There have been only 2 matches where a team has scored 5 or more behinds each quarter and 2 or fewer goals each quarter. Both have a remarkable similarity of badness. Fitzroy's 25 more behinds than goals in the 1928 match is also the biggest difference recorded. As well Geelong's winning margin of 83 points is the highest by a team with less scoring shots.

round 6 1928
Fitzroy	0.6-6		1.13-19		1.19-25		2.27-39
Geelong	4.3-27		8.5-53		15.7-97		19.8-122
round 5 1950
Hawthorn	0.5-5		1.13-19		2.18-30		4.24-48
Fitzroy	3.3-21		9.7-61		13.11-89		19.15-129

There have been only 5 matches where a team has scored 5 or more goals each quarter and 2 or fewer behinds each quarter. All are modern.

round 11 1994
Hawthorn	5.1-31		10.1-61		15.3-93		20.5-125
WB/Footscray	1.3-9		6.5-41		6.9-45		8.13-61
round 24 1994
Melbourne	8.2-50		14.2-86		21.4-130		27.5-167
Sydney/SM	6.4-40		11.6-72		14.10-94		18.13-121
round 19 1995
Sydney/SM	8.2-50		17.4-106		22.6-138		27.8-170
Fitzroy	2.2-14		2.3-15		4.7-31		6.8-44
round 14  2006
Geelong	5.0-30		11.1-67		17.2-104		23.4-142
Carlton	2.5-17		4.7-31		7.10-52		11.11-77
round 16 2012
Nth Melbourne	6.1-37		12.2-74		19.4-118		24.5-149
Carlton	3.4-22		6.9-45		9.9-63		14.12-96

(Melbourne's 27 goals in 1994 are the highest number kicked by a team scoring 5 or more times as many goals as behinds.)
 

The most goals scored by a single team in a quarter without a behind is 12.

round 16 1972
Carlton	4.4-28		16.4-100		17.7-109		20.13-133
Essendon	5.4-34		7.9-51		11.13-79		17.15-117
round 7 2015
West Coast	3.3-21		7.6-48		19.6-120		21.9-135
Gold Coast	1.1-7		1.2-8		2.6-18		6.7-43

The most combined goals scored in a quarter without a behind is 15.

round 2 1996
Collingwood	5.3-33		13.8-86		17.11-113		27.11-173
Melbourne	2.2-14		5.4-34		6.13-49		11.13-79

The most combined behinds scored in a quarter without a goal is 14.

round 9 1959
St Kilda	3.3-21		11.4-70		11.5-71		14.11-95
Geelong	3.4-22		4.7-31		4.20-44		6.22-58

The most goals scored to 1/4, 1/2, 3/4  and full time without a behind.

round 19 2009
Port Adelaide	10.0-60		10.4-64		14.5-89		14.8-92
Brisbane	3.2-20		7.5-47		12.8-80		16.11-107
round 6  2021
Adelaide	4.0-24		14.0-66		16.1-97		16.3-99
Hawthorn	5.2-32		9.5-592		13.6-84		15.12-102

round 1 1929
Collingwood	4.0-24		9.0-54		13.0-78		15.2-92
Richmond	3.1-19		4.4-28		9.7-63		11.9-75
round 12 1949
Hawthorn	0.0.-0		3.0-18		3.0-18		7.0-18
Fitzroy	2.5-17		5.7-37		12.12-84		16.16-112

The nearest to Collingwood's 13 goals without a behind by 3/4 time in 1929 is 8 goals 0 behinds by Collingwood in round 7 1936. (The most since 1936 has been GWS Giants 7.0-42 in round 9 2015.)

There have only been 5 scores with no behinds 1897-2019. The last being:
. 

round 5 1953
Fitzroy	0.0-0		0.0-0		0.0-0		1.0-6
WB/Footscray	2.2-14		5.3.33		8.5-53		10.6-66

The only team to be scoreless in the 1st quarter of its first League match.
 

round 1 1897
Geelong	0.0-0		0.4-4		1.5.11		3.6-24
Essendon	3.2-20		3.4-22		6.4-40		7.5-47

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Since 1897 there have been 134 occurrences of such scores.

64 out of 125 seasons 1897-2021 had no occurrences (51.2%)
14 only occurred before 1950.
15 occurred between 1950 and 1980.
72 of them have been scored in the last 20 seasons 2002-2021
17 have occurred in the last 5 seasons - 2017-2021

The highest percentage in a season is 2.47% of scores in 2020 (8/324). 
 2017 0.24% (1/414), 2018 0.97% (4/414), 2019 0.48% (2/414) and 2021
0.48% (2/414)

From 1994 there has been at least one occurrence each year except 2011, the most recent being Round 20 2021.  Carlton   scored 4.5 times more goals than behinds and 14 more goals than behinds.

Best combined accuracy in a match with 79.6% of scoring shots resulting in goals. One of only two matches* where both sides scored 3 times more goals than behinds. * Also: West Coast 16.5-101 vs St Kilda 14.4-189 (76.9%) in round 11 2018.

Setting a criteria of at least 10 more behinds than goals and at least 3.5 times more behinds scored than goals, the worst displays of inaccuracy have been:

Since 1897 there have been 285 occurrences of such scores.

143 occurred before 1925.
110 occurred 1925-1981.
17 have occurred this century 2001-21
The highest percentage occurred in 1919 - 7.24%% of scores (11/152). Next highest: 6.12% in 1917 (6/98) and 5.38%% in 1908 (10/128). 
The first season with less than 1% was 1925 - 0.94% (2/212).
The last season with more than 1% was 1984 - 1.09% (3/276)

Since 1960 when there were 6 occurrences, the most in one year has been three in 1965,1966,1984,1997 and 2012. There was one in 2017, one in 2018, 1 in 2019,  1 in 2020 and 2 in 2021.

There have been just 12 scores where there were 20 or more behinds than goals, Fitzroy scored 3 of them (including 2.27-39 v Geelong 19.8-122 in round 6 1928.) 10 of these scores were recorded between 1901 and 1957.

The last was in 1985

The worst combined inaccuracy in a match is 5% of scoring shots resulting in goals.

The worst combined inaccuracy in a match since 1981 is 21.3%.

round 4 2012
West Coast	0.8-8		0.12-12		2.16-28		5.21-51
Hawthorn	0.4-4		2.7-19		3.13-31		5.16-46

The above match holds the record for the highest first quarter aggregate ever  without a goal being scored, the most behinds behinds scored in a match where 10 goals were scored, and West Coast's 5.21  is the 2nd worst goal/behind ratio from 26 scoring shots ever recorded. Worst: Essendon  3.23 round 6, 1901.( Also the only match ever were both teams kicked 5 goals and 16 or more behinds.)