# The Mathematics of Hack-a-Howard

Ever since the days of Hack-a-Shaq, teams have been on the lookout for big men with poor free-throw shooting percentages so that they can exploit basketball’s free-throw rules to their advantage.  Sporting a career 57.7% free throw shooting percentage, Dwight Howard hovers tantalisingly around the level where such tactics are considered. Unless after 9 years of struggle Howard finally breaks through and lifts his numbers in this area out of the basement, it’s a fair bet that Rockets fans will be seeing more hacking than they have for quite some time in the coming season. The big question, then, is whether or not hacking is an effective strategy to employ – should Rockets supporters be cheering or worried when the free-throw parades inevitably start?

In this post, I’ll be delving into the mathematics of Hacking to try to answer that question. If for some reason you have an aversion to numbers and formulae in general (I can’t imagine why you would), then this may not be the post for you.

Before we begin, let’s step back and consider the strategic reasons why a team would consider indulging in a Hackathon (in the NBA sense of the term):

• It may reduce the rate at which the other team scores.
• It will give them more time with which to mount a comeback.

The first of these is the reason that most people look to in order to justify or dismiss the validity of Hacking. But in order to get to grips with whether it’s truly worth doing, you have to consider the extra possessions as well.

# Expected Value:

Questions of this nature always circle around to Expected Value eventually, and in this instance it’s an appropriate starting point. A naive way of looking at whether Hack-a-Howard (from now on HaH) is worth doing is to compare the expected value of two Dwight free-throws against that of an average Rockets possession. We have Howard’s career free throw percentage of 57.7%, and last year’s putrid 49.2% mark to use.

Rockets 2012-13: 1.067 Points per Possession (PPP)
HaH (career FT%): 1.154 PPP
HaH (last year’s FT%): 0.984 PPP

So on that basis it would seem that while Howard’s career average is enough to take him out of the Hack Zone, last year’s performance isn’t good enough to do so.

Accounting for Offensive Rebounds:

But wait! According to 82games.com (this page is pretty old, but I don’t see a good reason why that number would fluctuate very much), teams rebound 13.9% of their own free-throws.  Offensive rebounds are already factored in to PPP statistics (the formulae involved treat offensive rebounds as a continuation of the original possession rather than a new one), but not into the Expected Value of HaH. While in general teams tend to score pretty heavily on offensive rebounds, let’s assume that the Rockets’ hypothetical opponents are dedicated enough to the hacking strategy that they send him back to the line if the Rockets corral the rebound. This changes the calculation – the expected value of the first free-throw is the same, but on a miss of the second free-throw there is now the possibility of further shots, so it becomes:

`PPP = 2*FT%/100 + (1-FT%)*0.139*(PPP)`

When we fill in the two FT% numbers for Howard and solve for PPP, we get the following results:

HaH (career FT%): 1.226 PPP
HaH (last year’s FT%): 1.059 PPP

With this adjustment we start to edge closer to respectability – there appear to be marginal benefits to Hack-a-Howard if he is as miserable from the line as he was last year, but even a small improvement will tip the scales away from it in the long run. And it’s definitely better to avoid HaH if he’s back to his career average, right? Well, let’s see what happens when we factor in the other half of the equation.

# Accounting for Extra Possessions:

Thinking about the long run is all well and good, but as I’ve pointed out before, basketball games are not decided in the long run. In the context of an individual basketball game, the ideal strategy is not the one that will score you the most points if you were to keep playing until the end of time. Rather, it is the one that will score you the most points before the end of the game, and these are subtly different things.  Having a time-limit alters the strategies involved, sometimes quite dramatically.

How does this change things in the hacking debate? I’m going to analyse with the help of a fairly simple example. The NBA does not allow hacking in the last two minutes of a games. But imagine a situation in which there are about 2:35 on the clock and one team is down 7 having just scored.  In the short term, they would like the scores to be as close as possible when the window for hacking ends at 2:00. Should they hack? If they don’t hack, then each team will probably get one possession before the window for hacking closes. However, if they do hack, then the trailing team will get two possessions to try to close the gap against the other team’s free-throw shooting. So let’s work through the probabilities in each case.

