Sunday, March 2, 2008

Hack a Whomever - Why It Never Works

I hammer my boy Lawrence Frank for his poor in game coaching a lot, it's no secret. He can be a good coach in the NBA if he would leave his Byron Scott ideas about substitution and timeouts behind and just coach the in game situations as they arise.

So this little post is yet another attempt to dissuade him from the error of his ways. This time, however, I wish to appeal to his obvious respect for statistics and computing. This time, I have proof that what he is doing is essentially futile.

Frank, like Scott, is inordinately fond of hoarding timeouts for use at the end of the game in case he has to micro-manage it to erase a moderate lead late, say 7 points or less. This is essentially a self fulfilling strategy - IF you thus hoard, then you are almost ENSURING that you will need to use them, because your failure to use them earlier, to throw water on the other teams' runs or to settle down your own team when it is in disarray, guarantees that your leads will evaporate or close games will widen against you by the time the crunch arrives.

Frank does not see this. His strategy is akin to the Invasion of Iraq - there were no terrorists there, but your invasion gave them the opportunity to be there, and so they are there now. Similarly, the game was not close, but your coaching as if it would inevitably be close forced you to make it close, and thus it was.

There are a lot of time worn strategies in baseball that have never been challenged, such as playing the infield in. In this case, however, it occurred to me that we could indeed mathematically test the validity of the Hack a Whomever strategy at the end of the game. This blog is the results of that study.

Let's set the stage:

The Hack a Whomever strategy is one where one finds his team down by more than one score with less than 2 minutes remaining in the game. The idea is to foul the other team right away when they get possession, put them on the line, hope that they miss occasionally, and score as quickly as you can when you have the ball. If you get enough possessions, and the other team misses enough foul shots, you can narrow the gap to one score. Then "it's anybody's game".

Frank (and other coaches) further refine this strategy by relying on 2 point baskets, gambling that they can drive to the hoop and score 2 with greater percentage than 3s because the other team is not going to foul them.

There are various fallacies of this strategy, such as the unwillingness of the other team to foul you and make you earn it at the stripe. But without going there, I posed the simple question - Given this strategy, what is a reasonable expectation of points differential by using it?

I broke down the strategy into 6 identifiable and quantifiable variables:
SLG - Number of seconds left in the game
SYP - Number of seconds of your possessions
SFO - Number of seconds before you foul your opponent
YSP - Your shooting pct
OFP - Your opponent's free throw pct
COS - Whether you shoot 3s or 2s

Clearly, by the way, shooting pct varies with your choice of shooting 3s or 2s.

I began by constructing the formula. Given so many seconds left in the game (SLG), and given the amount of time in seconds it takes you to score (SYP) as well as how many seconds it takes you to foul the other team (SFO), the number of opportunities that both teams together within the time remaining will be:


For example, if there is 90 seconds left in the game, and it takes you 20 seconds to score and 10 seconds to foul, there will be at most 3 such exchanges of possession. If you can get your possessions down to 10 and can foul on average at 5, you can get 6 such exchanges.

Clearly, the number of possessions will not be an integer, so I modified the expression to take that into account, using the Greatest Integer Less Than function, or FLOOR:


So if we plug in 12 seconds to score and 7 seconds to foul, say, we'll get an integral value for the number of possessions.

Now, how many points can we expect to score? Take the number of possessions, take the kind of shot, and take a shooting pct for that kind of shot. Thus:


So, if we're gonna shoot 2s, and we have 3 possessions, and we shoot 67%, we'll should expect to score 4 points. If we shoot 3s, have 6 possessions and shoot 50%, we should expect to score 9 points.

Of course, the other team is not standing still. They're getting fouled (btw, it is assumed that you are over the limit, which, in this scenario, is the best case - otherwise more time will have to tick down as you foul repeatedly with the other team not having to shoot free throws) and sinking some shots. Remember, they shoot 2 shots. Thus they are scoring:


Given the NBA average of FT pct of 75%, and given those 3 possessions, the other team will score at least 4 points. If they have 6 possessions, they will score 9.

The expectation, therefore, of the strategy, is the difference between these two scoring expectations:


or, distributing out, we get:


This is mathematically the expectation for the net points you will get from such a strategy. Like it or not, this is the formula.

All that remains is to plug some values in.

As we can see in our above examples, their net scoring is 0. That is, nothing is gained from this strategy.

Well, a coach might argue, that assumes an NBA average for free throw shooting. But at the end of the game there is more pressure, especially if the team you're facing is on the road (ie, you're at home) and if you foul the right person, ie, one who's a bad foul shooter.

Okay, lets use these numbers, then:

SLG - 90
SYP - 15
SFO - 10
YSP - .500
COS - 3
OFP - .400

This says there's a minute and a half left in the game, it takes you 15 seconds on average in a possession during which you score half the time and when you do it's a three, while it takes you 10 seconds to foul the duffer at the line who only shoots 40%.

Expectation? +2 points.

That's it? That's all I can expect?

