# Category Archives: Statistical Analysis

My novice take on various statistical questions.

## Crying Foul

After the first weekend of the playoffs, I wrote a post about the astonishing 0.700 combined FTA/FGA ratio posted by Kevin Durant, Kobe Bryant, LeBron James, Derrick Rose, Chris Paul, Dirk Nowitzki and Dwight Howard. Not surprisingly, that number has come down over the past week. However, it hasn’t dropped as much as you’d expect. After four (or five) playoff games, that septet’s FTA/FGA ratio has fallen to 0.635.

In general, more fouls are called in the playoffs, which means more free throw attempts, which means that ratio will rise league-wide. In last week’s post we found that star players tend to create a much greater share of that change then your average player. This year we found that the FTA/FGA ratio had risen 0.068, from 0.300 in the regular season, 0.368 in the playoffs. We also found that if we removed the field goal and free throw attempts of those seven players, the increase was only 0.028, meaning this group was responsible for 58.8% of the increase.

A comment on that first post asked me to provide updated numbers to see if the pattern is holding steady. It certainly is. This table shows the FTA/FGA change from the regular season to the playoffs in each of the last 5 years.

This table shows the same numbers but with the seven top MVP vote getters removed. (For this season, it’s the Durant, Kobe, LeBron, Rose, Paul, Nowitzki, Howard group we already identified.)

This table shows the percentage of the change which can be traced to the contributions of those seven players we removed.

Although the league-wide gap between the FTA/FGA ratio in the regular season and playoffs has narrowed, our seven stars are actual responsible for a great share of the change than they were just a week ago.

It’s very probable that this pattern won’t hold past the first round, mostly because of the way I’ve calculated it. I’m removing the total contributions of those seven players from the total numbers, league-wide. Either Kobe or Paul will be eliminated, possibly with Dwight Howard joining them. As those players check out of the playoffs the league-wide totals will continue to grow without their contributions. Part of the reason the percentages were so low in 2010 and 2008 is because several of the MVP candidates were knocked out of the playoffs early on. My guess is that if the numbers were run on a round-by-round basis we would see consistent percentages closer to the 50% range.

There are plenty of possible reasons for this pattern, some reasonable, some slightly disconcerting. Whatever the reason, there can be no question that stars get more calls in the playoffs than their less-accomplished counterparts.

## As Close As Hands And Feet

A huge surprise over the last two months of the season was the play of the Denver Nuggets. Many assumed the team would shrivel up and blow away after sending Carmelo Anthony to New York at the trade deadline. Instead, they finished the season on an 18-7 tear, and entered the playoffs with a lot of buzz about their potential to upset the Oklahoma City Thunder. The first two games of the series have not gone well, with the Nuggets losing both by a combined 21 points.

Although they clearly gave up the most talented player in their deal with the Knicks, the Nuggets were able to extract several talented players in return for Anthony. One of those players was Raymond Felton, who had been having a terrific season for the Knicks. The Nuggets already had Ty Lawson designated as their point guard of the future, but when they had a chance to shed Chauncey Billups‘ salary while adding depth, the Nuggets jumped at the chance.

Felton has solid size and strength for the point guard position, which allowed the Nuggets to use him frequently in the backcourt alongside the diminuitve Lawson. It turned out to be an extremely successful combination. The Nuggets used Felton and Lawson together just under 31% of the time after the trade deadline. In those 25 games to finish the regular season, lineups with Felton and Lawson together outscored their opponents by nearly 20 points per 100 possessions.

With Arron Afflalo missing the first two games of the series due to injury, the Nuggets have been using the Lawson/Felton combination even more frequently, just under 46% of the minutes in the series. However, they’ve not been nearly as effective as they were in the regular season. The table below shows the Nuggets’ Offensive and Defensive Ratings for the percentage of the team’s minutes when Lawson and Felton were on the floor together in the regular season and playoffs.

The swing in performance has been a huge factor for the Nuggets. The Lawson/Felton combination has been bad but not atrocious. The real impact is not the -3.5 Net Rating in the playoffs, as much as the 22 point swing from the regular season. What was a powerful weapon has all but dissipated.

