Group	A	B	C	D	E	F	G	H
Winner	Bayern	Arsenal	Real Madrid	Real Sociedad	Atletico de Madrid	Dortmund	Man City	Barcelona
Runner-up	Copenhagen	PSV	Napoli	Inter	Lazio	Paris	Leipzig	FC Porto

• 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 10595 possible results of the draw in 2023. Intuitive: Fair draw should give each result a chance of 1/10595 = 9.438e-05 = 0.009438%.
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 0.008334% (approx. 1/11999) to 0.009919% (approx. 1/10082), corresponding to relative differences from -11.698% to 5.093%. Tableau with the smallest probability of being drawn by UEFA (approx. 1/11999) is

Copenhagen vs. Barcelona Lazio vs. Real Sociedad

PSV vs. Dortmund Paris vs. Arsenal

Napoli vs. Man City Leipzig vs. Real Madrid

Inter vs. Atletico de Madrid FC Porto vs. Bayern

Tableau with the highest probability of being drawn by UEFA (approx. 1/10082) is

Copenhagen vs. Dortmund Lazio vs. Arsenal

PSV vs. Barcelona Paris vs. Man City

Napoli vs. Atletico de Madrid Leipzig vs. Real Madrid

Inter vs. Bayern FC Porto vs. Real Sociedad

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	Bayern	Fair	Paris 17.0835	FC Porto 16.5833	Inter 16.5833	Lazio 16.5833	Napoli 16.5833	PSV 16.5833
		UEFA	Paris 17.3008	FC Porto 16.5398	Inter 16.5398	Lazio 16.5398	Napoli 16.5398	PSV 16.5398
	Copenhagen	Fair	Dortmund 17.0835	Man City 14.5824	Arsenal 13.6668	Atletico de Madrid 13.6668	Barcelona 13.6668	Real Madrid 13.6668	Real Sociedad 13.6668
		UEFA	Dortmund 17.3008	Man City 14.7547	Arsenal 13.5889	Atletico de Madrid 13.5889	Barcelona 13.5889	Real Madrid 13.5889	Real Sociedad 13.5889
B	Arsenal	Fair	Leipzig 20.0000	Copenhagen 13.6668	Paris 13.6668	FC Porto 13.1666	Inter 13.1666	Lazio 13.1666	Napoli 13.1666
		UEFA	Leipzig 20.0000	Copenhagen 13.5889	Paris 13.5889	FC Porto 13.2055	Inter 13.2055	Lazio 13.2055	Napoli 13.2055
	PSV	Fair	Bayern 16.5833	Dortmund 16.5833	Man City 14.1671	Atletico de Madrid 13.1666	Barcelona 13.1666	Real Madrid 13.1666	Real Sociedad 13.1666
		UEFA	Bayern 16.5398	Dortmund 16.5398	Man City 14.0981	Atletico de Madrid 13.2055	Barcelona 13.2055	Real Madrid 13.2055	Real Sociedad 13.2055
C	Real Madrid	Fair	Leipzig 20.0000	Copenhagen 13.6668	Paris 13.6668	FC Porto 13.1666	Inter 13.1666	Lazio 13.1666	PSV 13.1666
		UEFA	Leipzig 20.0000	Copenhagen 13.5889	Paris 13.5889	FC Porto 13.2055	Inter 13.2055	Lazio 13.2055	PSV 13.2055
	Napoli	Fair	Bayern 16.5833	Dortmund 16.5833	Man City 14.1671	Arsenal 13.1666	Atletico de Madrid 13.1666	Barcelona 13.1666	Real Sociedad 13.1666
