On Sunday night, with about five and half minutes to play and his team down eight points to the Rockets, Denver Nuggets' coach Brian Shaw tried the ol' Hack-a-Howard. It didn't work; Howard went 13 for 19 over a two and a half minute span and doubled the Rockets' lead to 16 points.

ESPN reports that Shaw "lamented using the [Hack-a-Howard] after the game":

"That goes against everything I'm about," Shaw said. "I don't believe in that and I don't think it's in the spirit of the game. So that is exactly what I get for doing that. I'm glad he made his free throws and it shows me to just be true to who you are."

Indeed, losing is exactly what Shaw deserved for resorting to the Hack-a-Howard. But not because the strategy is distasteful or morally questionable. No, Shaw and the Nuggets deserved to lose that game because the Hack-a-Howard is a terrible strategy.

The worst thing for Nuggets' fans is that this is old news. Patrick wrote a post on on the subject over a year ago, and he isn't the only person to note the ineffectiveness of the strategy; John Hollinger wrote about it in January of 2012, and Dave Berri and Dean Oliver wrote about it well before that. So not only did Shaw use an ineffective strategy, he used one that has been known to be ineffective for quite some time.

For those of you looking for a quick recap of the math behind the Hack-a-Howard, let me quote Dave Berri from Patrick's article:

The value of a point is 0.03260287. The value of a free throw attempt is -0.0151305; or, more precisely, 0.45032 * the value of a possession employed (or -0.0336).

Given these values, if a player took 100 free throw attempts, he would have to make 46.4085% to break-even. This is found by multiplying 100 * -0.01513505.  Then divide this by the value of a point, 0.03260287.

So any player who makes more than 46.41% of his free throws should to go to the line as much as possible.

Dwight Howard is at 57.6% shooting free throws for his career, which is well north of 46.4%. The decision to go for the Hack-a-Howard looks a bit better when we learn that Howard has shot around 49% on his free throws over the past two seasons (and was at 49% on the season going into tonight's game), but that would still be a bad idea, because 49% still makes it past our 46.4% cutoff.

The list of players that you should try to hack is very small. By my count, since 1979-80, this strategy would probably only work on four players. This because, while 116 players have shot worse than 46.4% on free throws over their NBA careers, only four of them -- Ben Wallace, Chris Dudley, DeAndre Jordan, and Andre Drummond -- ever ended up playing major minutes and would have a chance to be on the court near the end of a meaningful game.

The good news for Brian Shaw is that two of these players are currently playing! So if he actually wants use the Hack-a-Whoever stategy effectively, he'll try it against the Clippers or the Pistons.

Unless Shaw finds that actually winning games isn't being true to himself.