That's it. So if you're down 3, you can expect to lose. You're far better off letting your team play.

Of course, no coach is gonna go into the Hack-a-Whomever down by 3 with 90 seconds left. They'd more likely use it if they were down, say 5. But if your expectation is net +2, why in the world would you do it?

Even more to the point, this scenario assumes you shoot 3s. LFrank, and many other coaches, would say, well, we don't have to shoot 3s. Oh no? Clearly, given 50% shooting, and shooting 2s, our expectation should be LESS. Ie, we'll lose by a larger deficit!

Even if we crank up our shooting pct to 75% shooting 2s, our expectation in the same situation with the duffer and the time allotted yields:

Expectation? +2 points!

See? Altho the 2, given matador D due to a reluctance of the other team to foul, has a much higher percentage of success, the net comes out EXACTLY THE SAME because the 3 pointer COUNTS AS MORE POINTS!

This only makes sense, after all. The other team is shooting foul shots and will sink some of them. You're making up the difference, but at a rate so slow it can't possibly ever shrink to zero within the allotted time, ie, the time that's left when you elected to use the strategy.

Thus Frank's strategy of Foul-and-go-for-2 is just as futile as if he let his guys bomb away from downtown.

Wait - the coach might say - we don't use this because it is guaranteed to work, or even likely to work. We use it in the hope we get lucky.

Fair point. So then, exactly how lucky do we have to get?

Let's be generous and very optimistic with our luck, and reasonable about when we're gonna use it.

Let's say we're down by 7 with 2 minutes left. This is the earliest we would use the strategy, and we would have to be awfully alert to decide to use it with that much time left. Let's further say that we're gonna go on a roll and shoot 75% from 3, only take 10 seconds off the clock, and foul a 40% duffer (say, like Josh Boone) from the line with 5 seconds EVERY time.

Expectation? +11.6

So this WOULD work - BUT there are other considerations.

For example, not only would you need to be lottery lucky, the lead will evaporate long before the 2 minutes is up. In fact, you will tie it in 0:40, and take the lead with 30 seconds left. Will you continue with the strategy after then?

And what if the other coach, sensing your use of the strategy early, puts all guards out there, all of whom are at least 65% free throw shooters? The best you can hope for is a tie. And that's assuming you have the perspicacity to start using the strategy with 2 minutes left. If you waited until only a minute and a half left, you lose.

I did see this strategy work exactly once, and it was at the college level. Stanford used it with a little over 1 minute left vs Rhode Island in the 98 NCAAs to advance to the Final Four. But they were even luckier than the improbable scenario posed above. And again, they were young college players, not professionals used to playing tight games on the road in packed houses.

Frank, however, does not get this. He robotically uses it, uses the version less inclined to success, and uses it so often without positive results that he actually undermines his authority by demoralizing a team that sees what every other person in the building sees - IT NEVER WORKS. WHAT'S THE POINT??

Take Tuesday's game vs Orlando. With 1:31 left the Nets foul, down 8. They are shooting 43% for the game, 42% from 3 land. Orlando is shooting 67% from the line.

Let's be optimistic and hope that we can score in 10 and foul in 5.

Now, I have, at this moment, not figured out what the expectation should be. Let's plug in these numbers and see what our expectation should be, both shooting 2s and 3s.

Expectation shooting 2s: -2.88
Expectation shooting 3s: -0.48

Either way, and anything in between, the Nets should expect their deficit to WIDEN, not close. In fact, they lost by 10, an increase in the deficit by 2 points, EXACTLY AS PREDICTED.

In fact, in order to have won, the following numbers would have had to apply:

SLG - 90 (fixed)
SYP - 10 (optimistic)
SFO - 5 (very optimistic)
YSP - .750 (wildly optimistic)
COS - 3 (which Frank would never do)
OFP - .400 (wildly optimistic)

and EVEN THEN all they would have done is FORCED OVERTIME!

Even if they just played it out, held Orlando scoreless, kept them to 20 seconds per possession and scored a 3 every time down, they'd win by just 1. BUT AT LEAST THEY'D WIN. And how improbable is that scenario compared with the wildly optimistic Hack-a-whomever scenario above?

Of course, the best scenario is to NEVER HAVE LET THE DEFICIT GET TO 8 WITH 1:30 TO GO IN THE FIRST PLACE. The score had seesawed all game with no team having a lead bigger than 6 until the very end, when Frank's inability to call a well placed timeout let it get out of hand.

The bottom line, then, is this:
- The Hack-a-Whomever strategy is theoretically set up for failure in almost all circumstances when it would be used.
- The Foul-and-Go-For-2 variant is EVEN LESS LIKELY to succeed.

Thus it would appear, to any rational coach with a desire to win, to NOT HOARD TIMEOUTS for this eventuality and JUST KEEP PLAYING THE GAME.

I will try to communicate this to Frank and Rod Thorn, in the hope that perhaps, just maybe, if the facts are laid out for him, he will change his approach and COACH THE GAME THAT PRESENTS ITSELF, not the game he has a priori decided on.

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