The change in Defensive Rating has been just 0.9 points, but the Offensive Rating has dropped by 22.1 points. Although there are three other players on the floor with them, Lawson and Felton share much of the responsibility for this offensive decline. Lawson has actually been fairly efficient, shooting 55.0% for the series with a TOV% of 11.5%. However he’s using fewer possessions, 17.7% in the playoffs compared to 19.6% in the regular season.

Felton has gone the other way, posting a Usage Rate of 19.6% in the playoffs compared to 18.5% in the regular season with Denver. He’s been much less efficient scoring the ball, shooting 40.9% and making 2 of 8 three-pointers. Both players have also done far less creating for their teammates. Ty Lawson assisted on 28.3% of his teammate’s baskets while he was on the floor in the regular season. In the playoffs that percentage has fallen to 21.2%. Felton shows the same pattern, dropping from 31.1% with Denver in the regular season, to 26.0% in the playoffs.

Since joining forces, Lawson and Felton have been terrific at getting the ball inside either through penetration from isolations, or off of the pick-and-roll. This forced the defense to adjust, creating open jumpshots and interior opportunities for their teammates. In the playoffs, the length of the Thunder has gone a long way towards containing them. Even when the Thunder have gone small to matchup up with the Nuggets, Russell Westbrook, James Harden, Thabo Sefolosha and Daequan Cook leave them with a surplus of length in the backcourt.

Some home-cooking (and 5,000 or so feet of elevation) should give the Nuggets a boost as the series shifts back to Denver. However, the Lawson/Felton backcourt combination could continue to struggle against the Thunder’s perimeter defense. The answer may be looking to other lineup combinations to create mismatches. Ironically, the Nuggets’ SB Nation site, Denver Stiffs, has a post up right now making some of the same complaints but about a completely different alignment of players. Getting Arron Afflalo back should give George Karl some more options, but it’s going to be on him to find the right one.

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## Team Expected Scoring – Final Regular Season Numbers

On Monday, we looked at the final regular season Expected Scoring numbers for individual players. Today we’re moving on, looking at those same numbers at the team level. You can find all the data at the Expected Scoring – Statistics and Analysis page, or at this link.

Expected Scoring is a way of combining a player or team’s shot selection and shooting percentages into one measure of scoring efficiency. Here’s the longer explanation:

Expected Scoring uses a player’s FGA from each area of the floor and multiplies it by the average number of points scored on that type of shot to come up with an Expected Point total from that area. The Expected Point total can than be compared to the actual number of points a player scored from that area to arrive at a Point Differential. This Point Differential is an expression of how a player shot compared to the league average, but I like that the comparison is drawn with actual point totals.  The average values of shots by location that I use (At Rim – 1.208, <10ft. – 0.856, 10-15ft. – 0.783, 16-23ft. – 0.801, 3PT – 1.081, FT – 0.759) were calculated by Albert Lyu of ThinkBlueCrew.

All of the individual Expected Scoring numbers are per 40 minutes. For the team stats we look at everything per game. By overall Point Differential, the top five shooting teams in the league were:

• Miami: +5.72
• Dallas: +5.27
• San Antonio: +4.89
• Phoenix: +4.37
• Boston: +3.94

The bottom five were:

• Cleveland: -4.28
• Milwaukee: -3.71
• Washington: -2.94
• Charlotte: -2.74
• Sacramento: -2.35

The New Jersey Nets didn’t make the bottom five, but joined the Bucks and Cavaliers as the only offenses with a negative Point Differential from every area of the floor. The Miami Heat were the only team with a positive Point Differential from every area of the floor.

Looking at these numbers, now for the second season, I’m amazed at how much of a difference excelling or struggling from just one area of the floor can make. The Toronto Raptors scored right around the expected rate from every area of the floor, except for on three-pointers, where they posted a Point Differential of -1.78. If they had shot just the league average on three-pointers it would have taken their Point Differential from a -0.83 to a +0.95.

