Segment Information - Summary of Segment Information (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Segment revenues:
Total revenues	$ 1,294,562	$ 1,160,083	$ 1,000,146
Segment operating expense	(998,593)	(906,535)	(824,787)
Operating income	295,969	253,548	175,359
Unallocated share-based compensation expense	(93,681)	(82,973)	(74,814)
Unallocated amortization expense	(4,993)	(6,126)	(6,594)
Unallocated restructuring and impairment charges	(45,029)
Unallocated interest expense, net	(42,177)	(39,752)	(31,311)
Unallocated other income (expense), net	3,208	2,276	12,884
Income before income taxes	257,000	216,072	156,932
Depreciation expense	23,453	24,204	22,633
Applications
Segment revenues:
Total revenues	602,046	605,034	564,375
Scores
Segment revenues:
Total revenues	528,547	421,177	335,870
Decision Management Software
Segment revenues:
Total revenues	163,969	133,872	99,901
Operating Segments
Segment revenues:
Segment operating expense	(854,890)	(817,436)	(743,379)
Operating income	439,672	342,647	256,767
Operating Segments | Applications
Segment revenues:
Total revenues	602,046	605,034	564,375
Segment operating expense	(448,505)	(443,872)	(420,411)
Operating income	153,541	161,162	143,964
Depreciation expense	18,021	18,766	15,651
Operating Segments | Scores
Segment revenues:
Total revenues	528,547	421,177	335,870
Segment operating expense	(74,237)	(59,821)	(63,452)
Operating income	454,310	361,356	272,418
Depreciation expense	617	498	555
Operating Segments | Decision Management Software
Segment revenues:
Total revenues	163,969	133,872	99,901
Segment operating expense	(187,444)	(168,988)	(134,261)
Operating income	(23,475)	(35,116)	(34,360)
Depreciation expense	4,397	4,036	5,471
Unallocated Corporate Expenses
Segment revenues:
Segment operating expense	(144,704)	(144,755)	(125,255)
Operating income	(144,704)	(144,755)	(125,255)
Depreciation expense	418	904	956
Transactional and maintenance
Segment revenues:
Total revenues	973,933	860,948	750,603
Transactional and maintenance | Operating Segments | Applications
Segment revenues:
Total revenues	393,994	395,398	372,283
Transactional and maintenance | Operating Segments | Scores
Segment revenues:
Total revenues	517,024	415,288	331,662
Transactional and maintenance | Operating Segments | Decision Management Software
Segment revenues:
Total revenues	62,915	50,262	46,658
Professional services
Segment revenues:
Total revenues	183,040	184,095	176,910
Professional services | Operating Segments | Applications
Segment revenues:
Total revenues	136,677	137,258	142,736
Professional services | Operating Segments | Scores
Segment revenues:
Total revenues	1,600	2,157	1,900
Professional services | Operating Segments | Decision Management Software
Segment revenues:
Total revenues	44,763	44,680	32,274
License
Segment revenues:
Total revenues	137,589	115,040	72,633
License | Operating Segments | Applications
Segment revenues:
Total revenues	71,375	72,378	49,356
License | Operating Segments | Scores
Segment revenues:
Total revenues	9,923	3,732	2,308
License | Operating Segments | Decision Management Software
Segment revenues:
Total revenues	$ 56,291	$ 38,930	$ 20,969