I’m going to use the stats of the Oklahoma City Thunder as the hacking team in these calculations, because they were the last team to try it out against the Rockets. On any given possession, a team will score between 0-4 points. We can calculate the probability of each score happening and generate a distribution of the change in score over that possession. The number crunching involved is outside the scope of this article, but I went and calculated these numbers for both the Rockets and Thunder using numbers from NBAwowy and Hoopdata. (NB. Unfortunately I couldn’t find any good data on the number of 4 point play opportunities the teams get each year, so I’ve had to ignore them and just give find the probabilities of scoring between 0-3 instead).

Rockets:

```0 point possession: 54.48%
1 point possession: 3.77%
2 point possession: 30.24%
3 point possession: 11.51%```

Thunder:

```0 point possession: 51.43%
1 point possession: 3.14%
2 point possession: 36.60%
3 point possession: 8.83%```

Option 1: No Hacking

Using the above probabilities, we can generate the distribution of how we would expect the score to change if the Thunder decided not to do any hacking:

As you might expect given the Thunder’s excellent offense, in a 1 possession competition they are very slightly more likely to do well:

• 31% of the time they will make some inroads into the deficit,
• 40% of the time there will be no change in score differential,
• 29% of the time the Rockets would pull further away.
• The mean of the distribution is 0.04, so ever so slightly in the Thunder’s favour in the long run.

Option 2: Hacking

In this scenario, the Thunder are going to get two possessions to try to score and the Rockets are going to get 4 free throws from Howard. First let’s look at how things would shake out using Howard’s numbers from last season:

The first thing to notice here is that the probability of the score staying the same is much lower. This is a virtue of there being more possessions to work with – the more shots that are put up, the less likely that the score will stay the same. Overall, this distribution is skewed in the Thunder’s favour:

• 41% of the time the Thunder will make gains,
• 20% of the time the score will remain unchanged,
• 39% of the time the Rockets will extend their lead.

So in this scenario the Thunder have significantly improved their chances of improving their position (34%->41%). They are ahead on average as well – the mean of the distribution is 0.09. So if Howard’s free throw shooting remains at last season’s numbers it is well worth hacking. But we already knew that from the Expected Value calculations we did earlier.

The more interesting scenario is to run the same calculations, but with Howard’s career free throw percentage instead:

Eyeballing the graph would make it seem as though the Rockets are coming out ahead on balance. Here are some numbers from this graph:

• 34% of the time the Thunder will make gains,
• 20% of the time the score will remain unchanged,
• 46% of the time the Rockets will extend their lead.
• The mean of the distribution is -0.25, firmly in the Rockets’ favour.

Note though, that just because on average this strategy favours the Rockets does not mean that it’s not worth the Thunder doing. The numbers reveal a very interesting point: OKC are still more likely to make a gains using this strategy than they would be by not hacking (34% to 31%)! This gain is at the expense of giving the Rockets more of a shot at pulling away, but if you are losing by 7 then staying that far behind may be just as bad as falling further adrift. So there is a legitimate argument that it might still be better to employ this strategy than to let the game continue in the same vein.

The reason why this analysis works out differently is that the extra possessions make a big difference. This is not something you can see by only looking at expected value – you have to delve into the related distributions to see it properly. Hacking is a situational tool, and it is impossible to give a single threshold beyond which a team should hack. That calculation must take into account the number of additional possessions that will be gained by employing the tactic and the state of the game.

Ideally, you would combine this sort of analysis with data about the percentage chance of winning given the time left in the game and the score differential. Such data is available – for example, John Schumann uses it in his series of posts about the most important plays of the NBA finals. With tools like that you could make a fairly persuasive case about whether or not it made sense to hack in a given situation. When the season starts and the hacking begins, it may be possible to judge whether opposing teams are deploying it properly.

In the mean time, Rockets fans are going to have to live with the fact that there will almost certainly be situations where it is worth the other team’s while to send Howard to the free-throw line, even if he can improve his free throw shooting over the summer.

Rob Dover writes for Red94. You can find him on Twitter @Bored_Trevor.

