Law_Man

Definitions
“CA” refers to current ability (0-200)

“Max CA” refers to the generic maximum i.e. 200 CA, not the actual maximum CA (i.e the potential ability) of a player.

TATT – total attributes i.e. all the players attributes added together

Formatting
Hopefully what I've written will have come out ok but if not then any mod is welcome to put it right


Introduction
The relationship between current ability (CA) and player attributes has interested me for a while now, as dull as it sounds.

So the crux of this thread is how attributes relate to current ability. Primarily for now, the focus will be trying to determine whether for a player with CA X, there is a fixed (or fixed within upper and lower limits) minimum, maximum or average number of total attributes (and to as lesser extent whether it also might differ per position). And also to see if it is possible to accurately estimate a player’s CA (a hidden stat) by using a player’s total attributes (TATT)

For this I will have to go to the dark side and either use the editor or download FMM to check the current abilities, but it shall be in the name of research.

So, for example, if 10 players all have a CA of around 150, do they all have the same/a similar number of TATT?

Do they all have not less than X and/or not more than Y? What is the average number of total attributes?

And then further, comparing a player like Ronaldinho who has a very high CA with a lower ability player? I assume he will have a greater number of total attributes, but it will be interesting to explore this, especially to try and find out if there is a maximum number (out of 720) that a player can have (assuming they have 200 or close CA). I assume that there is indeed a theoretical maximum number (to stop players having 20s in everything for realism) but it might be interesting to try to establish what that number is.

Also, can we work out the current ability of a player just by looking at their TATT?


Predications
You could go on to assess the full total of attributes by including the hidden attributes in the analysis but I never use FMM normally in my games and don’t want to explore that avenue.

All figures are rounded up unless otherwise stated.

Obviously the maximum number of attributes is 720 (36 attributes with a max of 20 in each theoretically).

Also, I will be obviously including the mental attributes like aggression and determination that might not necessarily be influenced by CA but hopefully this won’t make such a big impact, and at least it will be consistent in approach.

GK are perhaps somewhat of a special case, so comparisons with outfield players might not be accurate.

I should say from the outset that I do not having anything in mind to prove or disprove in terms of improving my experience of FM. I am doing this purely out of interest and well, a pursuit of knowledge and exploration of something that interests me. It is not intended to hopefully produce some in-game advantage or to highlight any flaws in the game. Hopefully it will do neither. Obviously player A could have a higher TATT than player B, but I might still prefer player B because for the position I want to play him in, he has higher attribute values in those areas that I feel I want for that position. This is in the same way that player A might have a higher CA than player B but for those reasons and others, I might still pick player B. This research doesn’t intend to prove to the contrary.

Let the research commence
Ok well I thought I’d start with my Middlesbrough squad and work from there – this should hopefully also give us a range of positions, CAs and ages. (Players are listed in their ‘natural’ position(s) (regardless of whether I’m playing them there are not and all values are in May at the end of the first season).


GK – Almunia – CA 152 – TATT 430
DR – Young – CA 135 – TATT 448
DC – Huth – CA 152 – TATT 510
DLC – Pogatetz – CA 144 – TATT 488
DL – Taylor – CA – 134 – TATT 496
ML – Arca – CA 142 – TATT 475
DMC – Shawky – CA 138 – TATT 481
MC – Cattermole – CA 132 – TATT 477
MC/DMC – Rochemback – CA 147 – TATT 477
AMC – Piatti – CA 130 – TATT 422
AMC – Kapo – CA 146 – TATT 481
AMR – Torje – CA 135 – TATT 450
SC - Stancu – CA 138 - TATT 437

And then (not my players...!):

GK – Buffon – CA 185 – TATT 493
DL – Evra – CA 170 – TATT 534
DR – Alves – CA 179 – TATT 583
DC – Terry – CA 182 – TATT 534
AML – Ronaldinho – CA 188- TATT 527
AMR – Ronaldo - CA 192 – TATT 519
DMC – Mascherano – CA 175 – TATT 510
MC – Gerrard – CA 184 – TATT 549
AMC – Kaka – CA 192 – TATT 522
SC – Eto – CA 186 – TATT 522

