Shift
harvestgreen22 said: You are right.
I saw it in that same video's Comments section, A community player said it. He pointed out that growth is a roll of the dice, with a random chance of full growth or no growth. In terms of numbers, he thinks it's 0.25,0.5,0.75, corresponding to different green arrows.

I set the testing time as 1 season in the hope that this length can reduce the statistical error roughly. Then, for each test, there are 11 players, so the sample size is also increased. In the table, I usually test 3-8 seasons to further reduce the random error


The problem is that in earlier versions of the game, the training progress graph provided decimal values ​​for attributes, so you saw on this graph in Development->Progress tab that the dribbling attribute in October had a value of 15.3, in November 15.6, in December for example there were no changes, i.e. still 15.6, and the next change was for example in February and the attribute had a value of 16.2 because there was an increase of 0.6 in this case.

This pattern still exists, but in the latest versions, the graph only shows integers when hover your mouse over an individual month. You see that the graph line is going up from month to month but you don't know what the growth was. I remember values ​​around 0.3 and 0.6 from previous versions of the game and these were the smallest values. I think there are 3 levels of growth, and the highest is the green vertical arrow.

Currently I don't have any saves from these older versions of the game, but someone who does can load the save and check all values ​​in player profiles.
@harvestgreen22

If I understand correctly, you don't know why arrows appear in the player's profile and CA remains unchanged. Attributes have decimal values. During training progress, you can receive values ​​of 0.3, 0.6 or 1 (or 0.9, I don't remember exactly). This is shown by the colors of the arrows. The greener the arrow and more upwards, you get a larger value from this set, for example a vertical green arrow is the maximum growth.

What we see in a player profile is simply a rounded value. So, for example, if dribbling is 15.3, it is displayed as 15. In your case, you probably received a low value in training, for example 0.3, having a value for dribbling equal to exactly 15.0. This will give a value of 15.3, so the attribute in the profile will still remain 15 because it will be rounded down.

It is possible, but I have no concrete evidence for it, that the game simply uses integers for all calculations, e.g. CA or player performance on the pitch, etc. In your case, this integer attribute has not changed, so CA has not changed. Of course, the same pattern occurs when we talk about attribute drops.
I think this statement that coaches not having much influence on training may make a lot of sense. You can see that the best clubs in the game run by AI do not pay much attention to the number of coaches or their specializations. They do not hire coaches specifically for a given training category, but coaches who have more even skills. Additionally, in an AI team there are often only 2-3 general coaches and definitely more goalkeeping and fitness coaches - maybe even 2 or 3 times more. You would think that this team would have fantastic goalkeepers and fast, strong players in the future, and lack in technical and mental attributes. However, we see that the players in these clubs develop relatively proportionally in every aspect.

I think as already mentioned, the most important is professionalism and playing time. Training facilities also play a role, because when I used standard training programs after improving the facilities I noticed a clear improvement in development, so there is some influence.

Finally, I would like to mention a rather important thing that not everyone knows about. A player's monthly progress (I mean the arrows that appear in the player's profile next to the attributes, which show how the player's attributes have changed) is unique to each player.
What I mean is that every player develops on the exact same day every month. Which day? You have to check it in the first month of the game. For each player, it is usually a different day, but it can happen, for example, two players in a team will progress on the same day of the month.

Example:
Player X develops on the 18th day of the month. As a test, just save the game day before, load it a few times and you will see that the attributes in his profile will change differently each time. If the training rating on a given day is high and the player is young (in the development phase), there should be a lot of green arrows. However, if the rating is low, red arrows may appear.

It is also important to go to the Development->Progress tab every month because there is a certain UI-related bug in the game. If we go to a new month without entering this tab, the arrows from the previous month will not be removed in the main tab of the player's profile and when the player makes training progress in the new month, we will actually see progress from both months and it will be confusing. Entering the previously mentioned tab will solve this problem, it is important to do it after the player receives progress from training.

I want to mention this to you because I think it may help a little in further tests. The performed tests are great and a big thank you to @harvestgreen22 for a great job.