It sounds great on paper: ranking players throughout NBA (and ABA) history based on how they contributed to their team's chances of winning a championship. That's the goal of my championships added metric, which I used to rank the top-40 NBA players of all-time.
So how do we get from the statistics -- in this case, Basketball-Reference.com's win shares, tracked or estimated throughout all of NBA history -- to championships added?
Regular-season championships added
The first step of the process is relating a player's regular-season win shares to his team's chances of winning a championship. Starting with when the league expanded to 27 teams in 1989-90 (in order to provide a large sample from a league of similar size), I looked at how frequently players with various win shares ended up winning the title. Here's how that looks.
As you can see, the relationship isn't linear. Going from one win share to five adds less likelihood of winning a championship than going from five to eight, or from eight to 10. Truly elite performance determines titles. What is linear is the relationship between win shares and the denominator in the odds of winning a championship (e.g. one out of two, one out of four, etc.). Using that relationship produces the best-fit line on the chart.
There's only one more step needed to go from win shares to championships added: We have to subtract out the odds of winning a title at random just by being on the end of the bench -- a little better than 3 percent in this sample. Subtracting this shows that anyone with fewer than four win shares hasn't actually improved his team's chances of winning the championship and further emphasizes the importance of quality over quantity.
Also, all seasons are adjusted to 82 team games played, eliminating lockouts and the shorter schedules the NBA played in its early days from affecting a player's standing.
Playoff championships added
Using postseason win shares by player to estimate a team's chances of winning a championship is a little trickier. We can't go simply by total win shares because teams that advance deep in the playoffs naturally play more games and accumulate higher totals.
I eventually settled on looking at players whose teams reached the NBA Finals and comparing win shares per game to the outcome of the series. Based on this, I estimated how a player's win shares per game affect his team's chances of winning any given series.
From this, we can estimate their chances of winning the championship by taking the chances of winning one series to the power of the number of series. That is, a team with a 75 percent chance of winning each series has a 31.6 percent chance of winning four series and the championship (.75 to the fourth power).
I gave a team 50 percent chance of winning each series they didn't reach so as to give less credit to players whose teams were eliminated early. Lastly, I subtracted the chances of a team with a 50-50 shot of winning every series to again account for how likely a player is to win a championship by random chance.
Award championships added
Other people have come up with similar historical rankings using win shares. Neil Paine outlined a method he called championship probability added at Basketball-Reference.com in 2009, and Daniel Myers has been posting a "Hall Rating" on the APBRmetrics forum.
To go beyond these metrics, I wanted to also consider how players were evaluated by contemporaries using subjective factors. I settled on three of them: All-Star appearances, All-NBA First and Second Team appearances and MVP voting. For the most part, these three honors have existed throughout NBA history. The first All-Star Game was played in 1951, the MVP was awarded beginning in 1955-96 and the All-NBA Teams date back to the league's inception. (The Third Team wasn't added until 1987-88, so these selections are not included.)
Again, I valued these honors by the chances a player receiving them would win a championship. In a 30-team league, an All-Star berth translates to an additional 4.5 percent chance of winning a title (equivalent to about 10 win shares), an All-NBA Second Team spot 6.6 percent (about 11.5 win shares) and a First-Team pick a whopping 13.3 percent (about 15 win shares).
MVP voting is a bit trickier, but near-unanimous winners tended to make their teams favorites to win the championship, adding about 50 percent. A typical winner adds closer to 30 percent chances.
I adjusted all of those percentages based on the number of teams in the league, since it was easier to be picked All-NBA or win MVP in the early 1960s, when there were only nine teams as compared to 30 in the modern league.
Since players can and often do earn multiple honors in the same season, I used whatever the highest rating was among MVP voting, All-NBA and All-Star picks for them.
Adjusting for league quality
The last stop of the process is adjusting for how quality of play has evolved in the NBA over time. When I was ranking the top teams of all time last June, I used an adjustment based on whether players saw more or less playing time from one season to the next after accounting for aging.
That version worked well at the team level as far as dealing with expansion and the merger, but it doesn't seem to reflect the improvement of the league over time. Given the increased size of the player pool the NBA now draws from with the growth of the game internationally, it's hard to believe quality of play is really worse now than in the 1980s.
The solution turned it to be considering minutes played year over year without the aging factor. That results in the following graph of league quality dating back to 1946-47 and relative to 2014-15.
Now growth is apparent throughout the NBA's history, most rapid in the early years before expansion and relatively steady since the merger. (The red line reflects quality of play in the ABA, which started out several decades behind the NBA but nearly caught up by the time of the merger.)
Each player's championships added were multiplied by the level of the league relative to 2014-15 to provide adjusted ratings.
Adding it up
The final ratings used to create my top 40 average regular-season and awards championships added materialize (since awards are strictly based on the regular season) before adding to them championships added in the playoffs. Voila! It's one comprehensive attempt to rate every player in NBA history on a relatively level playing field.