I've been interested in this for a while, I'm going to post my findings so far here. Here is the relevant thread on APBR (not my post:
http://www.apbr.org/forum/viewtopic.php?f=27&t=4035
Basically, there were was a rule put in place prior to the 54-55 season:
1954-55
• The 24-second shot clock is introduced.
• A penalty free throw is awarded following a team’s sixth foul in any quarter.
Both rules had to be adopted to make each one work. The time limit made in unnecessary for the trailing team to foul deliberately, since it would get the ball after 24 seconds. The foul limit made it too costly to foul to prevent a chance at a basket.
• The penalty for a backcourt foul became two shots – three to make two if you are over the limit.
• Offensive fouls are treated as violations, no free throws and the defensive team gets possession. The foul would still count towards a player’s limit of six personal fouls.
and amended prior to the 66-67 season:
1966-67
• The team foul limit is reduced to five per quarter. In the last two minutes of any period, a team is allowed only one foul before the penalty, even if it hadn’t used up its allotment.
• The following language was added to the Zone Defense Rule: "After the offensive team has advanced the ball to its front court, a defensive player may not station himself in the key area longer than three seconds if it is apparent he is making no effort to play an opponent. The three second count starts when the offensive team is in clear control in the front court."
source: http://www.nba.com/analysis/rules_history.html
So an extra "penalty" free throw was attempted when teams were in the aforementioned situations if either FTA is missed on a 2-shot foul, or if an and-1 FTA is missed after a made shot.
What does this mean? The number of possessions used in the denominator of TS% is overstated, because some of the FTA are extra free throws from penalty situations. Before getting deeper into my investigation, I checked to make sure that the penalty FTA was indeed counted in box scores. The President Emeritus of the APBR informed me that it indeed was:
http://www.apbr.org/forum/viewtopic.php?f=27&t=4813
Process
Firstly, I needed to calculate the percentage of the time during the aforementioned situations that the penalty FTA was attempted. The following equation was used:
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p = 1-[A*(1-x)^2/(3-x)^2+(1-A)*B*(1-x)/(2-x)]where A is the percentage of 2-shot shooting fouls (in which the FGA was not made), and B is the percentage of non-possessional fouls which are and-1's. I used a partial data set from what I believe is the 04-05 season to come up with A=.885 and B=.715.
source: http://www.apbr.org/metrics/viewtopic.php?t=142&p=284
The other calculation necessary is the percentage of time during which the opposing team is in a penalty situation. From 54-55 through 65-66 I used this equation:
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s=4*(PFPG*.25-5)/PFPGwhere PFPG is PF committed by opposing teams per game. From 66-67 through 80-81 I changed slightly:
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s=4*(PFPG*A*.25-4)/PFPGResults
Here are the two relevant spreadsheets:
1) TS% Calculations.xls - http://www39.zippyshare.com/v/20327812/file.html
2) Chamberlain.xls - http://www39.zippyshare.com/v/71772393/file.html
The first has the calculations for some important players from the era (I could've done more guys from the 70s, but I'm a little lazy TBH): Wilt, Russell, West, Oscar, Baylor, and Pettit. Wilt aside, the difference (see last column for each page) isn't particularly relevant. Here are the only seasons for which the difference in TS% >= +0.5 but < +1.0:
Wilt - 71 (+0.7%), 61 playoffs (+0.5%), 65 playoffs (+0.6%), 64 Finals (+0.5%), 72 Finals (+0.8%)
Russell - 67 (+0.6%), 68 (+0.7%), 69 (+0.7%), 68 playoffs (+0.6%), 69 playoffs (+0.6%), 65 Finals (+0.7%), 68 Finals (+0.9%)
West - 68 playoffs (+0.5%)
guys for whom difference in TS% >= +1.0:
Wilt - 67 (+1.6%), 68 (+1.3%), 69 (+1.3%), 70 (+1.3%), 72 (+1.1%), 73 (+1.1%), 67 playoffs (+1.4%), 68 playoffs (+1.3%), 69 playoffs (+1.4%), 70 playoffs (+1.1%), 72 playoffs (+1.1%), 73 playoffs (+1.2%), 67 Finals (+2.0%), 69 Finals (+1.9%), 70 Finals (+1.1%), 73 Finals (+1.4%)
I did some isolated test cases too to try and find some others who might be affected (I assumed that the lists of those most affected would be populated by players who were bad foul shooters, and who took quite a few FTA). I only looked at 66-67 through 80-81 (since the differences from 54-55 through 65-66 were insignificant), and isolated players who took at least 40% as many FTA as FGA, and who shot <.550%.