		UEFA	Bayern 16.5398	Dortmund 16.5398	Man City 14.0981	Arsenal 13.2055	Atletico de Madrid 13.2055	Barcelona 13.2055	Real Sociedad 13.2055
D	Real Sociedad	Fair	Leipzig 20.0000	Copenhagen 13.6668	Paris 13.6668	FC Porto 13.1666	Lazio 13.1666	Napoli 13.1666	PSV 13.1666
		UEFA	Leipzig 20.0000	Copenhagen 13.5889	Paris 13.5889	FC Porto 13.2055	Lazio 13.2055	Napoli 13.2055	PSV 13.2055
	Inter	Fair	Bayern 16.5833	Dortmund 16.5833	Man City 14.1671	Arsenal 13.1666	Atletico de Madrid 13.1666	Barcelona 13.1666	Real Madrid 13.1666
		UEFA	Bayern 16.5398	Dortmund 16.5398	Man City 14.0981	Arsenal 13.2055	Atletico de Madrid 13.2055	Barcelona 13.2055	Real Madrid 13.2055
E	Atletico de Madrid	Fair	Leipzig 20.0000	Copenhagen 13.6668	Paris 13.6668	FC Porto 13.1666	Inter 13.1666	Napoli 13.1666	PSV 13.1666
		UEFA	Leipzig 20.0000	Copenhagen 13.5889	Paris 13.5889	FC Porto 13.2055	Inter 13.2055	Napoli 13.2055	PSV 13.2055
	Lazio	Fair	Bayern 16.5833	Dortmund 16.5833	Man City 14.1671	Arsenal 13.1666	Barcelona 13.1666	Real Madrid 13.1666	Real Sociedad 13.1666
		UEFA	Bayern 16.5398	Dortmund 16.5398	Man City 14.0981	Arsenal 13.2055	Barcelona 13.2055	Real Madrid 13.2055	Real Sociedad 13.2055
F	Dortmund	Fair	Copenhagen 17.0835	FC Porto 16.5833	Inter 16.5833	Lazio 16.5833	Napoli 16.5833	PSV 16.5833
		UEFA	Copenhagen 17.3008	FC Porto 16.5398	Inter 16.5398	Lazio 16.5398	Napoli 16.5398	PSV 16.5398
	Paris	Fair	Bayern 17.0835	Man City 14.5824	Arsenal 13.6668	Atletico de Madrid 13.6668	Barcelona 13.6668	Real Madrid 13.6668	Real Sociedad 13.6668
		UEFA	Bayern 17.3008	Man City 14.7547	Arsenal 13.5889	Atletico de Madrid 13.5889	Barcelona 13.5889	Real Madrid 13.5889	Real Sociedad 13.5889
G	Man City	Fair	Copenhagen 14.5824	Paris 14.5824	FC Porto 14.1671	Inter 14.1671	Lazio 14.1671	Napoli 14.1671	PSV 14.1671
		UEFA	Copenhagen 14.7547	Paris 14.7547	FC Porto 14.0981	Inter 14.0981	Lazio 14.0981	Napoli 14.0981	PSV 14.0981
	Leipzig	Fair	Arsenal 20.0000	Atletico de Madrid 20.0000	Barcelona 20.0000	Real Madrid 20.0000	Real Sociedad 20.0000
		UEFA	Arsenal 20.0000	Atletico de Madrid 20.0000	Barcelona 20.0000	Real Madrid 20.0000	Real Sociedad 20.0000
H	Barcelona	Fair	Leipzig 20.0000	Copenhagen 13.6668	Paris 13.6668	Inter 13.1666	Lazio 13.1666	Napoli 13.1666	PSV 13.1666
		UEFA	Leipzig 20.0000	Copenhagen 13.5889	Paris 13.5889	Inter 13.2055	Lazio 13.2055	Napoli 13.2055	PSV 13.2055
	FC Porto	Fair	Bayern 16.5833	Dortmund 16.5833	Man City 14.1671	Arsenal 13.1666	Atletico de Madrid 13.1666	Real Madrid 13.1666	Real Sociedad 13.1666
		UEFA	Bayern 16.5398	Dortmund 16.5398	Man City 14.0981	Arsenal 13.2055	Atletico de Madrid 13.2055	Real Madrid 13.2055	Real Sociedad 13.2055

