Are freethrows game-changers?

"And another missed free throw!"
"That's the story of the game right there, they just can't get those easy points from the charity line."

I've heard very similar discussions to this one over and over throughout the years from basketball commentators. Although not truly meaning it (at least I think), the commentator was heavily implying that the outcome of the game would be extremely different if a given team had made all, or significantly more, of its free throws.

Don't expect a sophisticated analysis here, I was just curious to explore the correlation between difference in final score and number of missed free throws.



So I wanted to investigate the two following questions:

1. If the losing team had made all its attempted free throws, would the outcome of the game have been different?
2. If the losing team AND the winning team had made all of their attempted free throws, would the outcome of the game have been different?

To answer those questions, I pulled all boxscores for regular season games from the 1999-2000 season to the last complete one, 2013-2014 and for each game tracked the final score difference, as well as the number of missed free throws for both the winning and losing teams.

Here's a first quick visual of the relationship between the number of missed free throws for each team (losing team on the lefthand graph, winning team on the righthand graph) and the final score difference:

Rather surprisingly, there does not appear to be any link between the number of missed free throws and the outcome of the came in terms of close game or huge blowout. It would have seemed natural to assume that the more free throws the loser team has, the more likely they are of getting blown out, and the opposite argument for the winning team.

How have these numbers evolved over time? Here's the evolution of the average score difference and missed free throws for those 15 seasons:

Not completely obvious trends emerge from the graph, but if anything can somewhat notice that:

• the lines for the winning and losing team are extremely similar
• average score difference has stayed flat or perhaps very slightly increased
• number of missed free throws has decreased (could be due to better shooting and/or less free throws attempted, and it's actually a little of both)

Now of course this analysis has been as naive as they come. You can't just expect free throws to go from missed to made and expect the entire game to follow its original course. Players might get confidence as they rack up easy points, and coaches might change strategies if what would have been a big lead is only a 2/3 point lead. The point of the exercise here was to compare the range of final point differential to number of missed free throws, and it would seem that free throws only account for about half the final gap. This could be a reason why teams, coaches, players don't put in crazy efforts to have all players shoot 99%. Their time is probably better spent on other types of training.

That being said, I just had to mention the other day's game which saw both teams shoot a combined 37% (16 for 43, 8 for 25 for the Clippers, 8 for 18 for the Nets) from the free throw line. To put things in perspective, Shaquille O'Neal who was criticized his entire career for those shots was 53% over his career (despite finding elaborate strategies to boost the percentage). Consider the Clippers lost by a mere two points 100-102, I'm sure they must be kicking themselves for their performance at the line.

Also worth noting, this game from 1999 between Portland and the Lakers. Portland won quite big - by 15 - but missed only one free throw. The Lakers missed 17! Had both teams been perfect, the Lakers could have actually won a game they lost by 15. This was the biggest outcome reversal I observed in the data if both teams had been perfect.

Fifteen seconds remaining, down by one....Who you gonna foul?

I was following the Mavericks - Kings game earlier this year. Exciting game which went into overtime. With 50 seconds left and the Kings down by two, Rajon Rondo fouled Jason Thompson and in the process sent him to the free throw line. He made the first shot. But before he could attempt the second, the Mavs called a timeout. After the timeout, Jason went back to shoot his second free throw, and missed it.

Did the timeout have any impact on the missed shot? You couldn't make a free throw any more straightforward. Unlike a penalty kick at soccer, there's nothing your opponents can do to alter that shot. Except call a timeout? Legendary coach Phil Jackson was (in)famous for calling timeouts between opponents free throws, but was this ploy effective at all? Thompson could have tied the game on his second free throw attempt, which would have shifted a considerable amount of pressure of his and his teammates' shoulders with less than a minute to go. With the timeout called, Thompson was left there brewing in these thoughts with mounting pressure.

That game made me want to investigate the timeout phenomenon, as well as other external factors that could influence the outcome of a free throw. I also wanted to follow up on an earlier post I made about measuring players' clutch performances via statistical models.

