The Pi-Rate Ratings

January 22, 2019

Fun Stuff For Stats Buffs-Part 3: Efficiency

Before getting into the meat of this final installment, I must apologize in advance for the brevity in this last segment.  Time constraints have made it impossible to thoroughly peruse individual offensive and defensive efficiency.

That may be a good thing for you the reader, because you can read the dictionary about as quickly as you can go through all the steps involved in calculating individual efficiency.  Suffice it to say that there are several parts to this calculation.  One must have a lengthy formula on a spreadsheet where a player’s and his team’s statistics can be inputted, and the spreadsheet spits out the numbers.

If you really want to know the entire process, then you absolutely must purchase the book by the number one authoritative source on the matter.

The book is: Basketball on Paper: Rules and Tools for Performance Analysis by Dean Oliver.  You might be able to find it in a library, as it is included in the catalog of more than 750 libraries throughout the nation, more than likely at a local college or university library near you.

Just to show you how involved the formulas are, it takes 18 separate calculations from start to finish for each player’s offensive number and almost as many for his defensive number.

The NCAA Selection Committee will use Team Offensive Efficiency and Team Defensive Efficiency in their process of picking the at-large teams and seeding all 68 teams.  This is rather simple and can be explained briefly.

Offensive Efficiency = Points scored per 100 possessions

Defensive Efficiency = Points allowed per 100 possessions.

In the 21st Century, possessions are kept as a statistic, but if you cannot find this number, you can estimate it very accurately by this formula.

Team Possessions = FG Attempts + (.475* FT Attempts) – Offensive Rebounds + Turnovers

In the NBA, substitute .44 for .475 in FT Attempts.

Obviously, round the product from the Free Throw Attempts formula to the nearest whole number.

Let’s look at some examples for a game, a season to date, and some past seasons.

Example #1. Nevada vs. Air Force, January 19, 2019

Nevada defeated Air Force 67-52 last Saturday in Reno.  The Wolfpack totally shut down the Falcons’ offense, while Air Force played capable defense on the perimeter, forcing Nevada players to hurry their three-point shots.

For the game, Nevada had 57 total field goal attempts, 23 free throw attempts, 9 offensive rebounds, and 14 turnovers.

To calculate possessions, plug the numbers into the equation:

57 + (.475 * 23) -9 + 14 = 73

For Air Force, their stat line included 51 total field goal attempts, just 9 free throw attempts, 3 offensive rebounds, and 21 turnovers.

51 + (.475 * 9) -3 + 21 = 73

Possessions must be equal or off by one or two between the teams, because after one team completes a possession, the other team gets the ball.  Two is the most advantageous one team can have over the other in possessions.  This comes about when the team that gets the opening tap also gets the last possession of the first half, as well as the first and last possession of the game.  It happens very rarely, because in order to have the first and last possession of both halves, there must be an odd number of jump ball calls in the first half so that the team that got the opening tap also gets the first possession of the second half..

Let’s get back to the calculation.

Nevada scored 67 points on 73 possessions

67/73 = 0.918 or 91.8 points per 100 possessions

Air Force scored 52 points on 73 possessions

52/73 = .712 or 71.2 points per 100 possessions


Example #2: Gonzaga vs. San Francisco, January 12, 2019

In this key West Coast Conference game with first place in the league on the line, Gonzaga went to the Bay and beat the Dons 96-83.

Gonzaga: 69 FGA, 21 FTA, 12 Off Reb, 4 TOV

69 + (.475 * 21) – 12 + 4 = 71 possessions

USF: 69 FGA, 25 FTA, 14 Off Reb, 5 TOV

69 + (.475 * 25) – 14 + 5 = 72 possessions

Gonzaga 96 points on 71 possessions = 1.352 points per possession or 135.2 points per 100 possessions.

San Francisco 83 points on 72 possessions = 1.153 points per possession or 115.3 points per 100 possessions.


Example 3: Michigan Wolverines to date

Michigan used to win games by three-point barrages and fast break points and limited defense.  Then, after assistant coach Luke Yaklich came to Ann Arbor to install his multiple defenses, the Maize and Blue became just as tough on the defensive side if not better defensively.

