I still believe that the answer to your problem is not to make up a new system of changing PA in-game (because aside from the research data not always being accurate, the system is OK), but to distribute the set PA randomly at the beginning of the game, the range determined by base CA and age. This will give a PA within reasonable limits but at the same time random so that any player could potentially be a star or a dud. I did some work on excel and put in some calculations but I'm not at home so I'll just write what I did:

1) I started by thinking about a player at age 16, when they first enter the game. I assumed that CA should predict PA, because if a young player is better than their peers at a young age (the researcher's ability to judge CA is not in question here), then they are likely (not always) to be better than their peers when they grow up. I also assumed that PA can never be below CA or above 200, and that the range of possible PA gets more narrow as players get older (until they reach the age that they do not improve anymore, when it should be equal or almost equal to their CA) because their trajectory of development is more easily determined holistically.

2) I also assumed that globally, PA should have a mean of 100.5

3) I drew a normal distribution with the 0 point being at the player's CA and the mean being the midpoint between that CA and 200 and used CA 50 as an example. What I mean is, if you count up all players beginning the game (age 16) at CA 50, then the total PA should have a mean of 125.

4) I worked out using PA values in the game that the top .135% of players with PA over 50 have PAs of around 161, and used this figure to estimate that a player at age 16 with CA 50 should have a PA within the range of 89 - 161 99.73% of the time. I worked out a standard deviation that would allow a random PA to fall within that range and generated 30,000 random samples of possible PAs for a new player and ended up with a normally distributed set of PAs, with a similar spread as that of the game.

5) I then divided the PA and standard deviation by 14 (with the assumption that players stop growing at 30 - this was a test run, numbers are not fully accurate) to model the predictions with players of increasing ages (modelling the increased knowledge that a researcher has for an older player and better knowledge of their limits). For example, I divided 75 by 14, and then took the result off 125 as used the new mean to predict for players at age 17, then took off another 75/14 for age 18 and so on. I generated another 30,000 random samples from this distribution for players with the ages 21, 26 and 29 and found reasonable-looking distributions that seem logical.

6) I tried to do the same with different CA levels and got a nice range of distributions with CAs of 100 and also 150. The sample distributions are shown below.

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In conclusion, if we are going to keep PA, then we should at least make it reasonable and logical. Random PA with a probability density function across the whole board of possible PAs is better than having a negative number and choosing a totally random PA in a small range. The way that I have suggested removes researcher's role to guess a player's PA, which we have agreed is not always accurate. This way, a player's development in the game will be less predictable, can change every game, but will not have to be dynamic

**and change the whole point of PA**. For newgens, the game can decide a player's starting CA at random but modified by nation and club factors, and then the system can generate a realistic PA based on that CA. It means that players who come through better systems (who tend to be better) have a PA range with a higher mean, but this will not guarantee that they will come good. This will also control the PA distribution of wonderkids that show up with high CA but have an unrealistically low PA (it will still happen, but less often). It also makes it possible for older players to improve, without their PA being blown out of proportion.

Yes, I finished a huge assignment last night and chose to do this to celebrate.

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