UEFA CL 2012-13 Simulations

Barcelona and Real Madrid re huge favorites to take the title. Part of the reason for that, is that many contenders might lose early to lesser teams and make the road easier for them.

Based on 100K simulations:

Group	Country	Team	Coefficients	Points	1st	2nd	3rd	4th	Round16	Quarter	Semi	Finalist	Champion
7	Esp	FC Barcelona	25.23	14.65	0.913	0.078	0.008	0.001	0.131	0.176	0.166	0.172	0.346
4	Esp	Real Madrid	22.66	11.87	0.643	0.237	0.097	0.023	0.142	0.167	0.153	0.154	0.264
8	Eng	Manchester United	20.43	13.56	0.842	0.126	0.028	0.004	0.304	0.294	0.192	0.103	0.074
6	Ger	Bayern München	19.25	12.21	0.638	0.250	0.102	0.010	0.307	0.258	0.167	0.089	0.068
1	Por	FC Porto	17.99	11.76	0.627	0.243	0.106	0.023	0.353	0.258	0.147	0.070	0.043
4	Eng	Manchester City	15.35	8.67	0.190	0.363	0.315	0.133	0.226	0.141	0.091	0.053	0.042
4	Ger	Borussia Dortmund	13.95	8.08	0.147	0.312	0.364	0.176	0.204	0.118	0.073	0.038	0.026
5	Eng	Chelsea	16.37	10.53	0.384	0.326	0.262	0.029	0.325	0.208	0.107	0.045	0.024
2	Eng	Arsenal	14.88	9.83	0.425	0.274	0.187	0.114	0.330	0.213	0.100	0.038	0.018
5	Ukr	Shakhtar Donetsk	15.24	10.01	0.311	0.330	0.320	0.039	0.329	0.179	0.085	0.032	0.016
5	Ita	Juventus	15.06	9.91	0.301	0.325	0.333	0.041	0.326	0.173	0.082	0.030	0.015
3	Ita	AC Milan	13.93	9.45	0.366	0.285	0.215	0.133	0.343	0.187	0.082	0.027	0.012
7	Por	Benfica	13.00	8.55	0.068	0.586	0.249	0.098	0.401	0.156	0.066	0.022	0.009
3	Rus	Zenit St. Petersburg	13.08	9.05	0.315	0.285	0.241	0.159	0.337	0.165	0.068	0.022	0.008
6	Esp	Valencia	13.90	9.38	0.212	0.395	0.332	0.061	0.336	0.172	0.069	0.022	0.008
2	Ger	Schalke 04	12.25	8.60	0.267	0.285	0.250	0.198	0.320	0.151	0.058	0.017	0.006
3	Esp	Málaga CF	11.56	8.25	0.228	0.267	0.280	0.225	0.286	0.142	0.050	0.013	0.004
1	Ukr	Dinamo Kiev	11.93	8.58	0.183	0.347	0.330	0.139	0.348	0.126	0.042	0.010	0.003
6	Fra	Lille OSC	12.09	8.57	0.146	0.325	0.436	0.093	0.307	0.111	0.040	0.011	0.003
1	Fra	Paris Saint-Germain	11.56	8.39	0.170	0.330	0.350	0.149	0.337	0.114	0.038	0.009	0.003
2	Gre	Olympiakos Piraeus	9.87	7.51	0.170	0.231	0.281	0.317	0.266	0.097	0.030	0.007	0.002
2	Fra	Montpellier	8.97	7.08	0.138	0.209	0.282	0.371	0.242	0.078	0.022	0.004	0.001
4	Ned	Ajax	5.49	4.70	0.020	0.088	0.224	0.668	0.072	0.024	0.009	0.002	0.001
8	Por	Sporting Braga	10.71	8.10	0.094	0.442	0.310	0.154	0.406	0.100	0.024	0.005	0.001
7	Rus	Spartak Moscow	7.57	5.94	0.014	0.223	0.433	0.329	0.182	0.042	0.011	0.002	0.000
3	Bel	Anderlecht	7.37	6.28	0.091	0.162	0.264	0.483	0.189	0.051	0.012	0.002	0.000
8	Tur	Galatasaray	8.66	7.02	0.053	0.312	0.387	0.249	0.295	0.057	0.011	0.001	0.000
7	Sco	Celtic	5.02	4.59	0.005	0.113	0.310	0.572	0.099	0.016	0.003	0.000	0.000
1	Cro	Dinamo Zagreb	4.56	4.59	0.019	0.080	0.213	0.688	0.086	0.012	0.001	0.000	0.000
8	Rom	CFR Cluj	4.90	4.83	0.012	0.120	0.275	0.593	0.119	0.012	0.001	0.000	0.000
6	Bls	BATE Borisov	3.02	3.36	0.004	0.030	0.130	0.836	0.031	0.003	0.000	0.000	0.000
5	Den	FC Nordsjælland	2.63	3.03	0.004	0.019	0.086	0.892	0.020	0.002	0.000	0.000	0.000

UEFA CL and EL 2012-13 Simulations Methodology

It has been a while since I last posted...
I've implemented a simulation program of all Champions League matches and draws.
The simulations are based on the wonderful ELO based rankings in the website: http://clubelo.com/
Many thanks for Lars, the owner of the site.
You can check out the site to know exactly how the rankings are made, but their basic is maximizing the prediction power of future games. There are many explanation and graphs there.
The number of home and away goals are assumed to be independent Random Poisson Variables with an expectancy of:
Goals for the Home team:
        if Proba < 0.5:
            Home Goals = 0.2 + 1.1*sqrt(Proba/0.5)
        else:
            Home Goals = 1.69 / (1.12*sqrt(2 -Proba/0.5)+0.18)

Goals for the Away team:
        if Proba < 0.8:
            Away goals = -0.96 + 1/(0.1+0.44*sqrt((Proba+

0.1)/0.9))
        else:
            Away goals = 0.72*sqrt((1 - Proba)/0.3)+0.3

"Proba" is the Winning Expectancy from the Elo Formula, ranging from 0 to 1.
Those values derived from Historical Data, and provided by Lars.
Of course the rankings are based mostly on last year, so take that into account if you want to use them for betting or any other purpose.