The Clippers had the 6th best Point Differential on shots at the rim, +2.63. However, they were atrocious from everywhere else on the floor posting Point Differentials worse than -1.0 from the free throw line, on three-pointers, from 16-23ft. and from 3-9ft. If they had finished at the league average on shots at the rim, their overall Point Differential would have been -4.44. Basically they dunking of Blake Griffin and DeAndre Jordan kept the Clippers from having the worst shooting offense in the league.

Stay tuned for a few more Expected Scoring pieces between now and the end of the playoffs!

## Last Night’s Numbers – 4/19/11

This is Last Night’s Numbers, a (mostly) daily feature where we run through the NBA games from the night before, highlighting one or two numbers I found particularly interesting from each game. All the stats are from Hoopdata’s box scores, which contain some additional advanced stats not available in traditional box scores.

Chicago 96 – Indiana 90

• For the second straight game, Chicago destroyed the Pacers on the glass. The Bulls grabbed 63.3% of the available rebounds with an ORR of 45.5%. Carlos Boozer and Joakim Noah combined for 26 rebounds, 11 at the offensive end.
• The Bulls’ rebounding edge helped overcome turning the ball over on 22.4% of their possessions. Derrick Rose turned the ball over 6 times in 40 minutes.
• The Pacers shot 41.6% for the game, while holding the Bulls to 38.6%. However, the Pacers made just 12 of 24 shots at the rim.

Miami 94 – Philadelphia 73

• The 76ers shot 34.2% for the game and made just 11 of 35 shots from inside of 10ft.
• Chris Bosh scored 21 points on a 73.3 TS%. He also added 11 rebounds, 3 steals and an assist, all without turning the ball over in 35 minutes.
• The 76ers perimeter players really struggled shooting the ball. Evan Turner was 6 of 10 from the field and made all 3 of his three-pointers. The rest of their guards shot 10 of 35, and were 3 of 11 on three-pointers.

# 0.700

That number, 0.700, is the combined FTA/FGA ratio of Dwight Howard, Derrick Rose, Kevin Durant, Chris Paul, Dirk Nowitzki, LeBron James and Kobe Bryant after the first weekend of the NBA playoffs. It’s also patently absurd. It means for every 10 shots that septet attempted, they also attempted 7 free throws. Just for comparison, the FTA/FGA ratio across the entire league this season was 0.300. Those seven players had a combined FTA/FGA ratio of 0.448 during the regular season.

Let me point out that I’m talking about the ratio of free throw attempts to field goal attempts. Sites like Basketball-Reference, usually display a ratio of free throws made to field goal attempts. I’m primarily concerned here with the rate at which fouls are being called, so whether the free throw is made or missed is largely irrelevant for this discussion.

After the first game in each series, we have a FTA/FGA ratio of 0.368 for the playoffs, a significant increase over the 0.300 league-wide mark for the regular season. In recent history, this pattern has been common. The table below shows the FTA/FGA ratio for each of the past five seasons, comparing the regular season to the playoffs.

Other than 2007, we see that pattern of fairly significant increase in FTA/FGA from the regular season to the playoffs. This seems to fit well with the common wisdom, play is more physical in the playoffs, hence more fouls are called. Brief Digression: This pattern would also seem to fit with the idea that stars receive more calls in the playoffs. Which of course, runs counter to the perception that referees swallow their whistles in the postseason and let the players play. I can’t tell you how much I enjoy when several stereotypes are held without question, despite them being in complete opposition to each other

Given the ridiculous free throw numbers posted by that handful of players this weekend, it stands to reason that some of that difference between regular season and playoffs could be attributed to just a few souls. In trying to identify similar players for comparison, I noticed that the seven players I mentioned above could all be considered top candidates for Most Valuable Player. MVP candidates work well as a data set for this analysis because they generally post very high usage rates, and therefore would be taking a high number of both shots and free throws. Also, if we are going to talk about the idea that stars are given preferrential treatment, no one would seem to pull more gravity from their reputation than an MVP candidate from that season.

This next table shows the same information as above, except I removed from my calculations the free throw attempts and field goal attempts of the top seven MVP candidates for each season, from both the regular season and playoff figures. Essentially, this table just shows us the numbers for everyone besides those seven stars.

