*“There really is nothing else in the game. These four responsibilities on the offensive side and these four responsibilities on the defensive side are it … If you aren’t shooting from the field, you better be doing a few of the other three things. If you don’t have the size to get defensive rebounds, you better force turnovers. If you can’t take care of the ball very well, you better get shots up before you turn it over, then go after the boards.”*

* -* Dean Oliver*, Basketball on Paper*

*Today at GotBuckets, we’re introducing a new set of stats called Four Factors APM (FFAPM). Like the name suggests, FFAPM applies the methodology of 2-Year Adjusted Plus Minus to player impact on the Four Factors instead of scoring efficiency differential (which APM, RAPM, and RPM use). We hope that the new tables add depth and context to the plus-minus metrics found on GotBuckets and elsewhere. Click here for 2012-2014 Offensive FFAPM and here for 2012-2014 Defensive FFAPM.*

In the age of advanced sports statistics—a now crowded room of efficiency ratings, Bayesian models, player values, data visualization, MIT Conferences, Holy Grail metrics, and a hipster’s disdain for anything so mainstream as a box score, it’s easy to feel overwhelmed. Like the ship has already sailed, and you would need to spend several months buried in old college textbooks and Wikipedia articles to catch up and fully appreciate the NBA in the information age. Of course this isn’t true, and the NBA fan’s enjoyment is not a function of his ability to explain the difference between Frequentest and Bayesian statistics. A certain level of information is preferable, but the game is mostly enjoyed on a visceral level; the data doled out by nerds with computers is purely supplementary. Today at GotBuckets, we’re launching a set of semi-new stats that mixes one of the more advanced concepts of Parents’ Basement Analytics with perhaps the most durable tool ever devised for basketball analysis: Dean Oliver’s Four Factors.

For all the brainpower and innovation finding its way into the league each year, I don’t think any concept in advanced basketball stats matches the power and simplicity offered by the Four Factors. If you’ve never encountered them before, Four Factors takes the most fundamental concepts of the game—shooting, turnovers, rebounding, and the free throw line—applies an extremely modest amount of arithmetic, and arrives at a wonderfully effective starting point to think about team or individual performance.

The durability of the Factors rest on the concrete terms it defines for the game—shooting is about twice as important as turnovers and rebounding, which are both slightly more important than getting to the line (and making) free throws. Each factor on offense has its counterpart on defense, revealing the inherent balance in basketball. You can spend five minutes digesting the concept, never think about math outside the scoreboard again, and easily carry a more“analytical” perspective for the rest of your hoops-watching career.

At a blog centered on something like “Regularized Adjusted Plus Minus” and “Two Year Adjusted Plus Minus” models, we’re clearly committed to writing about fancy, computationally intense basketball stats; but the value of these stats is only as high as the clarity (and context) that we’re able to provide along the way. For most of us who peruse plus/minus regression stat tables, the results are a veritable black box. At the end of the 2012-2013 season, LeBron James had a +8.0 RAPM, Kevin Garnett +6.3, Amir Johnson+5.8, and Kevin Durant +3.2. It is certainly satisfying that a metric, totally blind to individual box score stats, is able to identify great players. It’s quite frustrating, however, to take these seemingly arbitrary numbers at face-value. Where does the conversation go? The conversation does go *somewhere*— perhaps to team context, defense, screen-setting, “intangibles”, sample size, co-linearity, and probably the box score. There’s not a whole lot of room between these topics and imprecise speculation… Or downright confusion. And isn’t the whole point of advanced plus minus stats to “think outside the box score”?

With this in mind, and after gushing about the strengths of the Four Factors—a set of stats you could have calculated on toilet paper in Milan High School’s gym locker room in 1954—I wanted a plus-minus model variant that can sink its teeth into concrete basketball concepts.

**Shooting, Turnovers, Rebounding, and the Free Throw Line**

What if instead of measuring a player’s plus-minus impact on scoring differential, we use the same method to measure his plus-minus impact on the smaller measurable components of the game we’re all familiar with?

- Shooting: We know that Player X shoots at a high percentage from the field, but does his
*entire team*reap the benefits of it when he’s on the floor? How can we determine if Player X improves the scoring opportunities for entire team, or is merely benefiting himself in lieu of teammates? Using the method similar to 2-year APM, this regression uses Effective Field Goal % instead of Scoring Differential. If Team A shoots 55% and Team B shoots 45% during a stretch of play, the shooting “plus-minus” for Team A is +10%. - Turnovers: The model uses Turnover Rate (Turnovers per 100 possessions) to calculate a similar differential. If Team A loses the ball on 12% of its possessions and Team B turns it over on 18%, Team A records an advantage of +6%. From a player’s perspective– what if Player X is a point guard who records many turnovers himself, but handles the ball so frequently that his team actually has a
*better*turnover rate thanks to his good ball stewardship? Think of any Steve Nash or Chris Paul team. - Rebounding: The model uses the offensive rebounding rate differential. If Team A collected 35% of potential offensive boards and Team B collects only 20%, Team A scores a +15% advantage. Let’s say Player X uses his size and athleticism to grab a lot of rebounds for himself; but does he also effectively box out the opposition to create better rebounding opportunities for teammates? In theory, this stat is indifferent to players who pad the box score with “cheap” rebounds (i.e. rebounds that are uncontested). It rewards players whose teams truly rebound
*better*when he’s on the floor. - Free Throw Line: How often does a team get to the line compared to the opposition? On offense, can a player help teammates exploit the defense to draw fouls? It’s a common point of frustration in basketball statistics that “assisted” trips to the free throw line– that is, passes that lead to a shooting foul– are not counted in the box score. At least in theory, FFAPM will detect this effect, among others, like perhaps a nice screen set that frees a teammate to get to the basket and draw freebies. On defense, can a hulking center act as such a deterrent in the paint that his teammates have a reduced need to commit fouls, or opponents drive less, resulting in fewer fouls for the entire team? This stat calculates team free throw attempts per 100 possessions. If Team A takes 35 attempts and Team B takes 30, the plus-minus is +5 for Team A. Because Free Throw % is such a purely individualistic part of the game, the model does not account for actual made free throws– instead it measures the act of getting to line and preventing your opponents from doing so.

