Segment Information - Summary of Segment Information (Details) - USD ($) $ in Thousands	3 Months Ended								12 Months Ended
	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2017	Sep. 30, 2019	Sep. 30, 2018	Sep. 30, 2017
Segment revenues:
Revenue from Contract with Customer, Excluding Assessed Tax									$ 1,160,083	$ 1,000,146	$ 934,983
Segment operating expense									(906,535)	(824,787)	(752,824)
Operating income									253,548	175,359	182,159
Unallocated share-based compensation expense									(82,973)	(74,814)	(61,222)
Unallocated amortization expense	$ (500)	$ (500)	$ (500)	$ (500)	$ (500)	$ (600)	$ (600)	$ (700)	(6,126)	(6,594)	(12,709)
Unallocated restructuring and acquisition-related expenses									0	0	(4,471)
Unallocated interest expense, net									(39,752)	(31,311)	(25,790)
Unallocated other income (expense), net									2,276	12,884	(86)
Income before income taxes									216,072	156,932	156,283
Depreciation expense									24,204	22,633	22,980
Applications
Segment revenues:
Revenue from Contract with Customer, Excluding Assessed Tax									605,034	564,375	560,634
Scores
Segment revenues:
Revenue from Contract with Customer, Excluding Assessed Tax									421,177	335,870	259,537
Decision Management Software
Segment revenues:
Revenue from Contract with Customer, Excluding Assessed Tax									133,872	99,901	114,812
Operating Segments
Segment revenues:
Segment operating expense									(817,436)	(743,379)	(674,422)
Operating income									342,647	256,767	260,561
Operating Segments | Applications
Segment revenues:
Revenue from Contract with Customer, Excluding Assessed Tax									605,034	564,375	560,634
Segment operating expense									(443,872)	(420,411)	(392,307)
Operating income									161,162	143,964	168,327
Depreciation expense									18,766	15,651	15,857
Operating Segments | Scores
Segment revenues:
Revenue from Contract with Customer, Excluding Assessed Tax									421,177	335,870	259,537
Segment operating expense									(59,821)	(63,452)	(54,369)
Operating income									361,356	272,418	205,168
Depreciation expense									498	555	991
Operating Segments | Decision Management Software
Segment revenues:
Revenue from Contract with Customer, Excluding Assessed Tax									133,872	99,901	114,812
Segment operating expense									(168,988)	(134,261)	(122,839)
Operating income									(35,116)	(34,360)	(8,027)
Depreciation expense									4,036	5,471	4,783
Unallocated Corporate Expenses
Segment revenues:
Segment operating expense									(144,755)	(125,255)	(104,907)
Operating income									(144,755)	(125,255)	(104,907)
Depreciation expense									904	956	1,349
Transactional and maintenance
Segment revenues:
Revenue from Contract with Customer, Excluding Assessed Tax									860,948	750,603	633,927
Transactional and maintenance | Operating Segments | Applications
Segment revenues:
Revenue from Contract with Customer, Excluding Assessed Tax									395,398	372,283	335,560
Transactional and maintenance | Operating Segments | Scores
Segment revenues:
Revenue from Contract with Customer, Excluding Assessed Tax									415,288	331,662	254,424
Transactional and maintenance | Operating Segments | Decision Management Software
Segment revenues:
Revenue from Contract with Customer, Excluding Assessed Tax									50,262	46,658	43,943
Professional services
Segment revenues:
Revenue from Contract with Customer, Excluding Assessed Tax									184,095	176,910	177,904
Professional services | Operating Segments | Applications
Segment revenues:
Revenue from Contract with Customer, Excluding Assessed Tax									137,258	142,736	140,990
Professional services | Operating Segments | Scores
Segment revenues:
Revenue from Contract with Customer, Excluding Assessed Tax									2,157	1,900	2,869
Professional services | Operating Segments | Decision Management Software
Segment revenues:
Revenue from Contract with Customer, Excluding Assessed Tax									44,680	32,274	34,045
License
Segment revenues:
Revenue from Contract with Customer, Excluding Assessed Tax									115,040	72,633	123,152
License | Operating Segments | Applications
Segment revenues:
Revenue from Contract with Customer, Excluding Assessed Tax									72,378	49,356	84,084
License | Operating Segments | Scores
Segment revenues:
Revenue from Contract with Customer, Excluding Assessed Tax									3,732	2,308	2,244
License | Operating Segments | Decision Management Software
Segment revenues:
Revenue from Contract with Customer, Excluding Assessed Tax									$ 38,930	$ 20,969	$ 36,824