Except for 2007, we still see an increase from the regular season to the playoffs but it’s much less drastic without those seven stars included. In fact, in three of those seasons, the seven players I removed accounted for a tremendous portion of the overall difference. This last table shows the percentage of the difference between regular season and playoffs which can be traced to the performance of those seven players which were removed.

There are obviously great fluctuations from season to season. Part of that has to do with how deep each of the MVP candidates went in the playoffs. If a player participated in 5 playoff games his FTA/FGA ratio will have much less influence on these overall numbers than if they had played 25 games. If I went through each season subjectively selecting the “biggest stars” who’s teams went furthest in the playoffs, I’m sure I could come close to duplicating those 50% figures for every season.

Most of you probably won’t be reading this post until sometime on Tuesday. Statistics from Monday night’s games could change these numbers, but I would guess not enough to dilute my point. The bottom line here seems to be that stars get more calls in the playoffs, but we already knew that. This is attributable to a multitude of reasons, although probably not a malicious and diabolical system of collusion between the league and it’s officials. What seems especially striking here is how stars getting more calls in the playoffs diguises the real foul rate of everyone else. It’s true that there are more fouls called in the playoffs. However, it’s more true for some players than for others. One widely accepted truism obscures the real facts behind another.

## Individual Expected Scoring – Final Regular Season Numbers

I’ve missed that narrow window between the end of the regular season and the beginning of the playoffs, but the final Expected Scoring numbers have arrived at long last. You can find them here, or by following the link through the Expected Scoring – Statistics and Analysis page.

If you’ve haven’t been following my Expected Scoring posts this season, then congratulations, you’re in the vast majority of basketball fans. Expected Scoring is a way of combining a player’s shot selection and shooting percentages into one measure of scoring efficiency. Here’s the longer explanation:

Expected Scoring uses a player’s FGA from each area of the floor and multiplies it by the average number of points scored on that type of shot to come up with an Expected Point total from that area. The Expected Point total can than be compared to the actual number of points a player scored from that area to arrive at a Point Differential. This Point Differential is an expression of how a player shot compared to the league average, but I like that the comparison is drawn with actual point totals.  The average values of shots by location that I use (At Rim – 1.208, <10ft. – 0.856, 10-15ft. – 0.783, 16-23ft. – 0.801, 3PT – 1.081, FT – 0.759) were calculated by Albert Lyu of ThinkBlueCrew.

There’s a lot to look at, so I thought I would just pull out a few highlights and lowlights.

Overall

For the second straight season, the overall Point Differential leader was Dirk Nowitzki (minimum 500 minutes played). Not only was he the most efficient scorer in the league, but he belongs to a small and elite group of players who posted a positive Point Differential from every area of the floor: Chris Paul, Daequan Cook, Pau Gasol, Ray Allen, Beno Udrih, Gary Neal, Steve Nash, Elton Brand and Nowitzki.

Rookies

This list really underscores how rare it is to find a rookie who plays within themselves, understands their strengths and weaknesses, and can provide efficient scoring right off the bat. 34 rookies played at least 500 minutes this season. Only these five, and Trevor Booker, of the Washington Wizards, posted a positive Point Differential across the entire season.

Most Improved:

Here are some players who saw big improvement in their point differential versus last season.

Young received a lot of attention this year for making himself into a somewhat efficient scorer. His transformation was based largely on a career high, and possibly unsustainable, field goal percentage on long two-pointers. Darrell Arthur and DeAndre Jordan seem like more likely candidates to repeat their levels of scoring efficiency next season.

Not So Hot

These are the guys who make you dig your fingernails into your palm everytime they even look at the rim.

There’s a ton of information here, and I’ve only done a cursory job of reviewing it. If you find something interesting that I’ve missed, feel free to share it in the comments! Final team Expected Scoring numbers should be up later this week.

## Last Night’s Numbers – 4/18/11

This is Last Night’s Numbers, a (mostly) daily feature where we run through the NBA games from the night before, highlighting one or two numbers I found particularly interesting from each game. All the stats are from Hoopdata’s box scores, which contain some additional advanced stats not available in traditional box scores.

