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Mathematical Merits of Hack-a-Howard

Posted: Thu Dec 06, 2012 2:36 am
by Kathoro
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.

Re: Mathematical Merits of Hack-a-Howard

Posted: Thu Dec 06, 2012 9:30 am
by J.E.
Average offensive production is more around 1.08. Since Howard is shooting the FTs he's not in good position to grab FTRebounds, which make the chance that the Lakers get any less likely.
Also, most teams aren't stupid about who's going to foul Howard; they don't let their starting C do it, it's usually some guard with almost no foul trouble (from what I've seen).

Re: Mathematical Merits of Hack-a-Howard

Posted: Thu Dec 06, 2012 10:19 am
by Kathoro
That is a good point about Howard shooting the free throws rendering the Lakers less effective at free throw offensive rebounds.

Also, I know that teams are generally smart about who they chose to foul Howard with. I was simply just throwing in all the basic disadvantages of hack-a-howard strategy that go beyond offensive efficiency, regardless of how small they might be.

Re: Mathematical Merits of Hack-a-Howard

Posted: Thu Dec 06, 2012 12:30 pm
by Mike G
I'll guess it's a psychological ploy -- a belief that when he loses confidence in his shot, he'll keep missing them.

He's hit below 50% FT in 7 games -- in all 7, he got 9 or more FTA.
In all 6 games he's shot fewer than 9, he's hit 50% or better.

The 5 games when he's hit at least 66% of his FG include his worst FT-shooting nights: 3/12, 3/14, 7/19, 3/9 and 4/9.
There seems to be a correlation between making FG and missing FT.

Also, "Hack-a-Howard" really has no ring to it. What rhymes with Dwight?
Smite Dwight? .. Spite, bite, fight, blight, incite, ...

Re: Mathematical Merits of Hack-a-Howard

Posted: Thu Dec 06, 2012 2:35 pm
by v-zero
Mike G wrote:I'll guess it's a psychological ploy -- a belief that when he loses confidence in his shot, he'll keep missing them.

He's hit below 50% FT in 7 games -- in all 7, he got 9 or more FTA.
In all 6 games he's shot fewer than 9, he's hit 50% or better.

The 5 games when he's hit at least 66% of his FG include his worst FT-shooting nights: 3/12, 3/14, 7/19, 3/9 and 4/9.
There seems to be a correlation between making FG and missing FT.

Also, "Hack-a-Howard" really has no ring to it. What rhymes with Dwight?
Smite Dwight? .. Spite, bite, fight, blight, incite, ...
I've seen 'bite a Dwight' being thrown around.

I believe it has merit late in games where it would appear Howard is even more overtly aware of his free throw shooting weakness. The Rockets gave a perfect example of how controlling your opponent scoring rate (whilst never stopping it) allows you to form a strategy that will give you the best odds of winning late in games.

Re: Mathematical Merits of Hack-a-Howard

Posted: Thu Dec 06, 2012 5:39 pm
by xkonk
Hollinger had an article last year on Hack-a-Dwight, I believe, and probably Hack-a-Ben Wallace before that. He looked at it strictly from a expected points compared to league efficiency manner, like Kathoro did, if memory serves.

Re: Mathematical Merits of Hack-a-Howard

Posted: Thu Dec 06, 2012 5:46 pm
by Bobbofitos
I'm all for Smite a Howard.

Re: Mathematical Merits of Hack-a-Howard

Posted: Fri Dec 07, 2012 10:21 am
by J.E.
Wouldn't one of the major benefits of Smite-a-Dwight be that you could play your best offensive players and don't have to care whether they're also good defenders? OKC could go Martin and Collison instead of Perkins and Sefalosha, NYK could go with Novak instead of Brewer, MIL could go with Ilyasova instead of Sanders etc.

Re: Mathematical Merits of Hack-a-Howard

Posted: Fri Dec 07, 2012 12:09 pm
by Kathoro
That's a mind-expanding point right there. Had not even considered that. It would be interesting to study the offensive efficiency of the team employing hack-a-howard strategy during the offensive possessions occurring immediately after defensive possessions that end in fouling Howard.

Re: Mathematical Merits of Hack-a-Howard

Posted: Fri Dec 07, 2012 1:26 pm
by DSMok1
Kathoro wrote:That's a mind-expanding point right there. Had not even considered that. It would be interesting to study the offensive efficiency of the team employing hack-a-howard strategy during the offensive possessions occurring immediately after defensive possessions that end in fouling Howard.
Well, a possession beginning with either a made or missed free-throw is not going to be very high-efficiency (no steals or easy fast-breaks). Of course, if you're playing 3 guards and 2 forwards (nobody to guard Howard), then your shooting percentages would likely be good. Not a lot of offensive rebounds, though...