A few words on the data before jumping into the analysis. I focused on the most recent complete NBA season: 2013-2014. I pulled all the play-by-play data from nba.com, and pulled free throw season percentages for each player from espn.
Quite a bit of cleaning up was required, namely around players with same last name and same team the worst example being the Morris twins in Phoenix who also share same initial!
After cleaning everything up, I was left with just under 56K free throws taken in that season, ready to be analyzed!

I was primarily interested in the impact of free throws interrupted by timeouts, but also wanted to capture two additional factors: whether the shooter has homecourt advantage or not, and whether the situation is "clutch". There are countless definitions of "clutch time" available, some sparking heated debates. I have here defined it as "less than 2 minutes to play in the 4th quarter or in overtime, and less than 5 point differential between the teams' scores".

Before jumping into the data and analysis, let's first do some visual explorations.

How many free throws are taken by quarter?

Not surprisingly, significantly more free throws are taken in the fourth quarter than the first. The game is on the line, the defense goes up a notch, and voluntary fouls are committed to regain ball possession and prevent the opponent from running down the clock.

We can even go down one granularity level at look at the number of free throws made by minute played. Rather impressive to visualize the steady increase throughout each quarter, and the giant spike in the final minute of regulation with teams fouling on purpose in tight games.

We've looked at volume, let's know look at efficiency. How well do the home and road teams shoot the ball?

It appears that both teams shoot at very similar rates throughout the contest, with the home team always having an advantage although it is not a significant as one might have expected given the distractions often displayed by the home fans.

Both teams seem to do better in overtime, but we need to caution against the much smaller sample size there.

And now to the more interesting piece, how do teams execute in clutch time?

Quite surprisingly, the home team appears to be performing no differently, whereas the road team gets a nice boost of almost 5%. The fact that we observe a boost might seem counterintuitive for some: under pressure, with fatigue from close to 48 minutes of gameplay, wouldn't it be more difficult to concentrate and sink the shot? However, a reverse argument could be made that especially when games are close, or when a team expects the other one to intentionally foul, the coach might chose to place his best shooters on the floor. So teams aren't necessarily shooting better, just having better shooters take the shots. This however does not fully explain why the road team has a boost and not the home team.

The following graph shows the 1st quantile, median and third quantile for season free throw percentage of the players taking shots in and out of clutch. It is rather apparent that better shooters are on the floor in clutch moments.

Now that we have a better feel for the data, the analysis can begin. The data is extremely rich and offers multiple options from a statistical analysis point of view. We can leave the baseline free throw shooting percentages for each player be determined by the model fitting, or force these to be the players' season averages. But with different players taking a very different number of free throws within a season, and strong dependency in the success of a free throw for all those taken by the same player, a hierarchical structure emerges and a mixed effects model could make sense.

I actually played around with the three options just mentioned, and was satisfied at how close the numerical outputs were to each other.

The conclusions would indicate that:

• homecourt does have a positive effect on shooters' success, although the effect was only borderline significant
• calling a timeout before the second (or third) free throw had a negative but insignificant impact
• clutch time had a negative and significant impact

Regarding timeouts, the fact that the effect was not significant could be due to the low sample size of these events (84 cases in 2013-2014 out of 56K free throws taken), more coaches should test this strategy so I can tell them if it's effective or not!

As for clutch time, the conclusion seems to contradict the visual exploration where percentages were higher in clutch time. But recall that our explanation to this was that the coaches were putting better shooters on the court. The analysis would indicate that even if the best shooters are on the floor in the closing minutes, they are individually performing less well when the game is on the line than in the middle of the second quarter.

Now one might wonder if we could use the data to detect some of the leagues best clutch free throw shooters. Those cold-blooded killers who can step it up an extra notch when all eyes are on them. The Durants, James, Bryants...

I added some interaction terms for players with sufficient (20) in and out of clutch time free throws and see which ones had the potential to elevate their game. And the results are... no one! Out of the 26 players meeting my criteria, none could significantly increase their free throw percentage. This could again be due to small sample size, but even so most players had negative coefficients. While none had significant positive coefficients, two had significant negative coefficients: Chris Paul and Ramon Sessions.

So back to the post's title, if you're playing the Clippers, fifteen seconds to go and down by one, do you foul Chris Paul?