Group	A	B	C	D	E	F	G	H
Winner	ManC	Liverpool	Ajax	Real	Bayern	ManU	Lille	Juve
Runner-up	PSG	Atletico	Sporting	Inter	Benfica	Villarreal	Salzburg	Chelsea

• Runners-up are matched with group winners
• No matches allowed between teams from same association
• No matches allowed between teams from same group

These rules lead to 4781 possible results of the draw in 2021. Intuitive: Fair draw should give each result a chance of 1/4781 = 0.00020916 = 0.020916%.
UEFA's draw mechanism is quite complicated, for a description see Journal of Quantitative Analysis in Sports (2013), 9(3), 249-270. At first glance, it appears to be fair, however: closer inspection shows that probabilities of UEFA's draw mechanism are slightly different, ranging from 0.016988% (approx. 1/5886) to 0.023762% (approx. 1/4208), corresponding to relative differences from -18.778% to 13.604%. Tableau with the smallest probability of being drawn by UEFA (approx. 1/5886) is

PSG vs. Juve Benfica vs. Lille

Atletico vs. ManU Villarreal vs. Liverpool

Sporting vs. Bayern Salzburg vs. Ajax

Inter vs. ManC Chelsea vs. Real

Tableau with the highest probability of being drawn by UEFA (approx. 1/4208) is

PSG vs. Bayern Benfica vs. Real

Atletico vs. Juve Villarreal vs. Liverpool

Sporting vs. ManC Salzburg vs. Ajax

Inter vs. ManU Chelsea vs. Lille

The draw procedure employed by UEFA also leads to the probabilities of pairwise matches being slightly different from their values under a perfectly fair draw.

