The Pi-Rate Ratings

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:

https://piratings.wordpress.com/2019/01/09/advanced-basketball-statistics-fun-stuff-for-stats-buffs/

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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