So far this year, the Wolverines have these offensive and defensive stats through 18 games.

Offense: 1,021 FGA, 318 FTA, 165 Off. Rebounds, 175 Turnovers in 18 games

1021 + (.475 * 318) – 165 + 175 = 1,182 total possessions and 65.7 possessions per game.

Michigan has scored 1,306 points in 18 games.

1,306 / 1,182 * 100 = 110.5 points per 100 possessions.

Michigan’s Defense has given up: 1,003 FGA, 210 FTA, 142 off. Rebounds, and  237 turnovers.

1,003 + (.475 * 210) – 142 + 237 = 1,198 total possessions and 66.6 possessions per game.

Michigan has surrendered 1,027 points in 18 games.

1,027 / 1,198 * 100 = 85.7 points per 100 possessions.

A raw point spread between two teams can be estimated by combining their offensive and defensive points 100 possessions and factoring in strengths of schedule and home court advantage.

Let’s look at State vs. Tech in an imaginary matchup.

State has an offensive efficiency of 110 points per 100 possessions and a defensive efficiency of 90 points per 100 possessions against a schedule 3 points weaker than average.  They average 76 possessions per game, and their home court advantage is worth 3 points.

Tech has an offensive efficiency of 102 points per 100 possessions and a defensive efficiency of 99 points per 100 possessions against a schedule 8 points better than average.  They average 66 possessions per game.

For the year in question, the national average for possessions is 70 per game, so State plays at a tempo of about 8.6% above average, while Tech plays at a tempo of about 5.7% below average.  Because it is easier for one team to slow pace down more than it is for another team to speed pace up (unless they press full court for most of the game), it can be estimated that this game will have about 69 possessions.

If State outscores its opponents by 20 points per 100 possessions, in 69 possessions, this equates to 13.8 points.

If Tech outscores its opponents by 3 points per 100 possessions, in 69 possessions, this equates to 2.07 points.

To this point, State looks like an 11.73 point favorite over Tech, but this is not the case.  Schedule strength and home court advantage must be included.

If Tech’s schedule on average has been about 11 points tougher per game than State, you then add those 11 points in Tech’s favor.  Now, the State’s advantage has been reduced to 0.73 points.  Tech’s home court advantage is 3 points, so the expected outcome would be State by 3.73, or 4 points.

This is a crude method once used by the PiRate Ratings, as the Blue Rating.  We no longer use this method, as there are more accurate ways to determine pointspreads, namely using algorithms of the Four Factors with schedule strengths, home court advantage, and road team disadvantage.

Example 4: Villanova 2018 season

The Wildcats won their second national championship in three years last season, finishing with a 36-4 record.  They scored 3,463 points and allowed 2,807 points in 40 games.

Here are their pertinent stats to calculate efficiency.

Field Goal Attempts: 2,440

Opponents: 2,401

Free Throw Attempts: 718

Opponents: 641

Offensive Rebounds: 380

Opponents: 378

Turnovers: 426

Opponents: 512

Possessions: 2,440 + (.475 * 718) – 380 + 426 = 2,827 (70.7 possessions per game)

Opponents: 2,401 + (.475 * 641) – 378 + 512 = 2,839 (71.0 possessions per game)

Offensive Efficiency

3,463/2,827 * 100 = 122.5 points per 100 possessions

Defensive Efficiency

2,807/2839 * 100 = 98.9 points per 100 possessions


How does this compare to past national champions?  Because offensive rebounding stats were not officially kept until this century, it can only be estimated for the 20th Century.  No doubt the UCLA teams of 1967 thru 1969 and 1972 and 1973 would be off the charts great, as the Bruins dominated in every aspect of the game during their dynasty years.

There are some very fine teams that won championships in recent years, so let’s look at the national champions during this time.  The number shown is the total scoring margin per 100 possessions.  Of course, schedule strength is not equal for these teams, but on the whole, there is not a lot of difference, as these champions all played schedules between 5 and 10 points above the national average.

When adjusted to schedule strength, here are the 10 best teams in the 21st Century using the PiRate Ratings formula.