Season - http://bkref.com/tiny/DEPE7
Playoffs - http://bkref.com/tiny/oaZng
In the first spreadsheet, see the last sheet for some test cases (I checked the players who averaged at least 9.5PPG from the above B-R queries). All of them fell between 0.6%-0.8%. I think these are probably the player-seasons most affected by the rule (you can try others yourself, or nominate them for me to attempt). Here they are:
67 Russell (+0.7%), 68 Green (+0.6%), 69 Russell (+0.7%), 73 Bellamy (+0.8%), 81 McGinnis (+0.7%), 69 playoffs Caldwell (+0.7%), 69 playoffs Russell (+0.6%), 69 playoffs Kimball (+0.6%), 70 playoffs Ogden (+0.7%), 75 playoffs Rowe (+0.8%), 76 playoffs Shumate (+0.7%), 79 playoffs King (+0.8%).
The second spreadsheet is some bonus treatment for Wilt. For the rest of the players I used league average for PFPG (since opponent stats are not available for those seasons) when calculating the percentage of time during which opponents would be in the aforementioned situations. From a quick glance it seemed teams were in said situation 1/8 of the time from 54-55 through 65-66, and 1/4 of the time from 66-67 through 80-81. It's been suggested to me that Wilt's teams were fouled more on average than were other teams (for Hack-a-Shaq strategies).
To test this hypothesis, I searched through my files and found the PF by opponent teams for each and every one of Wilt's career games (well, except for 5 I can't find...I used average fouls against Wilt's teams to calculate estimates for those 5 games). In the regular season for the most part, his teams were fouled around as often as the league average (+1.4 in 62, -1.3 in 64, +1.7 in 67, +1.0 in 69, +2.5 in 70) but this strategy was far more prevalent in the playoffs (+3.5 in 61, +2.2 in 62, +2.5 in 65, +2.2 in 67, +2.2 in 68, +1.6 in 69, -2.6 in 71, +1.1 in 72, +2.3 in 73) and the Finals (+2.0 in 64, +4.1 in 67, +4.1 in 69, +4.2 in 73). So he's the only player for whom I have specific, more exact numbers as opposed to the 1/8 and 1/4 guesses above, but the one player for whom they're most relevant.
Anyhow, here are the adjusted numbers for Wilt (the numbers for other players can be found in the spreadsheets):
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Wilt tTS% tTSA ∆
1960 49.4% 38.2 0.2%
1961 52.3% 37.0 0.3%
1962 53.9% 47.0 0.3%
1963 55.2% 40.7 0.2%
1964 53.9% 34.3 0.2%
1965tot 51.6% 33.8 0.3%
1965sfw 49.7% 39.3 0.2%
1965phi 54.4% 27.9 0.4%
1966 55.1% 30.6 0.3%
1967 65.4% 19.0 1.6%
1968 57.0% 21.8 1.3%
1969 57.7% 18.2 1.3%
1970 56.7% 24.7 1.3%
1971 56.4% 18.5 0.7%
1972 62.0% 12.1 1.1%
1973 70.0% 9.6 1.1%
1960P 50.0% 33.4 0.2%
1961P 49.7% 37.6 0.5%
1962P 51.1% 34.5 0.3%
1964P 54.7% 31.9 0.4%
1965P 55.7% 26.5 0.6%
1966P 50.5% 28.0 0.4%
1967P 56.0% 19.9 1.4%
1968P 52.4% 23.2 1.3%
1969P 53.3% 13.4 1.4%
1970P 53.9% 20.9 1.1%
1971P 48.3% 19.1 0.4%
1972P 57.3% 13.0 1.1%
1973P 56.8% 9.4 1.2%
1964F 51.4% 28.7 0.5%
1967F 51.6% 17.8 2.0%
1969F 49.5% 12.3 1.9%
1970F 58.7% 20.2 1.1%
1972F 61.1% 16.1 0.8%
1973F 50.8% 11.7 1.4%Potential Improvements
1) Find the missing 5 games (lol well not really, these won't change the sample much) for Wilt's teams' opponents:
11/5/59 SYR, 11/20/59 STL, 12/7/62 DET, 12/8/62 STL, 2/5/63 CHZ
2) Much more importantly, improve the values "A" and "B" above. I posted on the APBRmetrics board:
http://www.apbr.org/metrics/viewtopic.php?f=2&t=8340
but haven't gotten any useful responses yet. I don't have any reason to assume that either changed significantly over time, but the larger sample would make me more comfortable, so that's the reason for my leaving this qualifier.