Summary

My Boro lads
Average CA: 140.38
Average CA as a percentage of maximum: 70.19%
Average TATT: 467.08
Average TATT as a percentage of maximum: 64.87%
Average CA as a percentage of average TATT: 30.05%
Huth CA as a percentage of TATT: 29.80%

Good players:
Average CA: 184.22
Average CA as a percentage of maximum: 92.11%
Average TATT: 531.44
Average TATT as a percentage of maximum: 73.81%
Average CA as a percentage of average TATT: 34.66%
Ronaldo CA as a percentage of TATT: 36.78%

From this we can see that whilst the difference between the average CAs of the two groups was over 20%, the difference in TATT was less than 10%. This is a very interesting result in my opinion. You would assume that CA would determine what level of TATT a player could “hold” if you will.

The biggest result was between Huth (76% of max CA) and Ronaldo (96% of max CA) with a difference of some 20%. Whereas, in terms of TTAT Huth (70.83% of max TATT) compares favourably with Ronaldo (72.08% of max TATT) with a difference of less than 2%. Does this tell us anything useful? I’m not sure really. It certainly tells us that Ronaldo is a better winger than Huth is a defender, because purely from their respective CA and TATT scores can see that Ronaldo’s attributes must be highly concentrated (assuming they are concentrated in the right areas – which they are) and Huths must by definition be fairly evenly spread given his much lower CA and similar TATT score. What use highlighting this is I’m not, except to encourage users to go for specific killer scores in key attributes.

The figures for average CA as a percentage of average TATT are also interesting. This way it might be possible to roughly work out (in-game) a players approximate current ability based on their stats. Obviously this can already be done fairly roughly at present i.e. if I look at Alves, he looks like he’s going to have a high current ability from all the high stats! But things might be deceptive. For example, Huth looks like he’s probably got a higher current ability than he has in my opinion. So if we take Huth and Ronaldo as the limits here than its possible to say that by using a players TATT, we can be accurate to within plus or minus 7% as to their CA score. Let’s call it 32.5% (the midpoint between 29% and 36%). Now, even as I’m writing this this sounds the most spurious of logic and I’m conscious of the fact that even if this is true, the phrase “so what...” springs to mind....but hey ho, its there.

To test this I’m going to pick players at random and then take their TATT score (in-game) and produce an approximate current ability and then test it by using FMM. Fingers crossed.

I’m a Bolton fan so let’s go there.

Diouf
TATT: 476
Predicted CA: 155 (476 x 32.5%)
Actual CA: 160
Difference: 2.5%
Age: 27
Peak Ages: 27-32

Andranik
TATT: 461
Predicted CA: 150 (461 x 32.5%)
Actual CA: 148
Difference: 1%
Age: 25
Peak Ages: 27-32

And Gks

Jussi
TATT: 435
Predicted CA: 141 (435 x 32.5%)
Actual CA: 161
CA as a percentage of TATT: 37%

It seems this doesn’t hold water for GKs! This is fairly understandable I think as you’re not comparing like for like between GKs and outfield players. Let’s just try 37% on some other GKs and see what happens......

Almunia
TATT: 430
Predicted CA: 159 (430 x 37%)
Actual CA: 152
Difference: 3.5%
CA as a percentage of TATT: 35%


Let’s try it with a younger GK. My prediction is that using 37% will vastly over predict a younger goalkeeper’s CA.

Brad Jones
TATT: 390
Predicted CA: 144 (390 x 37%)
Actual CA: 125
Difference: 10.5%
Age: 26
Peak Ages: 31-35
CA as a percentage of TATT: 32.05%

And youngsters

Zeefuik
TATT: 434
Predicted CA: 141 (434 x 32.5%)
Actual CA: 102
Difference: 19.5%
CA as a percentage of TATT: 23.50%
Age 17
Peak Ages: 26-31

It doesn't seem to work in this example of a youngster either. However, I think this can be explained (see below).