• thejohnnygold says 7 months ago

I understand that--truly. I'm not sure what the confusion is. I am basing my opinion of this off of what I believe will be a very strong defense for the Rockets. I think teams will struggle to maintain anything above 45% shooting against us. At the end of games, the only thing I see beating us is a barrage of three pointers--which probably would have succeeded whether they used a hack-attack or not. Thus, in my estimation there just isn't much to it. Teams win and lose this way all the time.

I appreciate the lengths you went to in order to analyze this, but for myself, there are still questions. The difference between a 3 point lead and an 8 point lead is one. The difference between gains and actually coming back to tie/win is another.

I can't help but look at these things with contextual questions as many of these scenarios will not fall into the median averages we are looking at.

Maybe I'm deluded, but in my mind it goes like this (roughly). Your scenario calls for 12-16 ft's (we'll use 14) and 6-8 possessions (we'll use 7). Say Dwight shoots 50% and we don't rebound any of his misses. That's 7 points. OK. Let's say our opponent makes 3 three pointers in that span going 3-7 (43%) for 9 points. OK. They made gains. But what was the scoring margin before that? If it was only 2 points would they have really employed the hack-attack since it has to happen before the 2 minute mark (to reasonably count 7 full possessions you'd need at least 70 seconds so they have to commit to this around 3:15 left in the game)? In my mind, this will typically occur with a larger scoring margin and the opposition will need to shoot at least 4/7 (57%) to make significant gains. While it does happen, and I recognize the statistical reasoning for it, it is just not something that concerns me more than the odds of losing a game in like manner without an opponent using a hacking strategy. Sometimes, one team just gets hot and the other goes cold at the end of the game.

Again, I understand why a team will statistically make this play as it gives them more of a chance. I'm not disagreeing with your findings. It's just something that does not concern me in regards to the Rockets' bottom line of winning and losing--at least when we have the lead. I have no doubt we will lose 2-3 games this year due to Howard's poor free throw shooting. I can live with that. In the playoffs we may have to make a more concerted effort to hide him as a single victory has much more value....or hopefully he's shooting 60%+ and it's not a concern : )

What are your thoughts regarding the difference in employing a hack-attack when our opponent is ahead by 6 points vs. behind by 6 points? Obviously, they would not do it to stop the clock, but to stop any shots we might take. It would eat time (presuming they execute it correctly) and keep Howard going to the line severely limiting our ability to outscore them--this actually concerns me more than a team trying to come back against us.

• Sir Thursday says 7 months ago

This has led me to a different thought. Which is more likely to occur at the end of a game? (let's assume 4 possessions) Dwight Howard goes 0-8 from the free throw line, or the Rockets' regular offense hits a small rut and goes 0-4?

I think you're making the mistake of missing out the extra possessions that happen if you're being hacked here. It's not a comparison of 4 possessions vs 8 free throws, it's more like 4 possessions each vs 12-16 freethrows and 6-8 possessions for your opponent. It's that extra time that makes the difference by giving the other team the chance to score more, not so much the amount you make yourself.

ST

• thejohnnygold says 7 months ago

As a follow-up, I just spent the last 30 minutes trying to find anything that had a corresponding win/loss statistic associated with the Hack-a-Howard strategy. I came up with nothing. Again, I can see why teams will do it, but I don't think it will hurt us much when protecting a lead (I'm sure it will happen 2-4 times, but that generally coincides with the opponent exceeding expectations on the offensive end as well). My concern is when we are behind and trying to come back. I think this is where the strategy can hurt us the most.

• thejohnnygold says 7 months ago

Hmm, you may have missed the point of the article slightly. The conclusion I ended up drawing was that teams will hack because it does give them a better chance of winning than it would otherwise. It's true that if the other team is hacking then they will be chasing the game (and therefore on balance the Rockets will be in a strong position from which they are likely to win the game), but nevertheless the team should be minimising the chances of the other team making a comeback, and that starts with better free-throw shooting.

ST

Perhaps...firstly, my post was in response to Steven's post about the difference in point value in relation to ft%.

I understand what you are stating about the opponent doing it despite the appearance of it's futility. Still, the bonus is a mere +3% difference and that difference is in regards to "gains" which does not imply victory. Certainly, as you allude to at the end of the article, there will be many opportunities to observe the situational use of this technique next season. My closing remark was in regards to some people's concerns that a hack-attack will hurt us overall in regards to winning and losing. I really don't believe it will.