2008: Kansas 124.0

2001: Duke 123.6

2018: Villanova 122.9

2010: Duke 122.1

2013: Louisville 121.8

2005: North Carolina 121.7

2012: Kentucky 121.5

2015: Duke 121.3 

2016: Villanova 120.9

2009: North Carolina 120.3

2007: Florida 120.1

2002: Maryland 119.6

2004: Connecticut 117.9

2006: Florida 117.1

2017: North Carolina 117.0

2011: Connecticut 115.8

2003: Syracuse 115.1

2014: Connecticut 111.6

Note that the national champions through these seasons were not necessarily the highest rated team by efficiency.  For instance, Connecticut was not considered a factor at the end of the 2011 regular season.  They finished tied for 9th in the Big East, and thus they had to play in the opening round of the conference tournament.  To win the conference tournament, they would have to do something never done before or since–win five games in five days.  The Huskies became the big story of Championship Week win Coach Jim Calhoun rode his star guard Kemba Walker to the title, winning five games in five days at Madison Square Garden, as Walker performed for his friends and family from the Bronx, averaging 26 points per game by taking it to the hoop and drawing enough fouls to shoot 54 free throws in just five games.

The Huskies were on a roll, and they won six more games in the Big Dance.  They finished 11-0 and still only rose to 15.8 points better than average against an average schedule.  Before this 11-game streak, UConn was just 9-9 in the conference.  However, the Huskies had played a very difficult schedule that included 18 ranked opponents, in which they went 12-6 in those games.  All nine of their losses came to NCAA Tournament teams, so strength of schedule was terribly important in factoring their adjusted efficiency.


2019 Top Efficiency

By now, you must want to know which teams are at the top in total efficiency?  It should come as no surprise that the NET Ratings and the Efficiency Ratings are about the same.

Virginia, Duke, Michigan State, Gonzaga, and Tennessee are at the tops in adjusted efficiency, or to put it bluntly, what the NCAA Selection Committee will look at.  Likewise, these are also the top five teams in NET Ratings, so if the Selection Committed picked the bracket today, four of these five would be your number one seeds, and the fifth would be the top number two seed.

This doesn’t mean that one of these five teams will win the national championship, but the odds are that from this group of five, there is about a 50-50 chance that one will win the title.  Of course, this is only a mid-season ranking.  The ranking on March 17.


Individual Efficiency

I won’t begin to explain individual offensive and defensive efficiency, as my only recommendation it to read Basketball on Paper, as Oliver is the Bill James (or Tom Tango) of basketball analysis.

Let me just list which players from the power conferences rate at the top.

Can you guess who is the current number one player in efficiency?  I bet if you had one free guess to win a car on a game show, you’d win the car.

The best player in college ball today is the best player in total efficiency.  It comes as no surprise that Duke’s Zion Williamson is number one, and he is far ahead of the field.  Gonzaga’s Brandon Clarke is a distant number two, and Wisconin’s Ethan Happ is almost as far being Clarke in third place as Clarke is behind Williamson.

Before you think that this rating is due to just these three players being great, let me add that their coaches and teammates are also important in this rating.  Coach Mike Krzyzewski has produced a lot of highly efficient players.  Sure, most of them were McDonald’s All-Americans, but there are some of these 5-star players in recent history that are not all that efficient.

Vanderbilt’s Simi Shittu was the Number 7 overall player in this current freshman class, a 5-star McDonald’s All-American.  The Commodores are one of the least efficient teams from a Power Conference, and Shittu’s numbers have headed south once SEC play began, and the opposition quickly learned his liabilities.  Shittu actually owns a negative offensive efficiency rating through 17 games, and an even worse rating in five conference games, as he has negative efficiency in both offense and defense.  It doesn’t help his efficiency when he has a 7.8% three-point accuracy, low free throw percentage, and a high turnover percentage.  I have heard comparisons made to former St. John’s 5-star player Wayne McKoy from the 1970’s, when McKoy went from top player in the freshman class to never playing in the NBA.












