TPA Model
The concept of total points added (TPA), isn’t particularly complicated. We’re looking at both defensive and offensive effectiveness on a per-possession basis while also incorporating the amount of playing time the contributor in question receives.
At the heart of the theory is this comparison between two hypothetical players:
- Player A makes an average team 5 points better per 100 possessions than an average player would in his spot, and he plays 500 possessions.
- Player B makes an average team 10 points better per 100 possessions than an average player would in his spot, and he plays 250 possessions.
Player B is more effective on a per-possession basis—twice as effective, in fact. But Player A spends twice as much time on the court. Theoretically, they should have identical values, as they would both add 25 points to an average team.
As such, the formula for TPA is rather simple. It’s broken down into two parts—offensive points added (OPA) and defensive points saved (DPS)—and each is calculated in the same vein.
OPA is derived by adjusting offensive box plus/minus (OBPM) to account for the number of possessions the player in question is present for. Similarly, DPS is derived from a similar adjustment of defensive box plus/minus (DBPM) with that same number of possessions. OBPM and DBPM, both calculated by Basketball-Reference.com, estimate the per-100-possessions value of a player on either end of the court.
Add OPA and DPS together, and you have TPA. A score of zero indicates a player was perfectly average (by no means a bad thing for rookies or lifelong end-of-bench players), while anything positive means they were better than an average-level replacement.
For scores prior to 1972-73, we’re estimating OBPM and DBPM using historical correlations with offensive and defensive win shares per 48 minutes. That data goes all the way back to 1951-52, allowing us to come up with rough estimates for the early legends of the sport. These numbers are by no means perfect, but they can still serve as baselines.
Era-Adjusted Model
The NBA is a constantly adjusting league, undergoing trends as teams strategize to counter recent developments from one another. For example, there’s often a give and take between offensive rebounding and transition defense, with some coaches opting to avoid crashing the glass for second-chance opportunities in favor of getting back to prevent easy buckets.
In a vacuum, the Four Factors originally developed by Dean Oliver—effective field-goal percentage (shooting), turnover percentage (turnovers), rebounding percentage (rebounding) and free throws per field goal attempt (fouling)—can be rather telling. They break down success or failure in the core components of the sport.
But we can make them mean even more in a historical contest by adjusting for the era.
The adjusted factors on each side of the court are rather easy to calculate. If a higher score is desired, divide the actual result by the league average during the year in question, then multiply by 100. A resulting mark of 100 indicates perfect averageness, while anything higher is a positive. If a lower score is the goal, divide the league average by the actual result, then multiply by 100. The scale of the results still applies in the same manner.
The benefit of this process is significant.
To show it, let’s take two teams with some of the best effective field-goal percentages of all time—the 1998-99 Houston Rockets (50.6 eFG%) and the 1983-84 Los Angeles Lakers (53.6). In a vacuum, the Lakers are clearly superior, but they also had the luxury of playing during a time in which it was far easier to shoot a higher percentage. The Rockets played during a lockout-shortened season that produced a remarkably low league average of 46.6 and was sandwiched between two campaigns at 47.8.
When we adjust for the eras, the Rockets (108.58 adjusted eFG%) jump ahead of the Lakers (108.28). Given the ever-changing context of the NBA, they were the better shooting team, even if the Lakers were more efficient on a surface level.
We can also do this with teams’ overall offensive and defensive ratings by following the exact same processes illustrated above.
Beyond that, we can calculate Team Rating by averaging the adjusted offensive and defensive scores. A Team Rating of exactly 100 indicates that a squad was perfectly average—whether by being perfectly average on both ends or by being as bad on one as it was good on the other.
Playoff Score Model
What makes a player great in the playoffs?
Winning titles can’t be all that matters. Basketball is, after all, a team sport. No matter how well an individual performs, he isn’t earning any hardware without support from the players surrounding him.
But team success also has to factor in, and that’s why Playoff Score contains two distinct elements: Individual Score and Advancement Share. Together, they give credit to contributors for longevity, performance and team success (adjusted for their impact on the proceedings).
Longevity is represented by games played—a rather simple way to measure how long a player’s postseason career lasted. Some standouts made a number of deep runs into the playoffs over a shorter period of time. But purely in terms of longevity, that shouldn’t be any more valuable than a plethora of early exits over a lengthy stretch.
Individual performance is measured by looking at Game Score, a John Hollinger creation that takes box-score figures and produces a singular output meant to function on the same scale as points. A game score of 10 is considered average, while 40 is outstanding. Even though this is a more simplistic metric with notable flaws, we’re using Game Score rather than Total Points Added because it allows us to analyze players who suited up before 1974. No rankings of playoff performers would be complete without looking at Bill Russell, for example.
Individual Score is a simple calculation: We multiply a player’s average Game Score by the number of postseason contests in which he participated. As such, these three players will receive the same score:
- Player A has an average Game Score of 20.0, earned over the course of a single five-game series.
- Player B has an average Game Score of 10.0, but he played in 10 contests during a single postseason before elimination.
- Player C has an average Game Score of 2.0, and he suited up 50 times over the course of multiple seasons.
- Advancement Share is a bit more complicated.
Players receive up to 50 points for reaching the conference finals, 100 for making the NBA Finals and 250 for winning a championship, and the share of those totals is based on their minutes played. For example, LeBron James played 39.1 minutes per game during the Cleveland Cavaliers’ 2016 title run, so he earns 203.65 points for the championship (39.1/48 times 250). Dahntay Jones, meanwhile, earns just 17.19 points for the same feat (3.3/4 times 250).
Adding together Individual Score and Advancement Share gives us Playoff Score. You can rank rather well if you never experienced much team success but thrived as an individual for a long time (Chris Paul, for example), but you can also do the same if you were a role player on one successful squad after another (Derek Fisher).
For WNBA calculations, two important variations exist. Games only last for 40 minutes, and the Advancement Share is adjusted accordingly. Additionally, the fewer number of games required to advance deep into the playoffs led us to eliminate credit for making the conference finals; only those who advanced to the NBA Finals or won a championship received boosts to their Advancement Shares.