I of course agree that better free throw shooting on our part minimizes this concern. I also agree that teams will utilize the strategy. For me, I view the two situations the same: excepting anomalies shooting averages will generally be adhered to. Thus, given the expected ppp for Houston, whether Hack-attacked or not, I expect our defense to be stout enough to maintain most leads.

This has led me to a different thought. Which is more likely to occur at the end of a game? (let's assume 4 possessions) Dwight Howard goes 0-8 from the free throw line, or the Rockets' regular offense hits a small rut and goes 0-4?

• Sir Thursday says 7 months ago

Obviously. No one predicted Nick Anderson would go 0% (0-4) from the line to close out game 1 of the Orlando Finals after shooting 70% for the season--but it happened.

The numbers are based off the average and nearly all averages have anomalies--sometimes that is a losing team's best hope.

Also, the article factored in rebounding--we've all seen games with two clanked free throws, but the offense grabs the rebound and seals the win anyways.

I seriously doubt anyone is saying, "We should just let Howard shoot free throws all game and we'll be the most efficient offense in the league!"

The point is to dispel the concern about any hack-attacks. The odds are we will be fine if this strategy is employed. Remember, the opposing team has to score too--which is the whole point. Barring ridiculous Monta-Ellis-35 ft.-running-sideways-chucks-at-the-rim that fall in we're going to be fine.

Hmm, you may have missed the point of the article slightly. The conclusion I ended up drawing was that teams will hack because it does give them a better chance of winning than it would otherwise. It's true that if the other team is hacking then they will be chasing the game (and therefore on balance the Rockets will be in a strong position from which they are likely to win the game), but nevertheless the team should be minimising the chances of the other team making a comeback, and that starts with better free-throw shooting.

ST

• Richards says 7 months ago

Teams use Hack-a-whatever-his-name-is in dire situation. Nobody start hacking DeAndre Jordan in the beginning. Teams will hack anybody if they are run out of time and to make a miracle come back. We all knew they will try to hack poor FT shooters first.

So doesn't matter Hacking-a-Howard is a good idea or not. They will hack. Expect for a lot of Hack-a-Howard festivals.

• thejohnnygold says 7 months ago

Obviously. No one predicted Nick Anderson would go 0% (0-4) from the line to close out game 1 of the Orlando Finals after shooting 70% for the season--but it happened.

The numbers are based off the average and nearly all averages have anomalies--sometimes that is a losing team's best hope.

Also, the article factored in rebounding--we've all seen games with two clanked free throws, but the offense grabs the rebound and seals the win anyways.

I seriously doubt anyone is saying, "We should just let Howard shoot free throws all game and we'll be the most efficient offense in the league!"

The point is to dispel the concern about any hack-attacks. The odds are we will be fine if this strategy is employed. Remember, the opposing team has to score too--which is the whole point. Barring ridiculous Monta-Ellis-35 ft.-running-sideways-chucks-at-the-rim that fall in we're going to be fine.

• Steven says 7 months ago

The shooter's rhythm is irrelevant to the point I was making. Rob's number on offensive efficiency isn't based on Howard shooting his free throws in a Hack-a-Dwight rhythm--it's based on his normal average. Even if the other teams alternated fouling Howard and Asik each possession, the Rockets could count on getting about 1.2 points per possession, which is an outstanding scoring rate. The Rockets offense would be in bigger trouble if the other team DIDN'T foul with those two on the floor.

Only if they hit 60% of the free throws. They hit 40% and its .8 PPP.
• Jeby says 7 months ago

Shaq said that he liked the hack-a-Shaq because he would get into a rythum this he would start knocking them down. This idiotic lineup would allow the teams to foul Howard one time and Asik the next. Thus neither would get the rythum that comes from the Hack-a-whoever. The two Cs should never step foot on the court at the same time, unless its the last 5 seconds on the clock and the Rockets are defending.

