## Historical Marginal Win Score

There are several variations of Marginal Win Score, all based upon the information available to me. Below I describe each one of them. In general, their reliability goes down slightly for each level you go up.

**Level One: Straight from the Play-by-Play**

I would consider this the most reliable, while at the same time the most difficult to gather, because I essentially have to roll up my sleeves and reverse engineer an NBA transcript.

**Level Two: 82games Counterpart Information**

This is based upon the “Production by Position” pages on 82games.com.

**Level Three: Box Score Marginal Win Score**

In this variation I use height/weight to position players on each team and then assign the opposition’s production accordingly.

**Level Four: Post 1977 Historical Marginal Win Score**

In this variation, I do everything I will explain below, except that I do not have to use inductive reasoning to estimate the Opponent Win Score.

**Level Five: Pre 1977 Historical Marginal Win Score**

By far the most difficult MWS48 calculation to do, but worthwhile, and I think still fairly reliable and interesting. The method for making historical estimates of unknown statistics is based upon the methods employed by Bill James and Pete Palmer to estimate defensive statistics in baseball for seasons without official Major League game transcripts. Its basically estimating the unknown from the known and past observations of similar situations – inductive reasoning.

**1. POSITION THE PLAYERS**

The first step is to break each team down by positional minutes. This is done by height and weight, and according to assumed defensive matchup. Thus, even though Oscar Robertson, for instance, is generally regarded as a point guard, for MWS48 purposes he is generally considered a shooting guard. This is because of his assumed defensive role. If you have the 6’5”, 200+ lbs Robertson on the court with a 6’1”, sub-200lbs fellow guard, no matter whether Robertson handles the ball on offense, on defense he will guard the oppositions larger guard. But that situation is rare. Where things get trickier is along the perimeter. Back in time a lot of smaller players were employed at small forward and even power forward. At times you must use judgment.

**2. FILL IN THE STATISTICAL GAPS**

Step two is an estimate of each player’s TOs, Blocks, and Steals. This is difficult, but somewhat less dicey than it may seem, because as Dean Oliver has indicated, the missing statistics for seasons prior to 1977 generally cancel each other out. Plus each player’s likely turnovers, which are by far the most impactful of the three missing statistics, are fairly easy to estimate based on each players field goal attempts, free throw attempts, and assists.

**3. CALCULATE POSITIONAL AVERAGES**

Once I’ve estimated (a) each player’s position, and (b) each player’s missing stats, then I calculate Win Scores for every single player for the particular season, and from that I calculate the NBA average at each position for that season. This positional average becomes important below.

**4. CALCULATE TEAM WIN SCORES**

Next, I calculate each team’s “Team Win Score”, again using the stats I have plus the estimates of missing stats.

**5. ESTIMATE OPPOSITION WIN SCORE AVERAGE**

Here’s where the “guesstimating” comes into play. Based upon each team’s Pythagorean Wins, and the Team Win Score calculated above, I estimate what their Opposition’s Win Score must have been. I can do this with a fair amount of confidence because past calculations of seasons where Opposition Win Score is known shows that you can calculate wins with about 95% accuracy using Team Win Score and Oppo Win Score. So, if I know how many wins a team had, and I think I’m pretty close on the Team’s Win Score, then I can put in a pretty good guess as to what their Oppo Win Score must have been.

**6. ESTIMATE NBA WS AVERAGES WITHOUT GIVEN TEAM**

This step is tricky, and makes the exercise time consuming, but it has to be done because of the small number of NBA teams pre-1977.

Here, I basically remove all of the Win Score numbers for the given team and then recalculate the NBA average at each position. Why? Because the ultimate goal is to charge each player with the production from his counterpart position. I don’t want to warp that number with the player’s own production.

For instance, in the 8 team NBA of 1965, if you remove Bill Russell’s numbers from the equation, you get a completely different Win Score average at the center position. If I’m being fair to Russell, I can’t charge him with his own production. So I have to remove his team’s numbers.

**7. DIVIDE OPPONENT PRODUCTION BY POSITION**

Okay, the final step then is to look at the NBA average Win Score per position sans the particular team, and then divide the estimated overall Opponent Win Score by that NBA average and charge it to each player according to position.

This is not a true example, but lets say the Celtics estimated Opponent Win Score average were 34.14. Lets further say that throughout the rest of the NBA, centers account for 35% of overall Win Score production per team. Thus, for every minute he played, I charge Bill Russell with 34.14 * .35% /48. That is then his estimated Oppo Win Score upon which I base his estimated win production.

Now, is this exact? In other words, is it exactly correct to say that because the NBA average production comes 35% from the center position that it will certainly be the case for each particular team? No. But it comes fairly close. And it provides fairly accurate information about past players that we can use to compare their performance with the players of today.

If you click on this sentence you can see this method applied to the entire 1965 season. Because of the foregoing, and even though their were only 9 teams that season, these calculations took forever to do.

If you have any questions, I would be happy to answer them.

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