These 15 matches have something in common

Round 7 1930 - Port vs South
Round 3 1936 - Torrens vs Sturt
Round 3 1938 - North vs Norwood
Round 5 1949 - Sturt vs South
Round 6 1955 - West vs Glenelg
Grand Final 1957 - Port vs Norwood
Round 12 1959 - Glenelg vs Port
Round 8 1963 - South vs Sturt
Round 6 1970 - South vs Port
Round 12 1974 - Glenelg vs Port
Round 6 1975 - Port vs North
Round 3 1980 - Central vs Glenelg
Round 6 1988 - Port vs West
Round 2 1998 - Glenelg vs North
Round 1 2000 - South vs North
To explain why, lets look at one of the matches quarter by quarter scores:
Round 8 1963
South 2.5 7.8 10.11 12.11 (83)
Sturt 0.3 4.7 8.9 11.12 (78)
Kensington, 5980
It may not be clear yet, but what is significant about that match is by looking at the numbers which make up the scores in each quarter:
South 2 5 7 8 10 11 12 11
Sturt 0 3 4 7 8 9 11 12
As you can see, all but one number there is in an increase, the South behind tally in the last quarter. There has never been a match in which all numbers increase in sequence, these 15 matches have all but one to do so.
Round 3 1936 - Torrens vs Sturt
Round 3 1938 - North vs Norwood
Round 5 1949 - Sturt vs South
Round 6 1955 - West vs Glenelg
Grand Final 1957 - Port vs Norwood
Round 12 1959 - Glenelg vs Port
Round 8 1963 - South vs Sturt
Round 6 1970 - South vs Port
Round 12 1974 - Glenelg vs Port
Round 6 1975 - Port vs North
Round 3 1980 - Central vs Glenelg
Round 6 1988 - Port vs West
Round 2 1998 - Glenelg vs North
Round 1 2000 - South vs North
To explain why, lets look at one of the matches quarter by quarter scores:
Round 8 1963
South 2.5 7.8 10.11 12.11 (83)
Sturt 0.3 4.7 8.9 11.12 (78)
Kensington, 5980
It may not be clear yet, but what is significant about that match is by looking at the numbers which make up the scores in each quarter:
South 2 5 7 8 10 11 12 11
Sturt 0 3 4 7 8 9 11 12
As you can see, all but one number there is in an increase, the South behind tally in the last quarter. There has never been a match in which all numbers increase in sequence, these 15 matches have all but one to do so.