Group	Team	Draw	Opponents ranked by decreasing probability
			Most probable	2nd most	3rd most	4th most	5th most	6th most	7th most
A	ManC	Fair	Atletico 18.5317	Inter 18.5317	Villarreal 18.5317	Salzburg 14.9550	Benfica 14.7250	Sporting 14.7250
		UEFA	Atletico 18.4439	Inter 18.4439	Villarreal 18.4439	Salzburg 15.1657	Benfica 14.7513	Sporting 14.7513
	PSG	Fair	Real 19.3892	Juve 17.8205	Liverpool 17.8205	ManU 17.8205	Ajax 13.5746	Bayern 13.5746
		UEFA	Real 19.3642	Juve 17.8561	Liverpool 17.8561	ManU 17.8561	Ajax 13.5338	Bayern 13.5338
B	Liverpool	Fair	Inter 18.5735	Villarreal 18.5735	PSG 17.8205	Salzburg 15.2060	Benfica 14.9132	Sporting 14.9132
		UEFA	Inter 18.7080	Villarreal 18.7080	PSG 17.8561	Salzburg 15.0834	Benfica 14.8223	Sporting 14.8223
	Atletico	Fair	Juve 18.5735	ManU 18.5735	ManC 18.5317	Lille 16.2518	Ajax 14.0347	Bayern 14.0347
		UEFA	Juve 18.7080	ManU 18.7080	ManC 18.4439	Lille 16.1824	Ajax 13.9789	Bayern 13.9789
C	Ajax	Fair	Chelsea 21.3763	Atletico 14.0347	Inter 14.0347	Villarreal 14.0347	PSG 13.5746	Salzburg 11.5875	Benfica 11.3575
		UEFA	Chelsea 21.7702	Atletico 13.9789	Inter 13.9789	Villarreal 13.9789	PSG 13.5338	Salzburg 11.4805	Benfica 11.2788
	Sporting	Fair	Real 16.0218	Juve 14.9132	Liverpool 14.9132	ManU 14.9132	ManC 14.7250	Lille 13.1562	Bayern 11.3575
		UEFA	Real 16.3711	Juve 14.8223	Liverpool 14.8223	ManU 14.8223	ManC 14.7513	Lille 13.1321	Bayern 11.2788
D	Real	Fair	Chelsea 32.3154	PSG 19.3892	Salzburg 16.2518	Benfica 16.0218	Sporting 16.0218
		UEFA	Chelsea 31.2707	PSG 19.3642	Salzburg 16.6229	Benfica 16.3711	Sporting 16.3711
	Inter	Fair	Liverpool 18.5735	ManU 18.5735	ManC 18.5317	Lille 16.2518	Ajax 14.0347	Bayern 14.0347
		UEFA	Liverpool 18.7080	ManU 18.7080	ManC 18.4439	Lille 16.1824	Ajax 13.9789	Bayern 13.9789
E	Bayern	Fair	Chelsea 21.3763	Atletico 14.0347	Inter 14.0347	Villarreal 14.0347	PSG 13.5746	Salzburg 11.5875	Sporting 11.3575
		UEFA	Chelsea 21.7702	Atletico 13.9789	Inter 13.9789	Villarreal 13.9789	PSG 13.5338	Salzburg 11.4805	Sporting 11.2788
	Benfica	Fair	Real 16.0218	Juve 14.9132	Liverpool 14.9132	ManU 14.9132	ManC 14.7250	Lille 13.1562	Ajax 11.3575
		UEFA	Real 16.3711	Juve 14.8223	Liverpool 14.8223	ManU 14.8223	ManC 14.7513	Lille 13.1321	Ajax 11.2788
F	ManU	Fair	Atletico 18.5735	Inter 18.5735	PSG 17.8205	Salzburg 15.2060	Benfica 14.9132	Sporting 14.9132
		UEFA	Atletico 18.7080	Inter 18.7080	PSG 17.8561	Salzburg 15.0834	Benfica 14.8223	Sporting 14.8223
	Villarreal	Fair	Juve 18.5735	Liverpool 18.5735	ManC 18.5317	Lille 16.2518	Ajax 14.0347	Bayern 14.0347
		UEFA	Juve 18.7080	Liverpool 18.7080	ManC 18.4439	Lille 16.1824	Ajax 13.9789	Bayern 13.9789
G	Lille	Fair	Chelsea 24.9320	Atletico 16.2518	Inter 16.2518	Villarreal 16.2518	Benfica 13.1562	Sporting 13.1562
		UEFA	Chelsea 25.1888	Atletico 16.1824	Inter 16.1824	Villarreal 16.1824	Benfica 13.1321	Sporting 13.1321
	Salzburg	Fair	Real 16.2518	Juve 15.2060	Liverpool 15.2060	ManU 15.2060	ManC 14.9550	Ajax 11.5875	Bayern 11.5875
		UEFA	Real 16.6229	ManC 15.1657	Juve 15.0834	Liverpool 15.0834	ManU 15.0834	Ajax 11.4805	Bayern 11.4805
H	Juve	Fair	Atletico 18.5735	Villarreal 18.5735	PSG 17.8205	Salzburg 15.2060	Benfica 14.9132	Sporting 14.9132
		UEFA	Atletico 18.7080	Villarreal 18.7080	PSG 17.8561	Salzburg 15.0834	Benfica 14.8223	Sporting 14.8223
	Chelsea	Fair	Real 32.3154	Lille 24.9320	Ajax 21.3763	Bayern 21.3763
		UEFA	Real 31.2707	Lille 25.1888	Ajax 21.7702	Bayern 21.7702

Teams get the following awards for reaching certain stages:

• reaching quarter-final is awarded with EUR 10.6 million
• reaching semi-final is awarded with additional EUR 12.5 million
• reaching final is awarded with additional EUR 15.5 million
• winning trophy is awarded with additional EUR 8 million (including award for UEFA Super Cup qualification)

Under a simple model (for details, see Journal of Quantitative Analysis in Sports (2013), 9(3), 249-270), with strengths being determined by weighted averages of team's UEFA coefficients of the last three years, this leads to the following expected payoffs and probabilities of reaching certain stages:

