Yes, exactly. Horses have 2 dates assigned to them - start of maturity, end of maturity.
So, for easy math, let’s take Horse A and Horse B, both born on January 1, 2016.
Horse A’s start of maturity is June 1, 2018 (age 2 1/2), end of maturity is January 1, 2020 (age 4), giving him an 18-month peak.
His bell curve would go from January 1, 2018 (start of age 2) to June 1, 2020 (length of peak + the 6 months pre-peak he had at age 2), so his curve is 2 1/2 years long, and 1 1/2 years of that is peak. It does a bit of extra stuff to make the peak part extra-peak-y (so the start/end 6 months are more flat than the middle when he’s actually peaking), but that’s roughly how it would work.
Depending on when you run him during that time his stats get affected differently (I made up numbers to represent the out-of-peak bit, don’t treat this as gospel):
1/1/18-3/1/18 - can’t race yet
4/1/18 - 6%
5/1/18 - 8%
6/1/18 - 10% - start the peak
7/1/18 - 19%
8/1/18 - 28%
9/1/18 - 37%
10/1/18 - 46%
11/1/18 - 55%
12/1/18 - 64%
1/1/19 - 73%
2/1/19 - 82%
3/1/19 - 91%
4/1/19 - 100% - peak
5/1/19 - 91%
6/1/19 - 82%
7/1/19 - 73%
8/1/19 - 64%
9/1/19 - 55%
10/1/19 - 46%
11/1/19 - 37%
12/1/19 - 28%
1/1/20 - 19%
2/1/20 - 10% - end the peak
3/1/20 - 8%
4/1/20 - 6%
5/1/20 - 4%
6/1/20 - 2%
7/1/20 - 0%
8/1/20… stats continue to decline slowly as he’s getting more and more of a has-been
Hopefully that shows that yes, he matured as a 3yo, but it’s not like he suddenly became super amazing - he could’ve raced quite well as a late 2yo, and on into his 4yo year.
For contrast
Horse B’s start of maturity is January 1, 2019 (age 3), end of maturity is June 1, 2021 (age 5 1/2), giving him a 30-month peak.
His bell curve would go from January 1, 2018 (start of age 2) to June 1, 2022 (length of peak + the 12 months pre-peak he had at age 2), so his curve is 4 1/2 years long, and 2 1/2 years of that is peak.
His numbers would be:
1/1/18-3/1/18 - can’t race yet
4/1/18 - 3%
5/1/18 - 3.8%
6/1/18 - 4.6%
7/1/18 - 5.4%
8/1/18 - 6.2%
9/1/18 - 7.0%
10/1/18 - 7.8%
11/1/18 - 8.6%
12/1/18 - 9.4%
1/1/19 - 10% - start the peak
2/1/19 - 16%
3/1/19 - 22%
4/1/19 - 28%
5/1/19 - 34%
6/1/19 - 40%
7/1/19 - 46%
8/1/19 - 52%
9/1/19 - 58%
10/1/19 - 64%
11/1/19 - 70%
12/1/19 - 76%
1/1/20 - 82%
2/1/20 - 88%
3/1/20 - 94%
4/1/20 - 100% - peak
5/1/20 - 94%
6/1/20 - 88%
7/1/20 - 82%
8/1/20 - 76%
9/1/20 - 70%
10/1/20 - 64%
11/1/20 - 58%
12/1/20 - 52%
1/1/21 - 46%
2/1/21 - 40%
3/1/21 - 34%
4/1/21 - 28%
5/1/21 - 22%
6/1/21 - 16%
7/1/21 - 10% - end the peak
8/1/21 - 9.4%
9/1/21 - 8.6%
10/1/21 - 7.8%
11/1/21 - 7.0%
12/1/21 - 6.2%
1/1/22 - 5.4%
2/1/22 - 4.6%
3/1/22 - 3.8%
4/1/22 - 3%
5/1/22 - 2.2%
6/1/22 - 1.4%
7/1/22 - 0.6%
8/1/22 - 0%
9/1/22… stats continue to decline slowly as he’s getting more and more of a has-been
You can see that Horse B’s curve is a lot longer but flatter. Over the course of 3 months you’d probably go “wow” a bit more with Horse A’s change in level, but Horse B’s curve lasts another 2 years.
Final note:
Bear in mind that these percentages are based on a small percentage of the stat itself. If the stat goes from 1-100, the amount affected by maturity is probably only 10-20, so running him at 18% maturity/has-been-ness doesn’t mean he’s got an 18 for the stat, he keeps at least 80 of it innately and the other 1.8-3.6 is what’s added by being at 18% maturity.
Hope that helps a bit.