Mathematical Merits of Hack-a-Howard
Posted: Thu Dec 06, 2012 2:36 am
It's hilarious to me how the mainstream media seems to think Howard's woeful free throw shooting is one of the major reasons for the Lakers' struggles this season. Mathematically it just seems like it has to be such a minor factor.
I am sure someone has done the math concerning type of strategy already. Just a shallow analysis by me follows:
Assume 50% free throw shooting, then Hack-a-Howard locks the Lakers into about 1.00 points per possession (actually a tiny bit more due to a few offensive rebounds off of misses on the second free throw), allows the Lakers to surge into the penalty, and may get some random players into foul trouble. If I am not mistaken, 1.00 points per possession is about average offensive production, and getting into the penalty and getting opponent players into foul trouble has to add some extra benefits.
Now here is what I am interested about. Hack-a-Howard generally comes in half-court offensive situations rather than the fast break situations. This would make Hack-a-Howard an even less successful strategy for the team that opposes the Lakers. The average offensive production in half-court offensive situations has got to be a little less than that of half-court+fast-break situations.
Has anyone compared the points per possession resulting from Hack-a-Howard vs the points per possession resulting from letting the Lakers run their regular half-court offense deep into the 4th quarter? The Lakers currently average 1.05 points per possession running the regular offense, and presumably less than that in the half-court set deep into the 4th quarter. Assuming 50% free throw shooting, Hack-a-Howard would seem to provide barely any advantage to the opposition at all, if any when you consider the effects of getting into the penalty in addition to the effects of getting opposing players into foul trouble, which may even make them play more tentatively on defense.
The only situation in which I see employing Hack-a-Howard as a clever strategy is when the opposition has a fairly sizable lead deep into the 4th quarter and if offensive efficiency resulting from purely free throw shooting is characterized by a smaller standard deviation than half-court offensive efficiency. If offensive efficiency resulting from purely free throw shooting is in fact characterized by a smaller standard deviation than half-court offensive efficiency, then an opposing team that has a fairly comfortable lead would gain an advantage by employing Hack-a-Howard strategy, because the Lakers would be less likely to put together an ultra efficient offensive run via an unexpected streak of hot Howard free throw shooting than they would through an unexpected streak of hot half-court offense.
In summary, I would interested to see:
1) Comparison of half-court offensive efficiency vs offensive efficiency resulting from poor free throw shooting
2) Standard deviation of offensive efficiency resulting from purely free throw shooting vs standard deviation of half-court offensive efficiency
In the first comparison, a square table could even be devised that plots half-court offensive efficiency on the y-axis and free throw % on the x-axis. In the squares, the net offensive efficiency resulting from the corresponding free throw % could be inscribed. With this table, a team could find the opposing teams' average half-court offensive efficiency on the y-axis, and then the free throw % of an opposing player on the x-axis. In this square, the team could see if employing Hack-a-_____ strategy would be the strategy of choice.
I am sure someone has done the math concerning type of strategy already. Just a shallow analysis by me follows:
Assume 50% free throw shooting, then Hack-a-Howard locks the Lakers into about 1.00 points per possession (actually a tiny bit more due to a few offensive rebounds off of misses on the second free throw), allows the Lakers to surge into the penalty, and may get some random players into foul trouble. If I am not mistaken, 1.00 points per possession is about average offensive production, and getting into the penalty and getting opponent players into foul trouble has to add some extra benefits.
Now here is what I am interested about. Hack-a-Howard generally comes in half-court offensive situations rather than the fast break situations. This would make Hack-a-Howard an even less successful strategy for the team that opposes the Lakers. The average offensive production in half-court offensive situations has got to be a little less than that of half-court+fast-break situations.
Has anyone compared the points per possession resulting from Hack-a-Howard vs the points per possession resulting from letting the Lakers run their regular half-court offense deep into the 4th quarter? The Lakers currently average 1.05 points per possession running the regular offense, and presumably less than that in the half-court set deep into the 4th quarter. Assuming 50% free throw shooting, Hack-a-Howard would seem to provide barely any advantage to the opposition at all, if any when you consider the effects of getting into the penalty in addition to the effects of getting opposing players into foul trouble, which may even make them play more tentatively on defense.
The only situation in which I see employing Hack-a-Howard as a clever strategy is when the opposition has a fairly sizable lead deep into the 4th quarter and if offensive efficiency resulting from purely free throw shooting is characterized by a smaller standard deviation than half-court offensive efficiency. If offensive efficiency resulting from purely free throw shooting is in fact characterized by a smaller standard deviation than half-court offensive efficiency, then an opposing team that has a fairly comfortable lead would gain an advantage by employing Hack-a-Howard strategy, because the Lakers would be less likely to put together an ultra efficient offensive run via an unexpected streak of hot Howard free throw shooting than they would through an unexpected streak of hot half-court offense.
In summary, I would interested to see:
1) Comparison of half-court offensive efficiency vs offensive efficiency resulting from poor free throw shooting
2) Standard deviation of offensive efficiency resulting from purely free throw shooting vs standard deviation of half-court offensive efficiency
In the first comparison, a square table could even be devised that plots half-court offensive efficiency on the y-axis and free throw % on the x-axis. In the squares, the net offensive efficiency resulting from the corresponding free throw % could be inscribed. With this table, a team could find the opposing teams' average half-court offensive efficiency on the y-axis, and then the free throw % of an opposing player on the x-axis. In this square, the team could see if employing Hack-a-_____ strategy would be the strategy of choice.