Saturday

Chicago 104 – Indiana 99

• The Bulls completely controlled the glass, grabbing 59% of the available rebounds, with an ORR of 50%. Joakim Noah had 11 rebounds, 8 coming at the offensive end.
• With a FTR of 0.390 the Bulls had a 15 point advantage at the free throw line. Derrick Rose made 19 of 21 at the line.
• The Pacers made just 10 of their 23 shots at the rim. Tyler Hansbrough was 2 of 8.

Dallas 89 – Portland 81

• With a FTR of 0.439, the Mavericks had a 16 point advantage at the free throw line. Dirk Nowitzki was 13 of 13.
• The Mavericks made 10 of 19 three-pointers. Jason Kidd led the way, making 6 of 10. The Trailblazers made just 2 of 16.
• Their three-point shooting and free throws helped compensate for the fact that the Mavs made just 7 of 23 shots from inside of 10ft.

Miami 97 – Philadelphia 89

• With a FTR 0.527, the Heat had a 19 point advantage at the free throw line. LeBron James was 13 of 14 from the line.
• The 76ers shot 41.2% for the game. They made just 14 of 50 shots from beyond 10ft.
• Thaddeus Young had 20 points for the 76ers on a 46.0 TS%. He was 7 of 11 on shots at the rim, and just 2 of 9 from everywhere else. Young also added 11 rebounds, 8 of which came at the offensive end.

Atlanta 103 – Orlando 93

• Dwight Howard scored 46 points on a 70.4 TS%. He added 19 rebounds, 6 offensive, but turned the ball over 8 times.
• The Hawks Offensive Rating for the game was 112.0. However, they turned the ball over on just 10.9% of their possessions, and made 48.2% of the long two-pointers. Those may not be sustainable levels of performance across the rest of the series.
• The Magic made 6 of 22 three-pointers. Jameer Nelson made 4 of 7, which means the rest of the team made 2 of 15.

Sunday

Memphis 101  – San Antonio 98

• The Grizzlies interior tandem of Marc Gasol and Zach Randolph overwhelmed the Spurs. They combined for 49 points on 19 of 25 shooting with 23 rebounds.
• The Spurs posted a FTR of 0.671, gaining a 15 point advantage at the free throw line. However, they shot only 40% from the field, and made just 10 of 30 shots from outside of 15ft.
• Mike Conley had 10 assists for the Grizzlies, 7 of which went for layups or three-pointers.

New Orleans 109 – L.A. Lakers 100

• Chris Paul carried the Hornets to victory. He scored 33 points on a 70.9 TS%. He also had 7 rebounds, 4 steals and 14 assists, 10 of which went for layups or three-pointers.
• Kobe Bryant scored 34 points but on a 57.6 TS%. He added 5 assists and 4 rebounds but also turned the ball over 5 times.
• Despite the Lakers huge size advantage, the Hornets were able to hold them to just 14 shot attempts at the rim. Andrew Bynum, Pau Gasol and Lamar Odom combined to score just 8 points at the rim.

Boston 87 – New York 85

• Ray Allen scored 24 points for the Celtics, on a 73.5 TS%. He made 3 of 5 three-pointers, including the game winner with 11 seconds left.
• Boston turned the ball over on 20.5% of their possessions, but compensated by controlling the glass. They grabbed 56.4% of the available rebounds with an ORR of 41.7%.
• Carmelo Anthony and Amare Stoudemire each took 18 shots for the Knicks. Stoudemire made 12 of those 18 for 28 points. Anthony made 5 of those 18 for 15 points.

Oklahoma City 107 – Denver 103

• Both teams turned the ball over on exactly 11.9% of their possessions. Shooting percentages were also very close, with Denver at 50.7%, Oklahoma city at 49.4%. The difference was the Thunder making 9 of 19 three-pointers, the Nuggets just 4 of 16.
• Kevin Durant scored 41 points for the Thunder on a 71.7 TS%. He was 12 of 15 at the free throw line and added 9 rebounds.
• The Nuggets did a great job scoring on the interior, making 21 of 24 at the rim. They were just 18 of 53 from everywhere else on the floor.