Verifying Chamberlain’s ridiculous season

As you may know, during the slow basketball days of summer I’ve been estimating wins and losses produced by the individual players on the NBA’s all-time greatest teams.

As you may further know, the system I use to assign win and loss “credits” is called  “Marginal Win Score” and it is a derivation of Professor David Berri’s Win Score metric.  To calculate the root Win Score you need certain statistics (blocks, steals, turnovers) and to get my Marginal Win Score you need each team’s opponent statistics.

This presents an historical challenge when calculating wins for players who played before modern statistical records were kept. Prior to 1977-78, the NBA did not record individual production in the three stats mentioned above, and prior to 1970-71, the NBA did not keep opponent statistics. (Thank God for the ABA, that’s all I can say).

But I’m not comfortable black-lining a quarter of NBA history.  I’d rather produce imperfect estimates, but only if those estimates have a high degree of reliability.  If the results produced were unreliable, it wouldn’t be worth my time.

Historical MWS: Filling  the Gaps

Based on the work of Bill James and this fellow, I came up with a “best step-by-step method” to fill in all of the missing pieces.

First I position each player on each team according to where that player would be expected to play on defense.  Defensive allocations are based on height and weight.

Then I use historical trends, analagous players, and other other such cues to produce “missing stat” estimates for each player (which are actually pretty easy to figure).

Finally, I calculate each team’s “Team Win Score” based on the numbers  generated above, and then I take the team’s Pythagorean win record (which has a 95.7% correlation with Win Credits) and use it to estimate each team’s “Opponent Win Score”.  (If you tell me the bus was pretty close to full when we arrived, then after the game I can count the seats, then count the number of heads on the bus,  and based on those two results I can fairly reliably estimate how many passengers, if  any, are missing).

Finally, to “individualize” Opponent Win Score I take the total NBA Win Score average at each position for the particular season, subtract the team’s Win Score average at each position, and then recalculate the NBA averages.  I do this so that I can parse out defensive responsibility without penalizing good players by considering their own stats.

Once all that is done, I parse defensive responsibility to each player through the team’s Opponent Win Score, the player’s position, and the “Rest of the NBA” average Win Score contribution generated by the position.  (Ex:  I’m doing Oscar Robertson, a player that probably guarded the oppo shooting guards.  I estimate the Cincinnati Royals Opponent Win Score per 48 was 42.92.  I further estimate that NBA shooting guards not playing for the Royals generated, on average, 11% of the overall NBA Team Win Score per 48 average.  I charge the Big O with an Oppo Win Score of 4.72).

Wilt Chamberlain’s outlier season

As you can see, there are a lot of unverifiable assumptions built into any pre-1977 win credit estimates, and even more assumptions built into any pre-1971 win credit estimates.  Whenever you have to fill in informational gaps with so many assumptions, any result produced that is far different from the normal results you produce when you have full information on hand tends to shake your confidence in your “assumption-based” model.  The results I calculated for Wilt Chamberlain in his 1966-67 season shook my confidence.

Using my assumption-based model, I calculated that in 1966-67 Wilt Chamberlain produced a MWS48 of +8.69 over the course of 3682 minutes of playing time for the Philadelphia Sixers.  If true, in 1967 Wilt achieved a level of productive dominance far beyond any other season for any other player that I’ve ever calculated or expect to calculate.  Wilt’s Win Credit total for the season comes out to 30 wins.  To put that in perspective, no player this century has produced a season with an MWS-based Win Credit total of even 20 wins.

To make me even more nervous about my results, the calculated distribution of wins for the 1966-67 Sixers was historically very odd.  Basically, if I was right, the team had one monster player, one very good player (Chet Walker), and a slew of average players.  Great teams aren’t usually composed that way.

Verifying Chamberlain’s huge season

There are two things that have quelled my fears, and by doing so given me greater confidence in the reliability of my assumption laden win model.

First, Chamberlain’s known statistics in 1966-67 are so overwhelmingly awesome, even if you err on the side of assuming Wilt produced unrealistically poor statistics in every unknown area, his personal Win Score is still so large that his Win Credit estimate remains near 30 wins.  For instance, if you plug in 100 steals, which pace-adjusted would put him well under average, 260 blocks, which considering opportunity would make Wilt half the shot blocker in 1967 that Roy Hibbert was last season, and 415 turnovers, which would exceed Artis Gilmore’s known record season amount by more than 50, you still come up with a Win Score 48 of 31.07 (last season’s center average WS48 was 12.42).  Based on all of those low-ball missing stat estimates, you would still credit Wilt with 28.9 wins.

WhatifSports:  Simulating Wilt’s 1966-67 season

Still I wasn’t quite buying my numbers.  Maybe my defensive estimates were unrealistic.  So I took it to another level by running a simulated 1966-67 Philadelphia 76ers season on WhatifSports.

The beauty of WhatifSports is that it generates statistically based estimated results in a play-by-play format.  So I could chart a simulated Chamberlain season as though I had every bit of information necessary.

In those days each team played every other team nine times.  Instead I ran three games against each, alternating home and away.

To my amazement, the MWS48 statistics generated were almost identical to my estimated numbers.  The numbers were what I thought they would be straight down the line.  Under the statistical numbers generated, Wilt Chamberlain’s MWS48 was +8.77, which is actually slightly more productive than my assumption based model estimated. (to be precise, the WhatifSports model has both Chamberlain and his opponents producing higher numbers than my model, but in direct proportion.  This is because, I believe, WhatifSports underestimates the likely number of turnovers per possession.  But as long as their estimates are uniform, that doesn’t cause a problem).

With these results I can now state with a high degree of confidence that Wilt Chamberlain’s 1966-67 season was the most valuable single season produced by any player in NBA history.

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3 Responses to “Verifying Chamberlain’s ridiculous season”

  1. Chicago Tim Says:

    It make me wonder if Chamberlain was too focused on scoring. 1966-67 was the first time in his career that he did not win the scoring title.

  2. Jerbil Says:

    You say, ” I’m doing Oscar Robertson, a player that probably guarded the oppo shooting guards.” You need to make many inferences. Something I’m curious about: If you want to know who the Big O guarded, why don’t you ask him? Or you could ask his coaches, team mates, or contemporary journalists. Maybe there are some facts that could be better ascertained this way than by your inferences?

  3. Geoffrey Hamilton Says:

    Tywill:
    Speaking of the Big O…. He and Wilt were my 2 favorite players growing up (I was born in 1953), but they only won single NBA championships . Any chance you can derive Oscar’s WP scores for his triple-double season, and/or the 2 seasons around it , since he ‘averaged’ a triple-double across the 3 years, and actually achieved it in 1? I’ve always felt he was the best non-giant ever (locked down the great Elgin Baylor during Allstar games). Speaking of Allstar games, believe Oscar’s teams won 8-9 in a row sometimes Western, sometimes Eastern conference…guess Cincinnati swapped back and forth, which I didn’t realize at the time. At anyrate, he had different teammates in the Allstar game , but no matter which conference Chamberlain/Russell/Thurmond/Baylor/Pettit etc played on, Oscar’s side kept winning…. the truest definition of the best “..He can take your’n and beat his’n or take his’n and beat your’n!” Awesome…
    Still think he’s #1 of all time , with Mike being 1A…:)

    Rally enjoy your stuff. Thanks

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