Good questions.
@T0dday: I am curious about your thoughts on two things you said.
One is that you would have most athletes (5'10 and taller) perform single leg jumps if the goal was to have them dunk ASAP. This is interesting to me because I believe that this is in contrast to what most would think to be the best method. I do not know, because as a volleyball player I have never performed single leg jumps, but I cannot see the reason why it should be easier to increase the single leg jump compared to double leg jump. Could you elaborate on this?
Sure. As you well know as a volleyball player, both jumps require a good deal of skill, (ie. someone who doesn't jump at all can initially increase their leap very quickly with practice). However, because of the greater approach speed involved in the single leg running jump, most athletes are essentially "least" skilled in this jump. I find if you instruct most non-jumpers (eg. not triple/high/long jumpers) to attempt a maximal long jump, they won't benefit much (if any) from an approach longer than about 5-6 steps, which suggests a lot of room for improvement if they learn to convert a greater amount of their sprint speed into the jump. Of course, this is the horizontal long jump (where takeoff velocities are higher)
AND I train primarily with sprinters (who reach much faster speeds as approach length increases than non-sprinters).... but I still believe most decent athletes are underperforming relative to their strength/speed more in the single leg jump than the double leg jump.
Essentially, I think the athlete in question LBSS will have difficulty at this point increasing his takeoff velocity in his double leg jump without getting stronger. While you provide excellent advice on how to get him stronger, the timeline is just not as immediate, he has to get stronger over multiple months, possibly gain a bit of weight, then learn how to express that strength in the double leg jump, etc. The beauty of the single leg jump is most athletes have a large surplus of horizontal velocity in our approach; converting slightly more of it into a running single leg jump can provide a decent increase to a running vertical over a very quick time period. The caveat being that this certainly won't continue to work (to the degree that increasing strength increases DLJ) as he get's more efficient at taking off at higher speeds. Additionally, if he is a seriously basketballer, it might be a little peculiar looking if his dunks require an approach of close to the entire the length of the court and a perfectly timed bounce of the basketball to provide him a dunk.... However, he ONLY asked to dunk, and if he's quite close (within a couple inches) and he's under a time crunch... I think the single leg jump is the best way to get their quickly.
The other thing is me wondering why you gave such a low recommendation for squat progress in the program you posted (30 lbs per 8 weeks). I said earlier that anything less than 100 lbs squat increase in 6 months would be "fooling around". Obviously this depends on level of training advancement quite a bit, but I stand by that in the case of a young, healthy, athletic and underweight person with less than a 2x bw squat. I tend to think that the 100 lbs is in fact a conservative number of what is possible to achieve in that time frame for a novice of said characteristics. In the given case, LBSS squatted 245 lbs x 3 x 8 as his last work-out. I say he could squat 380 lbs x 5, if not more, in half a year if he eats properly. Do you disagree?
As far as your 100 pound estimate, I agree, but I would add that it's hard in general to put an exact number on it as it depends on a lot of factors such as the squat style (ie high-bar/low-bar) and the build/strength-capacity of the athlete (ie a 6-7 skinny 220 pound athlete squatting 400 will have a harder time reaching 500 than a shorter athlete might have adding 100 pounds), but I would actually argue that this estimation is pretty similar to mine! I came up with my number from the argument that an athlete with the characteristics you describe should be able to add approximately 5 pounds most weeks if they have proper nutrition and recovery (8x5 = 40, [ 30 to be safe ]). So 30 pounds per 8 weeks after 26 weeks ( 6 months ) would come out to about 100 pounds, or your conservative estimate.
As far as LBSS in general, 380x5 in 6-months sounds doable but I don't know if I would would use it as a low-end goal for him. Especially because he is not a professional athlete (real world responsibilities tend to slow us down from goals which assume 6-months of really consistent training, he has already mentioned he has to travel often to far parts of the globe for work). Additionally, I think rep weight goals are also more difficult to predict that heavy singles. Assuming 245x8 equates to a training max of 315 then I think 405x1 is a reasonable training max for him to shoot for over your 6 month period, provided consistent training and good nutrition.