Group	Team	Strength	Draw	Probablity of reaching ... (in percent)				Exp. Payoff (EUR)
				quarter-final	semi-final	final	trophy
A	ManC	15	Fair UEFA UEFA-Fair	78.0191 78.0568 0.0377	48.6028 48.6226 0.0198	28.8849 28.8958 0.0109	15.1031 15.1086 0.0055	20,030,783.86 20,039,378.29 8,594.44
	PSG	13	Fair UEFA UEFA-Fair	54.8604 54.8629 0.0025	32.3859 32.3845 -0.0014	18.0469 18.0451 -0.0018	9.2805 9.2794 -0.0011	13,403,145.77 13,402,870.21 -275.57
B	Liverpool	12	Fair UEFA UEFA-Fair	70.9304 70.8737 -0.0567	40.1348 40.0981 -0.0367	21.3959 21.3748 -0.0211	10.8686 10.8576 -0.0109	16,721,333.62 16,706,586.59 -14,747.03
	Atletico	6	Fair UEFA UEFA-Fair	41.0037 40.9946 -0.0091	16.2281 16.2226 -0.0055	5.8779 5.8753 -0.0025	2.5926 2.5914 -0.0012	7,493,382.20 7,491,239.99 -2,142.21
C	Ajax	8	Fair UEFA UEFA-Fair	53.4865 53.3842 -0.1023	24.7531 24.7040 -0.0491	10.5844 10.5637 -0.0207	5.0348 5.0251 -0.0097	10,807,064.01 10,786,104.90 -20,959.11
	Sporting	1	Fair UEFA UEFA-Fair	10.6767 10.6716 -0.0051	1.1263 1.1256 -0.0007	0.1040 0.1040 -0.0001	0.0157 0.0157 -0.0000	1,289,905.29 1,289,257.11 -648.18
D	Real	11	Fair UEFA UEFA-Fair	62.7836 63.1913 0.4076	34.2294 34.4441 0.2147	17.5421 17.6481 0.1061	8.8202 8.8732 0.0530	14,358,376.01 14,449,102.31 90,726.29
	Inter	5	Fair UEFA UEFA-Fair	35.8610 35.8424 -0.0187	12.7305 12.7227 -0.0078	4.1153 4.1126 -0.0028	1.7049 1.7037 -0.0012	6,166,847.98 6,163,370.20 -3,477.78
E	Bayern	16	Fair UEFA UEFA-Fair	70.2646 70.1636 -0.1010	44.9736 44.9051 -0.0686	27.5704 27.5270 -0.0434	14.5841 14.5608 -0.0233	18,509,883.97 18,482,030.75 -27,853.22
	Benfica	4	Fair UEFA UEFA-Fair	31.8323 31.8132 -0.0191	9.7683 9.7613 -0.0070	2.7016 2.6996 -0.0020	1.0135 1.0128 -0.0007	5,095,085.25 5,091,824.94 -3,260.31
F	ManU	10	Fair UEFA UEFA-Fair	68.1134 68.0568 -0.0566	35.2757 35.2419 -0.0337	17.0593 17.0417 -0.0176	8.4481 8.4393 -0.0087	14,949,521.51 14,935,883.70 -13,637.81
	Villarreal	7	Fair UEFA UEFA-Fair	43.6612 43.6474 -0.0138	18.9187 18.9109 -0.0079	7.5479 7.5442 -0.0037	3.4842 3.4824 -0.0017	8,441,598.31 8,438,440.41 -3,157.90
G	Lille	2.5	Fair UEFA UEFA-Fair	32.7090 32.6595 -0.0495	6.9067 6.8962 -0.0106	1.3253 1.3234 -0.0020	0.3837 0.3832 -0.0006	4,566,624.42 4,559,701.33 -6,923.09
	Salzburg	2.5	Fair UEFA UEFA-Fair	18.4394 18.4260 -0.0134	4.2037 4.2000 -0.0037	0.8383 0.8375 -0.0008	0.2453 0.2451 -0.0002	2,629,609.66 2,627,587.78 -2,021.88
H	Juve	9	Fair UEFA UEFA-Fair	64.5287 64.4588 -0.0699	31.6791 31.6411 -0.0380	14.4504 14.4321 -0.0183	7.0319 7.0230 -0.0089	13,602,294.65 13,586,594.35 -15,700.31
	Chelsea	14	Fair UEFA UEFA-Fair	62.8298 62.8971 0.0674	38.0832 38.1193 0.0361	21.9554 21.9750 0.0197	11.3888 11.3986 0.0098	15,734,543.48 15,750,027.15 15,483.67