Game 7 Was Not a Referendum on Three Pointers or Houston’s Style of Play

But it might be a referendum on bad math and statistical analysis

The NBA Finals are here, and it’s a fourth straight meeting for the Golden State Warriors and the Cleveland Cavaliers. The Houston Rockets and Boston Celtics pushed both Conference Finals to seven games, but neither could finish the job on their home court. It was only the third time in NBA history in which two teams won a road Game 7 in the same round, the first since 1995. And in the end, we were left with the same old rematch, a litany of missed threes, and a lot of questions about style of play and if the 3>2 era is finally dead.

You’re probably not going to read much about the Warriors and Cavs the next few days. We know plenty about each, and we already know everything there is to know about the matchup at hand. The Warriors are currently -1200 to win the series, which means Vegas gives them over a 92% chance of winning the Finals. The way Cleveland has looked, that might be low.

Instead, you’ll probably find a lot of referendums on the Rockets and the Celtics this week as analysts autopsy the death of two huge missed opportunities. You’re going to find a lot of bad statistical analysis, and a lot of people are going to try to tell you Boston and Houston lost because they shot too many threes. NBA 90s stalwarts Shaq, Barkley, and Reggie Miller already started last night. The referendum is coming.

But it’s wrong, it’s all wrong. And I’m going to tell you why.

The Houston Rockets made 36.2% of their three pointers in the regular season. They missed 27 threes in a row in Game 7, an NBA playoff record. Using binomial probability (there’s going to be a lot of math in this piece, buckle up), we can calculate the odds of Houston missing 27 straight threes, and as you’d expect, it’s very low.

The odds of 27 straight misses comes out to 0.00054%, about 1 in 186,141. I’m sure a bunch of smart guys already tweeted out that calculation last night. Good for them.

It’s rubbish.

You see, stats require context, and that stat has none. As the statistical revolution has come to sports, it’s armed a lot of poor mathematicians with more numbers than they know what to do with and not many tools or understanding to use them.

Yes, the odds of a 36.2% shooting team taking 27 threes and missing them all is astronomically low. But that number only applies to those exact 27 shots. It’s the odds that that specific set of 27 shots in a row are missed. But Houston attempted an NBA record 4,146 threes this season. They had 4,120 unique strings of 27 consecutive threes, depending on where you start and stop counting. The odds of Houston throwing up a donut on those specific 27 threes were extremely low, but there’s over a 2% chance the Rockets would have missed 27 threes in a row at some point this season and a better than 1 in 3 chance that some NBA team would have done it this year. Houston just happened to do it at an extremely inopportune time.

It’s not just that, though.

You know what the crazy thing is about stats like “27 straight missed threes?” Without even checking the play-by-play data, I bet you can guess what happened on the three pointer after that streak — yep, Houston made it. So Houston did miss 27 threes in a row, but they also made 1 in 28 if you include that next shot. What are the odds of that happening? About 1 in 18,364, or roughly ten times as likely as the 0-for-27 stat that includes arbitrarily chosen end points to make it look as bad as possible.

Of course, Houston made the three pointer right before the streak too. So now they made 2 of 29 threes, and the odds of that are up to 1 in 3,499. That’s still not very good, but it’s 53 times more likely than the original math, and it’s not nearly impressive of a number.

It’s also not zooming out far enough.

Houston didn’t shoot 0 of 27, nor 1 of 28 or 2 of 29. They attempted 44 threes in Game 7 and made seven. The chances of that happening is about 0.27%, or around 1 in 372. It’s still not good, but it’s no longer horrifying.

Of course, all of this has been assuming that 36.2% three-point rate Houston made during the regular season. And that hardly seems fair, considering they were missing their best gunner in Chris Paul, a 38% shooter. That means worse players taking more threes, and that’s bound to bring the percentage down. They were also playing one of the league’s best defenses in the Warriors, which means more difficult contested threes, some farther from the basket. That 36.2% counts all those wide open regular season threes against the Kings and Suns, and the Ws don’t give you many of those. It’s also Game 7 and a chance to make the NBA Finals, so more than a little added pressure, and it’s clear Houston’s players were exhausted. That affects shots, too.