The shooter's rhythm is irrelevant to the point I was making. Rob's number on offensive efficiency isn't based on Howard shooting his free throws in a Hack-a-Dwight rhythm--it's based on his normal average. Even if the other teams alternated fouling Howard and Asik each possession, the Rockets could count on getting about 1.2 points per possession, which is an outstanding scoring rate. The Rockets offense would be in bigger trouble if the other team DIDN'T foul with those two on the floor.
• Steven says 7 months ago

Asik is CLUTCH. He has proven he is CLUTCH.

Asik took Rahat's job in the bear suit? How is he going to get the interviews?
• Buckko says 7 months ago

Shaq said that he liked the hack-a-Shaq because he would get into a rythum this he would start knocking them down. This idiotic lineup would allow the teams to foul Howard one time and Asik the next. Thus neither would get the rythum that comes from the Hack-a-whoever. The two Cs should never step foot on the court at the same time, unless its the last 5 seconds on the clock and the Rockets are defending.

Asik is CLUTCH. He has proven he is CLUTCH.

• feelingsupersonic says 7 months ago Great analysis Dover, thank you.
• Hockey the Harden Way says 7 months ago

I really wouldn't want them taking half-court shots in a Hack-a-Howard type situation. If you watch the tape of the sequence where OKC hacked Asik in Game 5 this year, there's one possession where Harden chucks up a shot from inside his own half, anticipating that Asik will get hacked. Instead, the refs swallowed their whistles and it was a turnover. It is a much better strategy to hold onto the ball and let the hacking happen than to throw up a prayer with a very small chance of going in and a much larger chance of not even getting free throws out of it.

ST

I remember that play too. When we did Hack-a-Dwight in the Laker game, Kobe was chucking up long shots.

Too bad they can't change the rules here. Purposefully hacking a player away from the ball should be free throws plus possession. Not just for the last two minutes of a quarter, but for the whole game.

• Stephen says 7 months ago

Dwight would be the best Rocket offensive rebounder,so I would expect the offensive rebounds to go down when Dwight is at FT line.
OTOH,Jones offensive rebounded at roughly Howard's %,so I would expect him to be paired w/Dwight in such situations.

For a evaluation of a hack-a-whoever,you would need to look at the trailing team's winning % when trailing by a particular amount and using the hacking and when they didn't.

• Steven says 7 months ago

Lightbulb moment: Hack-a-Dwight is one situation in which it would be ideal to play Dwight and Asik together. Since the Rockets' offensive output will be based solely on Dwight's FT shooting, they could put a 100 percent defensive team on the floor to punish the opposing team. Imagine a defensive lineup of Bev-Garcia-Parsons-Asik-Howard still operating with a 1.226 PPP offensive efficiency. That would be like combining the Bulls' defense with Miami's offense...

Shaq said that he liked the hack-a-Shaq because he would get into a rythum this he would start knocking them down. This idiotic lineup would allow the teams to foul Howard one time and Asik the next. Thus neither would get the rythum that comes from the Hack-a-whoever. The two Cs should never step foot on the court at the same time, unless its the last 5 seconds on the clock and the Rockets are defending.
• Sir Thursday says 7 months ago

The one moment most stuck in my mind from last season was that Laker game at Toyota Center...... We used the "Hack-a-Dwight" strategy and stole a game from the Lakers..... A good antidote for this is James Harden and Chandler Parsons practicing their half-court shooting............. The one way to stop "Hack-a-Dwight" cold is a few "four point play" opportunities.

I really wouldn't want them taking half-court shots in a Hack-a-Howard type situation. If you watch the tape of the sequence where OKC hacked Asik in Game 5 this year, there's one possession where Harden chucks up a shot from inside his own half, anticipating that Asik will get hacked. Instead, the refs swallowed their whistles and it was a turnover. It is a much better strategy to hold onto the ball and let the hacking happen than to throw up a prayer with a very small chance of going in and a much larger chance of not even getting free throws out of it.

ST

• 2016Champions says 7 months ago

Lightbulb moment: Hack-a-Dwight is one situation in which it would be ideal to play Dwight and Asik together. Since the Rockets' offensive output will be based solely on Dwight's FT shooting, they could put a 100 percent defensive team on the floor to punish the opposing team. Imagine a defensive lineup of Bev-Garcia-Parsons-Asik-Howard still operating with a 1.226 PPP offensive efficiency. That would be like combining the Bulls' defense with Miami's offense...

