Rondo is only shooting 41% on free throws this season and 62.1% for his career. You might think he is just a poor natural free throw shooter, but a closer look at his career splits reveals something:
October: 15 made, 29 attempted = 51.7%
November: 73 made, 145 attempted = 50.3%
December: 105 made, 156 attempted = 67.3%
January: 111 made, 176 attempted = 62.5%
February: 101 made, 170 attempted = 59.4%
March: 110 made, 156 attempted= 70.5%
April: 74 made, 116 attempted= 63.7%
This trend to warm up by mid December holds steady in every one of his seasons. While he still is not a great free throw shooter, if he was putting more effort into free throws during the off-season, he probably would be around 64.7% for his career (the average of free throws not in October or November, not a huge difference, but a pretty modest bump.) And it is likely that the extra work he put in would compound over the years.
Now let's take a look at his shot:
If you have 8:45, I recommend you just watch this video and skip the rest of my assessment. This video clears up shooting problems (mental and physical, Rondo's and anybody else's) better than I ever could.
The first mistake Rondo makes is bringing the ball from his right hand over to his left hand. This causes the elbow and the follow through to be crooked, which will cause the ball to go to the side of the basket. His right elbow should be placed at a 90 degree angle with his left elbow coming toward the ball, which will help his shot stay straight. (He does a good job of following through here and pointing his finger toward the basket.)
The other problem he has is that he is not getting enough power from his legs. Instead of coming back a little (somewhere between 45 degrees and 30 degrees) he goes straight up, meaning he is getting no help from his legs. This is why the ball falls short of the basket.
He does, however, do a good job getting up on his toes and keeping his hips square to the basket.
And most importantly, he does not get frustrated when he misses it (which could lead to affecting other aspects of his game.)
All he has to do is keep these fundamentals in mind and put more work into free throw shooting in the offseason. His improvement shooting long 2s over the last 3 years show he is capable of hitting and improving upon his shot, he just needs to shift his focus now from jump shots to a set free throw shot.
