Segment Information - Summary of Segment Information (Detail) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 31, 2020	Mar. 31, 2019	Mar. 31, 2020	Mar. 31, 2019
Segment revenues:
Revenues	$ 307,971	$ 278,234	$ 606,475	$ 540,490
Segment operating expense	(232,245)	(229,685)	(478,867)	(442,937)
Operating income	75,726	48,549	127,608	97,553
Unallocated share-based compensation expense	(22,788)	(20,482)	(45,933)	(42,336)
Unallocated amortization expense	(1,202)	(1,503)	(2,998)	(3,005)
Restructuring And Acquisition Related Cost	0	0	(3,104)	0
Unallocated interest expense	(11,254)	(10,008)	(21,022)	(19,684)
Unallocated other expense, net	(2,008)	1,433	(2,227)	(739)
Income before income taxes	62,464	39,974	104,359	77,130
Depreciation expense	5,960	5,995	11,636	12,139
Operating Segments
Segment revenues:
Segment operating expense	(208,255)	(207,700)	(426,832)	(397,596)
Operating income	99,716	70,534	179,643	142,894
Unallocated Corporate Expenses
Segment revenues:
Segment operating expense	(33,785)	(39,506)	(67,995)	(68,760)
Operating income	(33,785)	(39,506)	(67,995)	(68,760)
Depreciation expense	108	229	333	462
Applications
Segment revenues:
Revenues	140,279	141,815	292,457	289,474
Applications | Operating Segments
Segment revenues:
Revenues	140,279	141,815	292,457	289,474
Segment operating expense	(111,456)	(111,643)	(227,466)	(219,241)
Operating income	28,823	30,172	64,991	70,233
Depreciation expense	4,553	4,662	8,902	9,459
Scores
Segment revenues:
Revenues	129,148	104,403	244,286	190,086
Scores | Operating Segments
Segment revenues:
Revenues	129,148	104,403	244,286	190,086
Segment operating expense	(15,660)	(16,167)	(33,372)	(29,649)
Operating income	113,488	88,236	210,914	160,437
Depreciation expense	141	132	257	257
Decision Management Software
Segment revenues:
Revenues	38,544	32,016	69,732	60,930
Decision Management Software | Operating Segments
Segment revenues:
Revenues	38,544	32,016	69,732	60,930
Segment operating expense	(47,354)	(40,384)	(97,999)	(79,946)
Operating income	(8,810)	(8,368)	(28,267)	(19,016)
Depreciation expense	1,158	972	2,144	1,961
Transactional and Maintenance
Segment revenues:
Revenues	240,702	211,779	461,076	405,972
Transactional and Maintenance | Applications | Operating Segments
Segment revenues:
Revenues	97,789	97,074	196,626	194,239
Transactional and Maintenance | Scores | Operating Segments
Segment revenues:
Revenues	127,610	102,363	235,056	187,184
Transactional and Maintenance | Decision Management Software | Operating Segments
Segment revenues:
Revenues	15,303	12,342	29,394	24,549
Technology Service
Segment revenues:
Revenues	47,905	50,555	91,930	91,363
Technology Service | Applications | Operating Segments
Segment revenues:
Revenues	35,134	35,981	69,157	67,443
Technology Service | Scores | Operating Segments
Segment revenues:
Revenues	819	901	1,083	1,602
Technology Service | Decision Management Software | Operating Segments
Segment revenues:
Revenues	11,952	13,673	21,690	22,318
License
Segment revenues:
Revenues	19,364	15,900	53,469	43,155
License | Applications | Operating Segments
Segment revenues:
Revenues	7,356	8,760	26,674	27,792
License | Scores | Operating Segments
Segment revenues:
Revenues	719	1,139	8,147	1,300
License | Decision Management Software | Operating Segments
Segment revenues:
Revenues	$ 11,289	$ 6,001	$ 18,648	$ 14,063