Makes sense, good point.

• Jeby says 7 months ago

Lightbulb moment: Hack-a-Dwight is one situation in which it would be ideal to play Dwight and Asik together. Since the Rockets' offensive output will be based solely on Dwight's FT shooting, they could put a 100 percent defensive team on the floor to punish the opposing team. Imagine a defensive lineup of Bev-Garcia-Parsons-Asik-Howard still operating with a 1.226 PPP offensive efficiency. That would be like combining the Bulls' defense with Miami's offense...

• Hockey the Harden Way says 7 months ago

The one moment most stuck in my mind from last season was that Laker game at Toyota Center...... We used the "Hack-a-Dwight" strategy and stole a game from the Lakers..... A good antidote for this is James Harden and Chandler Parsons practicing their half-court shooting............. The one way to stop "Hack-a-Dwight" cold is a few "four point play" opportunities.

• 2016Champions says 7 months ago

The gist of Hollinger's analysis of Hack-a-Howard (from Jan. 2012):

Here's the thing about Hack-a-Dwight, or Hack-an-anybody: The player has to be an exceptionally bad foul shooter for this strategy to have much merit. Emphasis onexceptionally. It works withBen WallaceorDeAndre Jordan. With just about anyone else, it's highly questionable.

Take Thursday night, for instance.Dwight Howardis a career 59.5 percent foul shooter and has done slightly better than that each of the past three seasons. But let's take 59.5 percent as his chances of converting any given free throw. Sending him to the line for two shots produces an expected return of 1.19 points from the foul shots, a scoring rate better than that of any offensive team in the history of basketball. Just sending him to the line time after time is one of the worst percentage moves a team could possibly make.

It gets worse, though. Howard will miss 40.5 percent of those foul shots, and 20.25 percent of those misses will be on the back end of the pair. It's nice to assume that all 20.25 percent will end up with the defense, but it's also unrealistic. The offense rebounds about 1 in 10 missed free throws, and that mark tends to go up for a bad foul shooter. Simple observation backs up this point -- offensive players waste little effort pushing for position whenChauncey Billupsis at the stripe, but they fight like mad whenAndris Biedrinssteps up.

But let's say 1 in 10 of those boards goes back to Orlando, giving the Magic a new possession. That means 2.025 percent of Howard's misses still generate points; assume league-average efficiency on the new trip and that's another .021 points for the offense.

So now you're giving up an average of 1.211 points -- a breathtaking offensive efficiency level -- for the privilege of piling up fouls on your players. That's compared with a normal offensive season, but remember, too, that this year has been anything but normal. Offensive efficiency is down across the league, as noted below, so the points surrendered by this strategy are even more than normal.

Once you factor in offensive rebounding, the break-even point for this strategy in the 2011-12 season is about 48.5 percent -- slightly less for a team with a rebounding disadvantage, slightly more for one with a rebounding advantage. And that doesn't include the attrition factor from having players accumulate fouls.

Howard, at 59.5 percent, was far too proficient for this strategy to be likely to benefit Golden State. Instead it foiled a pretty good effort at the offensive end. The Warriors scored 109 points on just 99 trips against one of the league's better defensive teams … and still ended up losing, largely by riding Hack-a-Dwight down the toilet.

Bizarrely, the Warriors didn't foul Howard in the one situation when it made completely obvious sense -- with 21 seconds left in the third quarter and Orlando playing for the last shot. In that instance, the expected points of Howard free throws would have been nearly offset by the points Golden State scored on the offensive possession it just created.

Thanks, and welcome to the forum!

• pcorcoran says 7 months ago

The gist of Hollinger's analysis of Hack-a-Howard (from Jan. 2012):

Here's the thing about Hack-a-Dwight, or Hack-an-anybody: The player has to be an exceptionally bad foul shooter for this strategy to have much merit. Emphasis onexceptionally. It works withBen WallaceorDeAndre Jordan. With just about anyone else, it's highly questionable.