It would be silly to expect the Rockets to match their regular season 36.2% three-point rate in a Game 7 against a top defense without their best shooter. So what if we assume they should have shot, say… 33% instead?

Now the odds that the Rockets make only 7 of 44 shots have jumped to 0.92%, or 1 in 109. That’s still bad, but considering the Rockets played 99 games this season, it basically means Houston should have one shooting game this bad some point in the season. And sure enough, Game 7 was their worst shooting night of the year, their fewest threes made and worst percentage of the season by over 6%.

The math says Houston was always likely to have one game like this sometime this season. It just came at the worst possible time.

If you expand the scope to the last two seasons, suddenly you find six different Rockets games making 20% or fewer threes. In March 2017 they even shot an abysmal 3 for 35 against New Orleans, just 8.6% — and they won that game!

Houston shot really poorly in Game 7, historically poorly when you zoom in on just those 27 missed shots in a row. But math tells us that 27 misses in a row happen sometimes, that it is a mathematical certainty that some game must turn out to be the worst shooting game of the season.

In an average game where Houston shoots 44 threes, the math might expect them to make something like 15 or 16 of them instead of 7. That’s around 25 extra points for the Rockets, and suddenly Houston coasts to a blowout Game 7 win and looks likely to win the title.

One poorly timed night doesn’t make Houston’s style of play a failure. It just makes them really unlucky.

There are other problems with isolating the “27 misses in a row” streak. Statistics don’t happen in a vacuum, and Game 7 was more than just Houston missing 27 straight shots.

Everything in every game is a statistical improbability, when it comes down to it. If stats could precisely predict everything that was going to happen in every game, guess what? Sports would suck, and we’d all stop watching. Thankfully, that’s not how stats work.

There were plenty of other statistical improbabilities in Game 7 that weren’t quite as visible or painful as the 27 straight missed threes.

Houston was a bottom ten offensive rebounding team this season. They secured offensive rebounds on 21% of their missed shots, about 9 per game. In Game 7, they rebounded 17 of 54 misses, a 32% offensive rebounding rate. P.J. Tucker alone had 8 offensive rebounds, a career high. Offensive rebounds lead to second chance opportunities, one of their easiest, best ways to score. Houston had only about a 5% chance of grabbing at least 17 offensive rebounds in Game 7, making it one of their five best offensive rebounding games of the season. That’s a lot of extra chances in their favor.

Golden State was abysmal from the free throw line in Game 7, just 50% as a team. That included 7 for 12 from Kevin Durant and Klay Thompson, two of the best shooters in NBA history. Durant makes 89% of his free throws but went 7 for 10. Thompson shoots 84% but missed both of his. The odds of KD and Klay shooting that poorly are about 0.19%, or 1 in 523. It was likely the worst free throw shooting game the two will ever combine for, and it was around five times as unlikely to happen in Game 7 as the Rockets poor three-point shooting. Another statistical anomaly in Houston’s favor.

The more you zoom out, the less wild and crazy these stats seem. Houston attempted 277 threes against the Warriors this series, an NBA record. They made 87, a 31.4% shooting clip. Based on their regular season percentages, the odds of them making that few threes over an entire series was about 3.5%. But remember, this is against an outstanding defense, and Houston missed Chris Paul for part of the series. If you figure Houston would’ve been expected to make 34% of their threes instead of the 36.2% from the regular season, the odds of them shooting 87 for 277 jump to about 20%.

That’s 1 in 5, about the same chances as an 80% free throw shooter going 8 of 12 from the line. It’s a collective statistical shrug.

Houston shot a little worse this series than might have been expected. It happens.

The Boston Celtics made 7 of 39 threes in their Game 7, an awful 18% from deep. Like the Rockets, it felt like they shot their way out of the game, and viewers and announcers alike lamented as Terry Rozier and Marcus Morris bricked open three after open three as the game got away.

Shrug.