Just like Advanced Plus Minus models, FFAPM splits the results into its defensive and offensive components, arriving at 8 estimates of a player’s impact on different aspects of the game. If you’re still unsure about what the heck I’m actually doing here, feel free to review the “2 Year APM” methodology on our *What are These Stats? *page.

**Results!**

Using our 2-Year APM as a guide to identify the highest impact players on offense, Four Factors APM acts as the next layer of information, adding depth and context to the APM ratings.

Notice that the FFAPM metrics look a bit like video game ratings– I converted the results into percentile ratings, derived from from the historical set of results (going back to the 2004 season). The conversion vastly increases the intuitive handle of the tables. Without them, LeBron’s Offensive FFAPM line would look like this: **eFG: +4.7; TOV: +1.6; REB: +0.3; FT: +7.9**. Rather than make mental guesswork about what each estimate means, you know immediately where each player stands compared to the rest of the league. For LeBron– **eFG: 100; TOV: 90; REB: 59; FT:** **99**– says that he has a profound impact on the Heat’s shooting from the field and rate of getting to the free throw line, a very positive effect on team turnovers, and a modest effect on team offensive rebounding. (View the table on this page to view the estimates that correspond to each percentile)

FFAPM OFFENSE: Top 10 2-Year APM Offense Players, 4-25-2012 to 4-14-2014 (minimum 3000 minutes) |
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Player | APM – Offense | eFG | TOV | REB | FT | Minutes | |

1 | LeBron James | 11.41 | 100 | 90 | 59 | 99 | 7723 |

2 | Stephen Curry | 9.35 | 100 | 97 | 66 | 49 | 6325 |

3 | Kevin Durant | 8.66 | 99 | 56 | 42 | 98 | 7557 |

4 | Goran Dragic | 8.04 | 98 | 85 | 72 | 97 | 5284 |

5 | Kobe Bryant | 7.70 | 86 | 94 | 66 | 97 | 3666 |

6 | John Wall | 7.59 | 97 | 99 | 14 | 88 | 4611 |

7 | James Harden | 7.19 | 69 | 95 | 69 | 100 | 6635 |

8 | Mike Conley | 7.09 | 86 | 100 | 39 | 84 | 6045 |

9 | Damian Lillard | 6.94 | 93 | 98 | 16 | 78 | 6091 |

10 | Ty Lawson | 6.62 | 88 | 99 | 26 | 96 | 5276 |

Instead of wondering why a player’s APM estimate is so high, low, or middling, you can consult his impact on other facets of the game, where the estimates are calculated from the same data set as APM. How do the results relate to APM itself? I used a multivariate regression to predict *Offensive APM* from the Offensive Four Factors APM estimates. The graphic below depicts the results of this regression, where the area of each circle reflects the relative weight of importance for each stat in predicting a player’s impact on offense; shooting from the field is clearly the most important factor, followed by taking care of the ball, followed by offensive rebounding and getting to the line. The arrows emphasize how each factor contributes to the bottom line of team offense.

On the other side of the ball, perhaps more enlightening due to the lack of quantifiable measures of defense, we can take the same four estimates of each player’s impact on team defense. Like offense, a player’s impact on shooting efficiency is the most reliable way to impact defense overall, followed by the other three factors. Unlike offense, defensive FFAPM suggests that forcing low percentages from the field is nearly twice as important as any other factor, with turnovers losing ground to rebounding and getting to the line. It appears that forcing turnovers as a defender is less important than taking care of the ball as an offensive player; perhaps due to the “gambling” nature of playing the passing lanes.

FFAPM DEFENSE: Top 10 2-Year APM Defense Players, 4-25-2012 to 4-14-2014 (minimum 3000 minutes) |
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Player | APM – Defense | eFG | TOV | REB | FT | Minutes | |

1 | Kevin Garnett | 9.67 | 99 | 74 | 89 | 91 | 4076 |

2 | Roy Hibbert | 6.98 | 99 | 11 | 55 | 99 | 5719 |

3 | Omer Asik | 6.61 | 97 | 2 | 99 | 98 | 3799 |

4 | Dwight Howard | 6.41 | 96 | 19 | 92 | 93 | 5219 |

5 | Marc Gasol | 6.16 | 87 | 64 | 96 | 86 | 5622 |

6 | Nick Collison | 5.23 | 87 | 78 | 83 | 77 | 3452 |

7 | DeMarre Carroll | 5.04 | 89 | 88 | 43 | 60 | 3489 |

8 | Chris Bosh | 4.71 | 96 | 16 | 77 | 95 | 6176 |

9 | Tiago Splitter | 4.66 | 95 | 41 | 64 | 82 | 3811 |

10 | Amir Johnson | 4.56 | 74 | 61 | 92 | 97 | 4524 |

We’re not the first to independently apply the APM method to other basketball skills (see this 2012 Sloan Conference Article and some of Jeremias Engelmann’s new content on his site). We hope that our FFAPM tables add a useful second layer of information to metrics like @talkingpractice’s RAPM and our 2-Year APM.

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