Seeing the discussion here, I took the deep statistical dive I wanted to take - but didn't have time to before - to try to anticipate the effects of the rule change.
I used the text reports to spit out all player ratings and stats from this season. I matched all players currently on rosters with their stats. I then eliminated all players from consideration that played fewer than 500 minutes to make sure any statistical flukes that might be due to a small number of minutes played weren't affected (this eliminated 43 players from the analysis and left 304, which I think is a large enough sample size to work with).
Since how much playing time a player got could be due to DC settings instead of fouls, I looked at fouls per minute instead of fouls per game. As expected, the trend line was that the better a player's Foul rating, the fewer fouls per minute he committed (though there is quite a bit of noise in the graph).
If you can't read the equations very well, the R^2 value is 0.6612 and the slope equation is y = -0.001x + 0.1414
What does this equation mean? Well, it means that a player with a 0 foul rating should commit on average 0.141 fouls per minute (I'll drop the last digit since our X variable only has significant figures to the thousandths); and every point of foul rating a player possesses drops this by 0.001 (so a player with a 1 rating would commit 0.140 fouls per minute, a player with a 2 rating would commit 0.139, and so on up to a player with a 100 rating who will commit an average of 0.041).
How does this translate to in-game performance? A player committing 0.141 fouls per minute (a 0 rating) will collect 6 fouls and foul out in approximately 42.5 minutes (6 fouls divided by 0.141 fouls per minute). If training improves his rating by 5 points, he will now have an average of 0.136 fouls per minute and foul out in approximately 44.1 minutes (an added 1.6 minutes). Improve it by again and he fouls out in 45.8 minutes (an added 1.7 minutes).
In practice, though, players get benched sooner due to foul trouble and I think about the most I've ever seen a player ring up is 4.2 fouls per game. That 4.2 foul threshhold is a useful mark for telling us "how is this player's playing time limited by his foul rating" which is what we're really concerned about more than anything else, I think. So we'll use that as our benchmark instead of 6 fouls, meaning a player with a 0 foul rating can stay on the floor about 29.8 minutes per game. (Note: That already tells me that the 30 minutes per game benchmark probably needs to go since a player with 0 foul rating will have a hard time reaching it!) So we're looking at a "minutes limit" equation of m = 4.2/(0.1414 - 0.001x) where x is the player's foul rating.
The interesting thing about this kind of equation (with a negative x in the denominator) is that it isn't linear improvement as the rating increases - it's geometric improvement. Plotting the question of "how many minutes can we expect a player to be limited to by his foul rating" looks like this:
(Minutes are on the x-axis and Foul Rating on the y-axis of the graph above, hopefully that's obvious with a look at where the curve starts). For those of you scoring at home, a foul rating of 41 is the point at which that line crosses 40 minutes per game - or in other words, where a player is likely to get into foul trouble from time to time but is not likely to be limited by foul trouble constantly since that's about the most players put in anyway and stamina concerns start limiting play instead (obviously, NEVER guaranteed for a single game as this is a random sim and your opponent's ability to draw fouls comes into play as well).
THE PUNCH LINE:
After all, that, we can now guess about how much improvement it takes for a 0-foul-rating player whose P.T. is limited by foul trouble to become a player who isn't battling foul trouble every night... roughly 40 points. Do we feel this is a weakness that should take 2 years to overcome (at 20 points increased per training as Balls suggested), 4 years to overcome (at 10 points increased per training as Quail suggested), or 8 years to overcome (at 5 points per training as current)?
Now that I've had time to run the numbers, I'm going to reverse my original position and say 5 points is NOT the answer. 8 years is too long. On the other hand, I think 2 years is a little too short - "natural" TC can only increase 10 points of current in any rating and I think that's a good benchmark (it's also the limit on our "current trainings"). I think 4 years is about right, so I'd say 10 points of increase per year is the right amount.
Then we have to worry about costs. I'm still a little leery of allowing foul training in the upper rating areas (because once you get over 70-80 rating, you can almost never be coerced into foul trouble) so I think having a curve rather than a flat point value (as we do with other trainings) is a good idea. Quail's original idea was 15 points paid to increase the rating by 10, but I think 60 points to push from 0 to 40 might be a little steep. Balls wanted to curve it on bands. Let's meet in the middle...
Cost:
10 points to increase foul rating by 10 if rating is in F band.
15 points to increase foul rating by 10 if rating is in D band.
20 points to increase foul rating by 10 if rating is in C band.
25 points to increase foul rating by 10 if rating is in B band (maximum rating 85; if you have a 79 rating and increase it the rating goes to 85 not 89).
I'd also suggest an amendment to the new rookie training rules that in lieu of increasing a current rating by 1, a player can increase his foul rating by 1 instead (maximum of 85). This will help get rookies less foul-prone a touch faster if desired too.
How do folks feel about this?