Hmm.... there are some patterns to be found but so far its only “normal aged outfield players” and “older-aged” outfield players and “normal aged GKs” that we can see a pattern with.

So far so good. Let’s see if it still holds true for players past their prime:

Campo
TATT: 431
Predicted CA: 140
Actual CA: 108
Difference: 16%!!
CA as a percentage of TATT: 25.06% - a bench mark applicable to older players perhaps?

Speed
TATT: 422
Predicted CA: 137 (422 x 32.5%) or;
106 (422 x provisional 25% “older players” benchmark)
Actual CA: 100
Difference from “normal” players formula: 18.5%
Difference from “older” players formula: 3% - this is more acceptable
CA as a percentage of TATT: 23.7%

Giggs
TATT: 485
Predicted CA: 121 (485 x 25%)
Actual CA: 136
Difference: 7.5% - just about acceptable.
CA as a percentage of TATT: 28.04%

I think that obviously different players start to decline at different rates and Giggs is just going into decline on my game now so I think if a player has gone into decline the slightly lower “older players rate” should apply (god it sounds like tax law!). It looks like the older and/or more declined a player has become then the lower the rate you need to apply. The closer the player is to still being a “normal player” that you’d play week in week out, it seems that you should err progressively higher to the 32.5% benchmark for normal players.

Lets try another player.

Hamman (not as old as Speed at 34 (same as Giggs) but has gone into decline on the game in my opinion by this point)
TATT: 414
Predicted CA: 116 (414 x 28% same as Giggs)
Actual CA: 114
Difference: 1%
CA as a percentage of TATT: 27.54%



I am almost losing the will to live as I continue this journey – despite what the above might suggest, I really hate maths and never touched since leaving school – so could some other people chip in with some tests please!? Lol.

Conclusions - could it be that:

Youngest - Younger is approx. 23% - 28%
Older to Oldest is approx. 28% - 23%
Players within “normal” age range (but either only just into peak or not yet into peak) approx 32.5%
Players just into peak and into peaks its 33% - X%

I also think that these figures will be influenced by the determination (and possible other mental stats too) not just in terms of numerically, but also in terms of how hard that person will train, perhaps distorting CA disproportionately to TATT. Determination might also affect the rate of decline as a player gets older which could distort the formula slightly relative to age, and similarly with youngsters. But hopefully if people are willing we can do further testing on the above four types of players.

Based on the above I decided to do one last test:

Anelka
TATT: 470
Predicted CA: 165 (470 x 35% - as here’s into his peak in a comparable way to Jussi but is less determined so won’t train as hard– see below)
Actual CA: 165
Difference: 0%! (Well technically the predicted CA figure was 164.5 but I’m rounding all figures up for ease).

Further Research
Could someone test these out as I’ve been at this for hours, and have the new patch downloaded and haven’t even played a game with it yet!! (I know, poor me...).


Maths disclaimer
I’ve tried my best to ensure all workings out are accurate but if the odd one isn’t then it is purely through losing the will to live whilst doing this and simple human error. As I said I wasn’t really trying to prove anything in particular for my own ends or to discredit SI so I’ve got no reason to purposely distort any figures.

General disclaimer
I don’t say that all of the above is amazing research or even that it brings anything interesting to light, that’s for people reading it to decide. I also don’t claim that the above theories and conclusions are 100% watertight. As I’ve said, I’d like more people to test similar things to what I have just done as we need a bigger sample.

A big thank you in bold for getting to the bottom.

Cleon

Nice research, I've added it to the tactics bible

Law_Man

Cheers Cleon Hopefully it makes sense as I cannot describe how much I'm NOT a maths person......lol.