January 15, 2019

Advanced Basketball Statistics–Fun Stuff for Stats Buffs, Part 2

Last week, we introduced you to the basics of advanced basketball statistics, the Four Factors.

If you missed that feature, you can find it here:

This week, we hope to explain how to apply advanced stats to individual players. It is a bit more involved, but if you break it down, it is not difficult to understand.

Then, in our final installment next week, we will attempt to explain offensive and defensive efficiency, which is a multiple step process and quite involved, but once you have the formulas placed in a spreadsheet, you can have the same data that the Selection Committee will have in the room when they meet to select the field and seed the teams.

Let’s start with individual statistics.

True Shooting %
The basic shooting stat for an individual is True Shooting Percentage. It incorporates field goal shooting from behind the three-point line, inside the line, and foul shooting into one percentage that provides a decent look at how efficient a player is when he shoots the ball to his basket.

The formula for TS% is: College: Pts/(2*(FGA+(.465*FTA))) &

NBA Pts/(2*(FGA+(.44*FTA)))

Example: Let’s take a look at the incredible Markus Howard of Marquette. As of this afternoon (January 15, 2019), Howard has scored 439 points for the season. He has taken 301 field goal attempts and 116 free throw attempts.

439/(2*(301+(.465*116))) = .618 or 61.8%

Let’s now take a look at a big man and how Howard stacks up as a perimeter player. Let’s look at Gonzaga’s Rui Hachimura. As of this afternoon, the Bulldogs’ power forward has scored 374 points on 233 field goal attempts and 117 free throw attempts.

374/(2*(233+(.465*117)))= .651 or 65.1%
Hachimura is a little more efficient in scoring points when he shoots the ball for any reason than Howard, but they are both quite excellent at scoring for their teams.
How do they compare with a couple of all-time greats from the past?

Let’s look at Steph Curry’s and Bill Walton’s final years at Davidson and UCLA respectively.

Curry: 974/(2*(687+(.465*251)))= .606 or 60.6%, not as good as Howard so far this year.

Walton: 522/(2*(349+(.465*100)))=.660 or 66.%, which is a little better than Hachimura.

Hachimura has benefitted from some three-pointers that did not exist when Walton played at UCLA, but Walton would have never attempted a three-point shot playing in the low post for the Bruins. Walton also missed some games his senior year due to knee troubles, and he was a lousy foul shooter his last two years in Westwood, or else his TS% would have been even higher.

Offensive, Defensive, and Total Rebounding Percentage
For an individual player, the formula for offensive rebounding percentage is:

100 * [(Individual Player’s Offensive Rebounds * (Team Minutes Played/5)) / (Individual Player’s Minutes Played * (Team Offensive Rebounds + Opposing Team Defensive Rebounds))]

The formula looks bulky but it is quite easy to calculate and once you plug them into a spreadsheet, it is a quick process.

Defensive Rebounding percentage is just the opposite formula
100 * [(Individual Player’s Defensive Rebounds * (Team Minutes Played/5)) / (Individual Player’s Minutes Played * (Team Defensive Rebounds + Opposing Team Offensive Rebounds))]

And Total Rebounding Rebounding Percentage brings the whole into the parts.
100 * [(Individual Player’s Total Rebounds * Team Minutes Played/5) / (Individual Player’s Minutes Played * (Team Total Rebounds + Opposing Team Total Rebounds))]

Examples: Let’s compare the key board men from the hot rivals in the Big Ten: Kenny Goins of Michigan State and Jon Teske of Michigan

Goins offensive rebounding: 100 * [(41*3425/5)) / (450 * (201 + 356))] = 11.2%
Goins defensive rebounding: 100* [(119*3425/5)) / 450 * (543 + 185))] = 24.9%
Goins total rebounding: 100 * [(160 * 3425/5) / (450 * (744 + 541))] = 19.0%

Teske offensive rebounding: 100 * [(31 * 3400/5)) / (458 * (156 + 415))] = 8.1%
Teske defensive rebounding: 100 * [(82 * 3400/5)) / (458 * (463+135))] = 20.4%
Teske total rebounding: 100 * [(113 * 3400/5)) / (450 * (619+550))] = 14.6%

Because Michigan and Michigan State have played comparable schedules this year, Goins is a little better on both the offensive and defensive glass than the seven-foot Teske.

