Inside the Numbers: Scoring from the Line

Everyone knows that Paul Pierce is one of the best players in the NBA at scoring from the free throw line. But when we examine the frequency with which other Celtics get to the line, the results may surprise you...

How frequently a player gets to the free throw line is one of the most overlooked statistics in basketball. Newspapers often report a player's field goal percentage and a player's free throw percentage, but without knowing how many free throws and field goal attempts ("shots") a player took, it is hard to know how important either of these is. For example, if a player got the ball 10 times in a game, shot twice, making one shot, and was fouled and sent to the line the other eight times, his field goal percentage would be listed at 50%. But if he only made 4 of his 16 free throws, fans of his team would care much more that he shot 25% from the line than that he shot 50% from the field. As a result, when evaluating players' ability to score, it is important to understand how frequently they get to the line.

To figure out how good a player is at getting to the line, Celtics coaches use a number we call "Free Throw Attempt Rate." This stat simply answers this question: How many free throws does player X attempt for each of his team's possessions he's responsible for using? Calculating this stat is not difficult - you first need to determine how many possessions a player used. A player can use a possession by taking a shot, getting to the line for two or three shots, or turning the ball over. You can estimate this amount by adding a player's shots, turnovers, and 0.44 times his free throws. (The multiplier accounts for "and-1s" and technical free throws.) Then you simply take the number of non-technical free throw attempts the player had, and divide by the number of possessions for which he accounted.

FTA Rate*: FTA / (FGA + TO + (0.44 x FTA))

Even when you subtract technical free throws (not reflected in this sample equation), most of the best scorers in the league have an FTA Rate of over 0.33. For example, Paul Pierce has an FTA Rate of 0.37, meaning he averages 0.37 free throws per Celtics possession where he shoots, gets to the line, or turns the ball over.

Of course, as in the example above, a player could be really good at getting to the line but then be a terrible free throw shooter. (And as Shaquille O'Neal and Ben Wallace could tell you, the fact that a player shoots so poorly from the line could be one reason why he gets there so much!) So what Celtic coaches really are interested in knowing is not only how good a player is at getting to the line, but also how good a player is at getting to the line and then scoring when he gets there. In other words, we need a stat that accounts for both the number of free throws a player attempted and the player's free throw percentage. For this, Celtic coaches use a stat called "Free Throw Rate." This is simply the number of points scored from the free throw line per possession used, and is calculated by replacing FTA in the equation above with made free throws ("FTM").

FT Rate: FTM / (FGA + TO + (0.44 x FTA))

Even when you subtract technical free throws (not reflected in this equation), most of the best scorers in the league have an FT Rate of over 0.20. For example, Paul Pierce has an FTA Rate of 0.29, meaning he averages 0.29 points from the line per Celtics possession he uses.

A good way to keep the two stats straight in your mind is to remember that FTA Rate is about how often a player gets to the line, whereas FT Rate is about how good a player is at scoring from the line, both through getting there and through shooting well once he's there.

So how good are the Celtics at scoring from the line? Everyone knows that Paul Pierce is one of the best in the league at going to the hoop and drawing fouls, and the numbers bear this out - last year with an FT Rate of 0.30 points from the line per possession used he was 8th among all players who averaged at least 25 minutes per game. This year, with the emergence of interior scoring threat Al Jefferson, Paul is taking far more three point shots - they account for 34% of his shots this year, up from 21% last year. And yet Paul is still among the league leaders in FT Rate - at 0.29 he's 13th among players who average at least 25 minutes per game. Given his higher rate of shooting threes, this means that Paul has been even more effective at getting to the line when he goes to the hoop this year than he was last year.

Celtics' Scoring From The Line 2006-07, through 1/1/07
Powe64.9%0.5280.343
Pierce80.1%0.3660.293
Allen78.3%0.3430.269
Szczerbiak88.9%0.2790.248
Gomes81.8%0.2800.229
Jefferson67.4%0.2810.190
Telfair84.7%0.1970.167
West93.9%0.1700.159
Green74.4%0.1900.141
Rondo55.6%0.2450.136
Perkins32.0%0.2580.082
League Avg. Player68.9%0.2450.174
Celtics Team (league rank)76.8% (12th)0.305 (4th)0.234 (4th)
League Avg. Team76.6%0.2800.209

(Excludes Scalabrine, Ray, Olowokandi, and Ratliff, each of whom has attempted fewer than 10 FT. League average team stats are different from league average player stats because a small number of players account for most of most teams' free throw attempts, and thus team overall stats are weighted in favor of the star players' stats.)

But Paul Pierce is not the only Celtic with an impressive FT Rate. Tony Allen has recently been moving up the league rankings in getting to the line, averaging 0.34 free throw attempts per possession used, good for 27th in the league (tied with Allen Iverson and LeBron James). Tony's ability to attack the basket and get to the line while staying under control is one reason why he has been the team's second most efficient scorer (behind Gerald Green) during Pierce's recent stint on the inactive list.

In fact, four Celtics are in the top 50 in the league (min 200 possessions) in FT Rate: Pierce (0.30, 13th), Allen (0.27, 27th), Wally Szczerbiak (0.25, 34th), and Ryan Gomes (0.23, 45th). No other team has four of the top 50 scorers from the free throw line.

Other Celtics have been impressing from the free throw line as well. Delonte West gets most of his offense from jump shots, so his FT Rate is only 0.16, but he has been impressive on the relatively rare occasions he has found himself at the line; Delonte is currently second in the league in free throw percentage at 94%, having missed only three free throws all year so far. In addition, Al Jefferson has also shown an impressive ability to get to the line; his FTA rate is 55th in the league (0.28), but his 67% shooting from the line so far this year means his FT Rate is only just above the league average, at 0.19.

These guys are all big parts of the reason the Celtics are currently fourth in the league in team FT Rate. But none of them has been the best Celtic at getting to, or scoring from, the line so far this year. That honor goes to rookie Leon Powe, who is second in the entire league (min 10 games played) at FTA Rate, averaging 0.53 free throw attempts per possession used. He's been so good at getting to the line that he's still eighth in the league in FT Rate at 0.34 (just ahead of Chauncey Billups), despite shooting only 65% from the line.

Michael Zarren is the Celtics' Basketball Operations Analyst, responsible for assisting team decisionmaking through the use of quantitative and legal analyses.

* This formula is an estimation; obviously the team uses the actual number of possession-ending free throws.

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