Hopefully some people will use it as a base for more extensive testing.

isuckatfm

Law Man if you really want to know the relationship between CA and attributes you could create a model making some base assumptions about the weightings applied to different attributes (the accuracy of the model would largely be influenced by the accuracy of this assumption) and solving the simultaneous equations. Someone who studies Maths and has access to the right software could do this pretty easily, or if you were dedicated to it you could do it the old fashioned tedious way of stepping through the model.

The basic model for outfield players (where * indicates 'multiplied by')

CA = (w1*A1) + (w2*A2) + (w3*A3) + ........... + (w35*A35) + (w36*A36)

where

CA = Current Ability
wn = weighting n applied to attribute An for n = (0,1,2,3,..........,35,36)
An = attribute n for n = (0,1,2,3,.........,35,36)

1. Assumption 1: Weightings are a numeric value between 0 and 1 and are not in themselves functions of other variables

2. Assumption 2: Weightings are applied based on natural position only

3. Assumption 3: Only visible attributes are incorporated in the model

You could add another assumption about certain variables being independent of CA. Not knowing precisely which attributes are part of the CA calculation will create potential inaccuracies but the model could still serve as a decent rough approximation.

These assumptions allow for simplicity but at the same time this simplicity could lead to inaccuracies.

So using the assumptions you take 36 players for each natural position and solve the simultaneous equations for the weighting values. Then you have a model for the relationship between CA and attributes. With the right software this could be done easily but doing it by hand would go way beyond tedious, and this in itself could lead to mistakes.

Law_Man

Go for it My brain really doesn't work that way so if yours does then great, lets try and do some further research

isuckatfm

I tried to do it before out of curiosity but the tedium lead me to stop pretty early in my attempt. Unless I'm getting paid I prefer not to spend my leisure time solving simultaneous equations. But I thought from the effort you put into your post I might be able to cajol you into doing it. I guess I was wrong

Maybe an FM playing Maths student with access to software for solving simultaneous equations might drift into this thread and do it the easy way .

Law_Man

Hehe well good effort anyway Sadly I have neither the software nor the expertise - I'm very much a words man...... In fact, I used to hate simultaneous equations in maths at school!

But at least you flagged the opportunity up, so if there's anyone out there who fancies it.......

kolobok

If someone can tell me how to pull all attributes for a bunch of players, I could run a simple regression to determine those weights, and maybe even tests which attributes are more significant for each position. The problem is that it's too time consuming to pull data player by player. Though I am pretty sure it could be done relatively easy.

Law_Man

I don't know how to do this, but hopefully someone more knowledgeable than I might be able to access the database somehow

What's a "regression"? I am massively out of my depth with anything maths based!

Completely agree it would be too time consuming doing it 'by hand' so to speak player by player and I wouldn't encourage anyone to be mad enough to attempt to do so. Its important that we get as big as sample as possible.

isuckatfm

Pulling data is a key issue especially if you were to attempt to use regression. Also another issue with regression is that it's necessary that each of the variables have a similar statistical distribution to reduce the errors which I don't know if that would be the case. Then again it's been a few years since I studied this stuff so I could be completely wrong as my memory seems to be deteriorating as I get older .

That's why I suggested that simple model. If the assumptions hold true then theoretically all you need is 36 players with the same natural position to solve the set of equations for that position. With the right software solving these equations would be a breeze. Doing it by hand is tedious to say the least. There's probably an easier way to do it using matrices rather than by a stepping sequence but as with regression it's been years since I did that stuff and it's all just a hazy blur at this point in time.

If the mood strikes I might give it a go but I wouldn't hold my breath.

If the program kolobok intends to use takes excel as input, and we can get enough contributors it might be possible to get a sample of reasonable size. It won't exactly be within the desired sample size to produce a high level of confidence but it could give a rough idea of the relationship.

The model produced could be significant to training aswell as it could be used to see how you could redistribute attribute points within a given CA by adjusting training sliders.