For what it is worth, Blake Griffin’s total rebounding percentage in 2009 at Oklahoma was 24.0, so Goins and Teske are not quite up to his lofty standards.

Turnover Percentage

The formula for individual TOV% is: 100 * TOV / (FGA + (.465 * FTA) + TOV)

It is rather simple to calculate, but it has its limitations, because point guards handle the ball much more per possession than other players, and this formula does not include assists which might show that it is worth a couple extra points of TOV% for a point guard to have higher numbers of assists. Additionally, some point guards do not attempt many shots, so the denominator of this equation is skewed too low.

We’ll combine this stat with the next stat to come up with an improvement over assist to turnover rate.

Let’s look at a couple of outstanding playmakers–Cassius Winston of Michigan State and Jared Harper of Auburn.

Winston: 100 * 42 / (205 + (.465 * 69) + 42) = 15.0%
Harper: 100 * 32 / (183 + (.465 * 53) + 32) = 13.4%

Assist Percentage
Now we give the playmakers a chance to shine and balance out the bad turnover percentages they receive for having possession of the ball more than others (like a running back in football will fumble the ball more than the tight end per team possession).
The formula for individial AST% is: 100 * AST / (((MP / (Team MP/5)) * Team FG) – FG)

Winston: 100 * 125 / (((528/(3425/5)) * 517) – 100) = 41.9%
Harper: 100 * 101 / (((506/(3050/5)) * 452) -69) = 33.0%

Assist Percentage to Turnover Percentage

Simply divide AST%/TOV% to get a better ratio than the standard AST/TOV.

Winston: 41.9/15.0 = 2.8
Harper: 33.0/13.4 = 2.5

Both of these rates are outstanding. For Michigan State, the Spartans have an outstanding playmaker in Winston, an outstanding dominator on the glass in Goins, and an outstanding group of shooters and defenders. Coach Tom Izzo has a Final Four caliber team for sure.

Block Percentage
Blocks are very important defensive tools. Obviously every time a player blocks a shot, it is also a missed field goal attempt for the other team. Obviously, a blocked shot is not as valuable as the non-blocked missed field goal attempt, because not every blocked shot would have been a made shot, and more blocked shots become offensive rebounds or offensive team rebounds than regular missed shots. However, an intimidator underneath the basket can influence a lot of shots that he does not block, thus lowering non-blocked field goal percentages. There are multiple algorithms used to calculate how valuable a blocked shot is worth in points with and without the inclusion of intimidation.

We like to compare this variable to baseball’s stolen base variable, where traditional sabermetrics lovers hate the stolen base attempt due to the effects on WAR not being great and needing a base stealer that can consistently steal better than 75% of the bases he attempts. They don’t factor in the extracurricular events such as middle infielders having to cheat a step closer to second base, pitchers worried about throwing off-speed (non fastball) pitches, pitchers having to throw to first a lot to reduce leads, and even the first baseman having to delay by a fraction of a second before moving out to cover his area.

For instance, when Maury Wills was stealing bases left and right for the Los Angeles Dodgers in the early 1960’s, Jim Gilliam benefited from being the next batter in the batting order. Gilliam liked to take a lot of pitches, so taking a couple to give Wills a chance to steal didn’t harm him. Actually, because pitchers worried so much, Gilliam was frequently ahead in the count. A veteran with a 2-0 count can hit about 100 points higher than when he has an 0-2 count. Also, Gilliam was an excellent placement hitter. He could hit the ball in the open space created by the first baseman holding Wills on base. When the switch-hitting Gilliam faced a left-handed batter, and the second baseman was covering the bag, while the first baseman was holding Wills on, Gilliam saw a monstrous hole to slap grounders towards right field that allowed Wills to take third base.

Editorial over

Here is the formula for Block Percentage
100 * (Blk * (Team MP/5)) / (MP * (Opponents FGA – Opponents 3-Point Attempts))

Example: Brandon Clarke of Gonzaga is a true intimidator in the paint. His ability to swat balls away has helped the Zags hold teams to just 38.8% field goal shooting. Here is his BLK%.

