic and allows for death and sacking players.

I will try to post an example that makes the point tommorrow, but in general, what the equation shows is that the structure of the 4 equations which determine the earnings dynamics when placed together (team rating, fan factor, gate, winnings) ensures that you cannot make enough of a difference to prevent the outcome. You can only delay it.

By how much? I was trying to avoid the high math. But perhaps it's time...
since we can find an answer to the below:

What is the target TR then? At what level should one start keeping the TR stable? There is not a single answer, but the answers depend most notably on these factors:
1)Coaching ability (absolute and compared to other coaches)
2)Overall TR level of the league
3)Team race
4)FF (own and others)
5)and a few others.

The only one I wouldn't agree with is #2. Your opponent's TR has no bearing on how much money you make. His fan factor, yes, and from the math, we know that it's actually better to leech off of your opponent (since if you have the high fan factor, you much pay the -1 mod for being greater than 10 plus it counts against your TR since 1FF=1TR.) But TR would only be important in a relative sense but would already be factored into your #1(relative coaching ability).

Race would only be important in terms of how much your players and rerolls cost in order to get to a full roster, and after I looked at a couple examples, it doesn't make a huge difference in that regard because in general, expensive players have cheap rerolls and vice versa.


Oh well. I will have to sleep on it and if some door finally opens, I'll be sure to let you know...and hopefully it will be a little shorter...

[Mestari]

[quote="High & Mighty]What is the target TR then? At what level should one start keeping the TR stable? There is not a single answer, but the answers depend most notably on these factors:
1)Coaching ability (absolute and compared to other coaches)
2)Overall TR level of the league
3)Team race
4)FF (own and others)
5)and a few others.

The only one I wouldn't agree with is #2. Your opponent's TR has no bearing on how much money you make.[/quote]

No it doesn't, but it has a bearing on what level of TR is sustainable. If the TR you are attempting to sustain is below the league average, you are generally better off if it is assumed that the higher TR's are to some extent due to bloat and needless clutter: you will get handicap even though your team is as competitive. This in turn results in better game outcomes, which in turn make it easier to sustain the TR level, as you can quicker counter the setbacks (casualties) that you inevitably will get and avoid an uncontrollable downfall.
If in turn your target TR is above the league average, you will be handing out handicap, which probably makes that TR unsustainable - if that particular TR is high enough for the other contributing factors of the downfall to kick in, handicaps will contribute to the beginning of the downfall at some point.

To me it seems that after reaching a certain TR, controlling the oscillation of the TR value becomes the most important team management aspect.

I don't have a mathematical theory for it at the moment, but I'll see what I can do in the weekend. However, the theorem above with its justifications seem like it will stand mathematical evaluation.

[Longshot]

hum,
i didnt read everything but i will still get a low FF.
For example to spiky, The roll that i really dont want are Pitch invasion and Get the ref and throw a rock...lets take riot only for the mathematic that follows:
1/36+1/36+2/36+2/36=6/36=>1/6.
I succeed evrything on a 2+ with HE, so that is the same thing

[High & Mighty]

No it doesn't, but it has a bearing on what level of TR is sustainable. If the TR you are attempting to sustain is below the league average, you are generally better off if it is assumed that the higher TR's are to some extent due to bloat and needless clutter: you will get handicap even though your team is as competitive. This in turn results in better game outcomes, which in turn make it easier to sustain the TR level, as you can quicker counter the setbacks (casualties) that you inevitably will get and avoid an uncontrollable downfall.
If in turn your target TR is above the league average, you will be handing out handicap, which probably makes that TR unsustainable - if that particular TR is high enough for the other contributing factors of the downfall to kick in, handicaps will contribute to the beginning of the downfall at some point.

Agree 100% with everything you say, except coaching ability is something that would be very wishy washy to model.

Actually, if you wanted to include that dynamic in the model, TR differential would be a factor in determining the win percentage I guess...hmm....easy enough to replace the W variable in there with the factors affecting a win and see where it goes. It actually might hold a some promise just for the fact that you have TR elsewhere in the equation so things are going to factor out.

To me it seems that after reaching a certain TR, controlling the oscillation of the TR value becomes the most important team management aspect.

Yup. That's where I'm trying to get to, too. I still think the system of equations above is correct with one caveat that your comment made me look through again.

Sacking and dying players still plays no part whatsoever in reducing your team rating per se. The act of firing and hiring the same player achieves the same goal as freebooting a wizard or a star player. It's money thrown away. Since a full roster is a fixed variable, it only goes to 15/16 and every coach has 15/16 at their max. But what does need to be constrained are the SPPs. In the equation above, I was taking average SPPs per game and multiplying by the number of games.

So over time, the equation doesn't allow for losing SPPs which those dead/retired players had. So instead of average spps times number of games, the correct variable is average spps times players on the roster (since if you multiply the average spps times the total players you get total spps). This will effectively cap the spps and model the coach trying to manage the roster by maintaining a constant level of average spps per player to suit their taste (so say a coach trying to keep all his players at an average of two skills).

I don't have a mathematical theory for it at the moment, but I'll see what I can do in the weekend. However, the theorem above with its justifications seem like it will stand mathematical evaluation.

Excellent. It's not as hard as it seems at first because as you replace variables, it simplifies nicely. The only thing I'm having trouble with trying to make simpler is the fan factor purchased after creation. Over time, it's simply equal to the sum of all the d6 rolls plus mods you made in each game. The problem is the pesky -1 mod for losing contradicting the 6 always increases. Leaves it undefined in certain cases so I think my equation above is actually slightly overstating fan factor increases over time.

[Zombie]

Actually, you're inflating that number a lot. When i ran the numbers a year ago, i was very surprised at how slowly fan factor goes up. Read my article on FF on Bloodbowl.net to find out more.

[High & Mighty]

Actually, you're inflating that number a lot. When i ran the numbers a year ago, i was very surprised at how slowly fan factor goes up. Read my article on FF on Bloodbowl.net to find out more.

It's a great article. I read it when you posted in on TBB and again when you mentioned here a couple days ago to compare my own numbers.

My numbers run 100% fine if you assume the coach is always winning and are off by 1 FF every six games if you assume that the coach always loses. So at an intermediate step, if a coach wins 50% of his games and scores two TDs and 2 casualties in 50% of his games, after 36 games, my numbers will be inflated by 3FF.

I'm not too worried about it but would like to fix it.

If you want to see:

Code: Select all

FF=Starting FF+FF gained or lost after creation
         FF after creation=[N(1+W+T+K-L-H)]/6

Where N=# of games played
          W=win percentage
          T=% of games with 2+ TDs
          K=% of games with 2+ Cas
          L=% of games lost
          H=neg mod for FF>10

So in one game, if you win, you will earn 2/6 of a FF, etc. But as you can see, if you were to lose the game but score 2 TDs, your FF should statistically stay at zero [+1 mod for TDs, -1 mod for losing, leaving you at a straight d6 that on a 1 will go down, a 6 go up, and 2-5 stay the same--a statistical wash], but the equation would have it increase by 1/6. But I'm having a brain fart as to how to fix it.

[High & Mighty]

but the equation would have it increase by 1/6. But I'm having a brain fart as to how to fix it.

Brain fart over.

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FF=(W+T+K-L-H)/6

Since I need to add 1 if you win but not add one if you lose, making 2W covers that.

And since your losing percentage=1-winning percentage:

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FF=(2W+T+K-H-1)/6

Alright. Now I've got to go plug that back in along with Mestari's suggestions.

[Deathwing]

Hope you're following all this Joshua, you asked for the numbers..

Me, I'm totally 'lost'!