Take Thursday night, for instance.Dwight Howardis a career 59.5 percent foul shooter and has done slightly better than that each of the past three seasons. But let's take 59.5 percent as his chances of converting any given free throw. Sending him to the line for two shots produces an expected return of 1.19 points from the foul shots, a scoring rate better than that of any offensive team in the history of basketball. Just sending him to the line time after time is one of the worst percentage moves a team could possibly make.

It gets worse, though. Howard will miss 40.5 percent of those foul shots, and 20.25 percent of those misses will be on the back end of the pair. It's nice to assume that all 20.25 percent will end up with the defense, but it's also unrealistic. The offense rebounds about 1 in 10 missed free throws, and that mark tends to go up for a bad foul shooter. Simple observation backs up this point -- offensive players waste little effort pushing for position whenChauncey Billupsis at the stripe, but they fight like mad whenAndris Biedrinssteps up.

But let's say 1 in 10 of those boards goes back to Orlando, giving the Magic a new possession. That means 2.025 percent of Howard's misses still generate points; assume league-average efficiency on the new trip and that's another .021 points for the offense.

So now you're giving up an average of 1.211 points -- a breathtaking offensive efficiency level -- for the privilege of piling up fouls on your players. That's compared with a normal offensive season, but remember, too, that this year has been anything but normal. Offensive efficiency is down across the league, as noted below, so the points surrendered by this strategy are even more than normal.

Once you factor in offensive rebounding, the break-even point for this strategy in the 2011-12 season is about 48.5 percent -- slightly less for a team with a rebounding disadvantage, slightly more for one with a rebounding advantage. And that doesn't include the attrition factor from having players accumulate fouls.

Howard, at 59.5 percent, was far too proficient for this strategy to be likely to benefit Golden State. Instead it foiled a pretty good effort at the offensive end. The Warriors scored 109 points on just 99 trips against one of the league's better defensive teams … and still ended up losing, largely by riding Hack-a-Dwight down the toilet.

Bizarrely, the Warriors didn't foul Howard in the one situation when it made completely obvious sense -- with 21 seconds left in the third quarter and Orlando playing for the last shot. In that instance, the expected points of Howard free throws would have been nearly offset by the points Golden State scored on the offensive possession it just created.

• NorEastern says 7 months ago

Just one hell of an analysis Rob. One of the best reads I have had in a while.

• 2016Champions says 7 months ago

My take on it is basically this: Hack-A-Dwight doesn't work unless Dwight shoots even lower than his usual rate at the free throw line, and the opposing offense scores at a very elite rate. I don't think we have to worry much considering how we will probably be a good defensive team, and there are only a few teams that will score at an elite rate (and by elite I'm thinking 1 PPP or higher).

Even though it doesn't really work, it's a tactic that will probably still be used simply because it creates more possessions which is something teams would want if they're down late in the 4th.

• Sir Thursday says 7 months ago

This is outstanding. However, I would throw one more wrinkle in there: OKC's expected output should probably be based on their half-court offensive efficiency rather than their overall offensive efficiency. Free throws, either made or missed, rarely fuel fast breaks.

Yeah, you're probably right. Another limitation is that while I took Offensive Rebounds into account in the Expected Value section, I didn't include them in the Additional Possessions bit. You could add them in but it would make all the calculations a lot more complicated. Since that part was more of an illustrative example than anything else, I figured it wasn't too big a deal if the numbers weren't perfect.

ST

• Jeby says 7 months ago

This is outstanding. However, I would throw one more wrinkle in there: OKC's expected output should probably be based on their half-court offensive efficiency rather than their overall offensive efficiency. Free throws, either made or missed, rarely fuel fast breaks.

• 2016Champions says 7 months ago

Very interesting.

Does anyone here have insider? Because I would like to also read Hollinger's take on the issue and compare notes:http://insider.espn.go.com/nba/story/_/page/PERDiem-120113/nba-dwight-howard-foul-strategy

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Red94 is ESPN.com's TrueHoop Network Houston Rockets Affiliate. We feature daily news, game coverage, and analysis. Navigate the blog through the categories/tags listed at the bottom of the page. Click here to participate in our reader discussion forum. The forum is mirrored with our front page, so all comments to our articles can be accessed from both ends.
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Rahat Huq

### NEWS EDITOR

Mitchell Felker

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