100 * (58 * (3600/5)) / 497 * (1148-418) = 11.5%

When a player has a double digit BLK%, it is almost a fact that he is also an intimidator in the paint, which means other teams will miss three or four shots that they normally would make against other teams. This is in addition to the blocks that would have been made baskets had they not been blocked.
If an opposing team normally averages 27 field goals on 58 attempts for 46.6%, but with Clarke’s blocks and intimidation this opponent hits only 21 of their 58 attempts for 36.2%. That is a 10% difference created mostly by one intimidating player. Block percentage is one of the most underrated defensive tools in basketball.

Steal Percentage
The steal is a dying art but for a reason. Ninety-five to ninety-nine percent of the time, the steal comes from an intercepted pass and not from a player actually stealing the ball off a player’s dribble. So, steals should be renamed as interceptions like in football. Because so many teams cannot pass the ball worth a darn these days, steals have been dropping in number for several years. This does not mean that the monotonous dribbling of the ball is the way for offenses to score. It is easier to guard the movement of a dribbled ball opposed to the movement of a passed ball, because a dribbler can rarely exceed 15 MPH, while a weak pass is double that speed and a crisp pass is triple that speed or more. When you see a player dribble the ball all the way up the floor on a fast break attempt, he is actually hurting his team’s chances of scoring points on that break. Two quick passes up the floor can result in a wide open basket and/or defensive foul. Many times, the dribbling player is the last of the 10 players to enter the scoring zone, and then the fast break is dead.

Once again editorial over.

The formula for steal percentage is: (100 * Steals * (Team MP/5)) / (Player MP * Opponents Possessions)

You can find team possessions in many locations today, but if you need to calculate this from scratch, team possessions can be very accurately estimated by this calculation:

FGA + (.465 * FTA) – Off. Rebounds + Turnovers {for college}

FGA + (.44 * FTA) – Off. Rebounds + Turnovers {for NBA}

If you are trying to calculate this for your high school, middle school, or youth league team, you will have to adjust the constant that you multiple with FTA. Unfortunately, we do not know what to use for the constants.

Example: Tremont Waters of LSU has come close this year to recording a triple double the hard way with points, assists, and steals. He needed two more steals against UL-Monroe to pull off a feat that is extremely rare in the 21st Century.
Here is Waters’ Steal %.
(100 * 45 * 3050/5) (478 * 1088) = 5.28%

This is an excellent percentage, but it does not approach the percentages of past years, especially when more teams used full-court pressure defense for 40 minutes per game. Some of the Kentucky players under Coach Rick Pitino exceeded 6%.

Usage Percentage
Usage percentage attempts tp gauge the percentage of team plays in which a specific player was key to the possession. It actually measures percentage of team plays USED by an individual while he was on the floor.

The formula for USG % is: 100 * ((FGA + (.465*FTA) + TOV) * (Team MP/5)) / (MP * (Team FGA + (.465* Team FTA)+Team TOV))

Example: Carsen Edwards of Purdue is heavily involved in all of the Boilermakers’ possessions.

100 * ((313 + (.465 * 90) + 52) * (3225/5)) / (537 * (985 + (.465*194)+174)) = 39.1%

At the same time, teammate Ryan Cline plays about the same number of minutes per game but has a USG% that is less than half of Edwards. Thus, Edwards is vital to Purdue’s offensive success. If Edwards gets in foul trouble, Purdue is in much worse shape than if Cline gets in foul trouble. Of course, Matt Painter doesn’t want either star getting into foul trouble, as they both play better than 33 minutes per game.

In our final installment of Fun Stuff for Stats Buffs, we will attempt to explain offensive and defensive efficiency ratings, the big advance metric that the Selection Committee will use as part of their selection and seeding criteria. It is quite bulky and involves multiple steps to figure. If you ever tried to calculate Base Runs in baseball, you know how involved that calculation was. oRAT and dRAT make base runs calculations look like simple addition.

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