Related Person Transactions - Revenue from Related Parties (Details) - USD ($) $ in Thousands	3 Months Ended								12 Months Ended
	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Related Party Transaction [Line Items]
Revenue from related parties									$ 588,640	$ 712,740	$ 403,257
Percentage of revenue from related parties									99.90%	99.90%	99.60%
Revenues from unrelated parties									$ 865	$ 628	$ 1,722
Percentage of revenue from unrelated parties									0.10%	0.10%	0.40%
Revenues, net	$ 150,103	$ 138,649	$ 140,861	$ 159,892	$ 159,244	$ 143,715	$ 130,096	$ 280,313	$ 589,505	$ 713,368	$ 404,979
Percentage of revenue, net									100.00%	100.00%	100.00%
Managed Equity REITs
Related Party Transaction [Line Items]
Revenue from related parties									$ 527,191	$ 643,133	$ 364,107
Percentage of revenue from related parties									89.50%	90.10%	89.90%
DHC
Related Party Transaction [Line Items]
Revenue from related parties									$ 175,082	$ 210,728	$ 118,301
Percentage of revenue from related parties									29.70%	29.50%	29.20%
ILPT
Related Party Transaction [Line Items]
Revenue from related parties									$ 48,056	$ 43,242	$ 10,935
Percentage of revenue from related parties									8.20%	6.10%	2.70%
OPI
Related Party Transaction [Line Items]
Revenue from related parties									$ 242,217	$ 239,291	$ 53,954
Percentage of revenue from related parties									41.10%	33.50%	13.30%
SIR
Related Party Transaction [Line Items]
Revenue from related parties									$ 0	$ 47,843	$ 62,321
Percentage of revenue from related parties									0.00%	6.70%	15.40%
SVC
Related Party Transaction [Line Items]
Revenue from related parties									$ 61,836	$ 102,029	$ 118,596
Percentage of revenue from related parties									10.50%	14.30%	29.30%
Managed Operators
Related Party Transaction [Line Items]
Revenue from related parties									$ 24,387	$ 27,079	$ 28,044
Percentage of revenue from related parties									4.10%	3.80%	6.90%
Five Star
Related Party Transaction [Line Items]
Revenue from related parties									$ 9,084	$ 9,702	$ 9,840
Percentage of revenue from related parties									1.50%	1.40%	2.40%
Sonesta
Related Party Transaction [Line Items]
Revenue from related parties									$ 1,738	$ 3,186	$ 2,847
Percentage of revenue from related parties									0.30%	0.40%	0.70%
TA
Related Party Transaction [Line Items]
Revenue from related parties									$ 13,565	$ 14,191	$ 15,357
Percentage of revenue from related parties									2.30%	2.00%	3.80%
Other Client Companies
Related Party Transaction [Line Items]
Revenue from related parties									$ 37,062	$ 42,528	$ 11,106
Percentage of revenue from related parties									6.30%	6.00%	2.80%
ABP Trust
Related Party Transaction [Line Items]
Revenue from related parties									$ 12,544	$ 15,070	$ 4,865
Percentage of revenue from related parties									2.20%	2.10%	1.20%
AIC
Related Party Transaction [Line Items]
Revenue from related parties									$ 98	$ 570	$ 240
Percentage of revenue from related parties									0.00%	0.10%	0.10%
Open End Fund
Related Party Transaction [Line Items]
Revenue from related parties									$ 18,988	$ 20,366	$ 608
Percentage of revenue from related parties									3.20%	2.90%	0.20%
RMRM
Related Party Transaction [Line Items]
Revenue from related parties									$ 2,767	$ 3,013	$ 2,888
Percentage of revenue from related parties									0.50%	0.40%	0.70%
TRMT
Related Party Transaction [Line Items]
Revenue from related parties									$ 2,546	$ 3,509	$ 2,505
Percentage of revenue from related parties									0.40%	0.50%	0.60%
Centre Street
Related Party Transaction [Line Items]
Revenue from related parties									$ 119	$ 0	$ 0
Percentage of revenue from related parties									0.00%	0.00%	0.00%