Boston had the second highest three-point percentage in the NBA this season, behind only the Warriors. Their chances of shooting 7 of 39 in a game were around 0.6%, or 1 in 153. And of course it was Game 7 and they were missing Kyrie Irving, so factor that in and the odds probably end up around 1 or 2%. Like Houston, the Celtics simply picked an unlucky time to have one of their worst shooting nights of the season.

Boston was getting good clean looks on open threes. They were right to keep shooting. It’s a make or miss league, and Boston and Houston unfortunately missed a lot of shots at the worst time possible.

That they did is not a referendum on 3>2 or style of play or anything else. That they missed all those shots is simply random variance, and variance is what makes sports great. Play those two Game 7s again the exact same way and take all the exact same shots and we might well have seen two double-digit home victories and be talking about the end of the LeBron era and the failure of the Warriors dynasty. Single game data points are not referenda on anything. They’re just statistical noise.

There are a lot of reasons the Rockets lost Game 7. Missing a lot of threes is certainly one of them. Here are some other reasons they lost:

• Klay Thompson picked up two fouls in the first minute and a third three minutes later, but Steve Kerr smartly didn’t sit his All Star for the half and barely changed his rotation at all. Thompson finished with four fouls and scored 19 important points.
• Houston was in the bonus 72 seconds into the first quarter but failed to take advantage. During the remainder of the quarter they had five turnovers and jacked ten threes. They shot only five more free throws the entire quarter, two of them on a Hack-a-Capela.
• Houston had the Warriors on the ropes early with what Steve Kerr called one of their worst quarters ever. Instead of stepping on the throttle with his best lineup in and the champs staggering, Mike D’Antonio subbed in little-used Ryan Anderson and Joe Johnson. Anderson finished -12 in eight minutes and never attempted a single shot. Exactly what is Ryan Anderson doing on an NBA court if he’s not shooting the ball?
• The Rockets had double-digit offensive rebounds and forced double-digit turnovers in the first half, and they held a 48–33 lead at home with under 29 minutes to play, but they failed to put the Warriors away.
• James Harden made a few costly lazy plays. In the first quarter he didn’t pay attention to an inbounds pass, then stood and watched Curry pick the ball up and hit an uncontested three. In the second quarter, Harden jacked up a wild three trying to draw a foul, then didn’t get back on D and gave up a wide open corner three to Thompson. That’s six free points given away.
• Most pundits said before the series that it might come down to Houston’s role players outplaying Golden State’s. P.J. Tucker set career highs in threes, offensive rebounds, and defensive rebounds, and he did it in three different games. Draymond Green and Andre Iguodala made two threes combined the entire series. Houston still lost.
• Houston was missing Chris Paul. Duh. It’s silly to think that wouldn’t have mattered over a final two games in which Houston led by double digits at the half in both and struggled with turnovers all game.
• Houston was effectively missing Luc Mbah a Moute. LRMAM hurt his shoulder on the final night of the season and was never healthy. He was Houston’s defensive jackknife, its one real Kevin Durant defender, another 3-and-D weapon they sorely missed. Mbah a Moute was more important to the Rockets this season than Andre Iguodala was to the Warriors.
• The Warriors have four top 20 players and one of the best teams ever assembled, including a two-time MVP who got hot two straight games and buried them. Talent kills.

It’s lazy and incorrect to look at these two Game 7s and conclude that three pointers are bad or that too many three-point attempts cost Boston and Houston a chance at the Finals. After all, that same three-point weapon is the one Golden State used at its deadliest to come back in Games 6 and 7 against the Rockets and knock them out.

Three is still greater than two, and it’s no coincidence that two of the league’s best shooting teams are meeting in the Finals a fourth straight time. They just happened to beat two other outstanding shooting teams along the way on their worst shooting nights of the season.

If you enjoyed this piece, give it a few claps 👏 👏 so others will see it too! Follow Brandon on Medium or @wheatonbrando for more sports, humor, and life musings. Visit Brandon’s writing archives here. Thanks to Basketball Reference and to binomial probability calculators everywhere.