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	Bayern	14	Fair UEFA UEFA-Fair	66.9467 66.9241 -0.0226	41.0083 40.9937 -0.0146	23.8300 23.8211 -0.0090	12.4045 12.3997 -0.0047	16,908,391.68 16,902,403.97 -5,987.71
	Copenhagen	2	Fair UEFA UEFA-Fair	21.3963 21.3627 -0.0337	3.9971 3.9917 -0.0054	0.6576 0.6568 -0.0008	0.1660 0.1659 -0.0002	2,882,858.70 2,878,477.83 -4,380.87
B	Arsenal	6	Fair UEFA UEFA-Fair	47.7146 47.7018 -0.0129	19.0783 19.0729 -0.0054	6.9591 6.9571 -0.0020	3.0634 3.0625 -0.0009	8,766,271.45 8,763,855.97 -2,415.48
	PSV	3	Fair UEFA UEFA-Fair	26.2141 26.2337 0.0196	6.7120 6.7160 0.0040	1.5277 1.5284 0.0007	0.4982 0.4984 0.0002	3,894,340.76 3,897,047.79 2,707.02
C	Real Madrid	15	Fair UEFA UEFA-Fair	70.5711 70.5703 -0.0008	44.4223 44.4214 -0.0009	26.6470 26.6463 -0.0007	14.0079 14.0075 -0.0004	18,284,246.34 18,283,905.31 -341.03
	Napoli	12	Fair UEFA UEFA-Fair	59.6952 59.7275 0.0323	34.1788 34.1961 0.0174	18.3909 18.3996 0.0087	9.3689 9.3732 0.0044	14,200,134.49 14,207,428.89 7,294.40
D	Real Sociedad	7	Fair UEFA UEFA-Fair	55.5695 55.5701 0.0006	24.1462 24.1462 -0.0000	9.6348 9.6347 -0.0001	4.4333 4.4333 -0.0001	10,756,703.75 10,756,744.68 40.94
	Inter	13	Fair UEFA UEFA-Fair	59.0620 59.0865 0.0246	35.0719 35.0851 0.0132	19.6772 19.6840 0.0068	10.1360 10.1394 0.0034	14,505,406.79 14,510,982.77 5,575.97
E	Atletico de Madrid	5	Fair UEFA UEFA-Fair	41.2032 41.1826 -0.0206	14.7289 14.7216 -0.0072	4.7718 4.7695 -0.0023	1.9700 1.9691 -0.0010	7,105,881.43 7,102,360.49 -3,520.94
	Lazio	1	Fair UEFA UEFA-Fair	10.6675 10.6766 0.0091	1.1584 1.1592 0.0007	0.1080 0.1080 0.0001	0.0164 0.0164 0.0000	1,293,609.60 1,294,680.01 1,070.41
F	Dortmund	8.5	Fair UEFA UEFA-Fair	62.6483 62.6962 0.0480	30.2583 30.2797 0.0214	13.5352 13.5443 0.0090	6.5202 6.5245 0.0043	13,042,578.95 13,052,080.89 9,501.94
	Paris	10	Fair UEFA UEFA-Fair	53.6478 53.5713 -0.0765	28.2720 28.2333 -0.0388	13.8846 13.8667 -0.0179	6.8971 6.8883 -0.0088	11,924,544.94 11,908,105.83 -16,439.12
G	Man City	16	Fair UEFA UEFA-Fair	72.3634 72.3773 0.0139	46.7213 46.7294 0.0081	28.8671 28.8718 0.0047	15.3385 15.3409 0.0024	19,212,165.32 19,215,569.20 3,403.88
	Leipzig	11	Fair UEFA UEFA-Fair	62.0416 62.0416 0.0000	34.0382 34.0381 -0.0001	17.4643 17.4642 -0.0001	8.7846 8.7845 -0.0001	14,240,917.03 14,240,873.22 -43.80
H	Barcelona	4	Fair UEFA UEFA-Fair	42.7961 42.7942 -0.0019	13.0566 13.0557 -0.0008	3.6214 3.6211 -0.0003	1.3613 1.3612 -0.0001	6,838,675.74 6,838,320.92 -354.82
	FC Porto	8.5	Fair UEFA UEFA-Fair	47.4627 47.4835 0.0208	23.1514 23.1599 0.0085	10.4232 10.4265 0.0033	5.0337 5.0352 0.0015	9,943,273.02 9,947,162.23 3,889.21