After looking at the inputs several different ways the way the data seemed to best fit reality was to put both height and velocity into a third order equation and then use that to plot velocity vs. height for given ages. If someone wants to I can send them an image of the plot and they can upload it and send me the url and I'll then add it to this post.
Please be aware that this data reflects a fairly elite pitcher. For example a 5'10" just turned 13yo is predicted to cruise at 69 mph. This is within a couple mph of the hardest throwing pitcher in this year's LLWS (who would have just turned 13) and probably typically for a very good select pitcher of that age.
Results:
Increase in velocity from age:
(No height increase)
12 to 13 ~ 3.3 mph
13 to 14 ~ 4.0 mph
14 to 15 ~ 4.0 mph
15 to 16 ~ 3.4 mph
16 to 17 ~ 2.0 mph
17 to 18 ~ 0 mph
Increase in velocity due to height:
(No age increase)
12yo .65 mph/in
13yo .61 mph/in
14yo .58 mph/in
15yo .70 mph/in
16yo .76 mph/in
17yo .76 mph/in
What does this mean?
If your player doesn't grow for a year he could still expect to get the velocity increases over that year as shown above. If your player also grows a few inches as is normal you can also expect some additional velocity gains.
For example a pitcher who goes from 13yo to 14yo and grows 3" during that time would be expected to have a velocity increase of about 4.0 mph due to maturity and an additional increase of a little under 2 mph due to increased height for a total increase of about 5.8 mph.
Another example would be a pitcher who goes from 17 to 18yo and grows 2". No increase due to age would be predicted but a 1.5 mph increase would be predicted due to a gain in height.
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