Here are the EXACT
#draw
#probabilities
for the round of 16 of the
#ChampionsLeague
. Bayern-Liverpool most likely matchup; Porto-PSG and Benfica-Brugge least likely
Borussia M'Gladbach est l'adversaire le plus probable du PSG en 8emes de finale de Ligue des champions (19.4%). Voici le tableau complet des VRAIES probabilites (400 000 simulations du tirage suivant la procedure officielle UEFA, erreur < 0.1%)
@AfterRMC
@ManuBojan
@RMCsport
Here are the CORRECT
#draw
#probabilities
for the round of 16 of the
#ChampionsLeague
, based on 2,000,000 simulations of the OFFICIAL DRAW PROCEDURE (which is quite complicated). Man City-Atletico is the most likely matchup: 28.2% followed closely by Man City-Schalke 04!
@2010MisterChip
@VillarrealCF
Aquí las probabilidades correctas (soy matemático profesional). Tu error es que no tomas en cuenta el modo secuencial del sorteo, que es muy importante para calcular las probabilidades correctas, como lo explico aquí :
Happy to share that my paper "Risk of Collusion: Will Groups of 3 Ruin the FIFA World Cup?" has won the 2nd prize at the MIT Sloan Sports Analytics Conference. Thanks to the jurors for rewarding tournament design research! Paper in free access ⬇️
#SSAC21
La
#Ligue1
, c'est fini pour 2019-20. Voici le
#classement
final que je propose, qui corrige certains biais du classement actuel (force des adversaires & nb de matchs à domicile/extérieur restant à jouer). J'explique ma méthode ici :
@ggaretier
@ManuBojan
Note that Bayern-Liverpool is very likely: 37%+ probability! Bayern is the most likely opponent of PSG, but PSG is the least likely opponent of Bayern. Ah, the beauty of maths :)
1) La
#Ligue2
, c'est fini pour cette saison. Voici le
#classement
final attendu, qui corrige certains biais du classement actuel (force des adversaires & nb de matchs à domicile/extérieur restant à jouer). J'explique ma méthode ici :
@ggaretier
@ManuBojan
UPDATE WITH 1M SIMULATIONS Here are the CORRECT
#draw
#probabilities
for the round of 16 of the
#ChampionsLeague
based on 1M simuls of the REAL draw procedure (up to sampling error). Real-Leipzig most likely (30.4%). Liverpool or Chelsea-Porto least likely (10.6%)
@martynziegler
Here are the *correct*
#draw
#probabilities
of the knockout round playoff of the
@UEFA
@EuropaLeague
🤓 NEW: play with the draw simulator and use the live probability calculator during the actual draw!
Il y a 4 ans j'appelais la
#FIFA
à changer les règles injustes du tirage au sort du Mondial. Je proposais des solutions. Pari réussi ! La FIFA a entendu le message et la
#CoupeDuMonde2018
est plus équitable. Je raconte l'aventure dans The Conversation
With Villarreal advancing, here are the CORRECT and EXACT
#draw
#probabilities
for the round of 16 of the
#ChampionsLeague
. Chelsea-Real most likely matchup; Benfica-Ajax, Sporting-Bayern least likely
Bonjour
@lequipedusoir
! Voici les (vraies) probabilités du tirage au sort de la Ligue des champions. Real, adversaire le + probable du
@PSG_inside
. Chelsea, du
@losclive
.
Ce soir, sur la saison de Coupes d'Europe 2021-22, la France est 3e du coefficient UEFA (6,416 pts), derrière P-B et Angleterre. Déjà quasiment aussi bien que sur l'ensemble de la saison dernière (7,916) ! Et mieux que le Portugal (5,75), concurrent direct
@ManuBojan
@RMCsport
#FIFA
finally announced
#WorldCupDraw
procedure. Here are the draw
#probabilities
for
#England
, based on 100,000 simulations using the official rules. Small fluctuations due to finite nb of simulations. Watch the impact of geographic constraints + how they mess up with Russia
@2010MisterChip
Alexis, es quasi correcto pero no son las probabilidades exactas. Aqui las probabilidades correctas, basadas sobre 400,000 simulaciones de la PROCEDURA OFICIAL, que es un poco complicada (error: +- 0.1%) No basta calcular casos favorables/casos posibles porque el sorteo no es asi
1) UPDATE WITH OFFICIAL TV PAIRINGS: Here are the
#UCLdraw
#probabilities
for Pots 1 & 2 based on 4K simulations of the official procedure, incl. TV pairings (see below). Small probability variations due to sampling error.
#ChampionsLeague
#draw
Bayern, adversaire le plus probable du
@PSG_inside
en 8e de finale de la Ligue des Champions (19,5%). Mais le PSG est aussi l'adversaire le moins probable du Bayern (avec Bruges) ! Real et Porto, adversaires les moins probables du PSG
@lequipe
@lequipedusoir
@AfterRMC
@RMCsport
France & Denmark just needed a draw to advance. They almost didn't attack each other, producing the most boring game of this
#WorldCup
. You can expect a lot more of these boring games in 2026 due to the new format (16 groups of 3), as I explain in
@nytimes
I'm proud to announce that
#UEFA
has followed my suggestion to adopt a new
#fairer
#bracket
for Euro 2020: Structure 6 in my Journal of Sports Analytics article (free access to pdf). No group will be over (dis)advantaged, like group A (E) was in 2016
@2010MisterChip
Hey, your calculations are still wrong, as I explained 2 years ago in El Pais
@ElPaisDeportes
Here are the CORRECT probabilities, based on 1000000 simulations of the OFFICIAL draw procedure (up to sampling error)
Very happy that my long fight for a better & fairer format for the 2026 World Cup is finally paying off! I contacted FIFA several years ago to alert them about the problems posed by groups of 3, and thank God they now seem ready to move to a better format.
Groupe compliqué en perspective pour les
#Bleus
: la
#France
sera dans le pot 2 du
#tirage
de l'
#EURO2020
et tombera forcément contre Italie (A), Angleterre (D), Espagne (E) ou Allemagne (F).
@ggaretier
@equipedefrance
Gpe B : Belgique Russie Danemark
Gpe C : Ukraine Pays-Bas
UPDATE WITH 65K SIMULATIONS Here are the
#UCLdraw
#probabilities
for Pots 1 & 2 based on 65K sim of the official UEFA procedure, incl. TV pairings. Small probability variations due to sampling error (eg, Juve-PSG-Porto should have exactly the same columns)
#ChampionsLeague
#draw
Comment calcule-t-on les probabilités du tirage au sort des 8e de finale de Ligue des Champions ? Pourquoi varient-elles autant ? Quelles sont les erreurs de raisonnement classiques à éviter ? J'explique tout ça dans
@lemondefr
@ggaretier
#TirageLDC
Borussia M'Gladbach est l'adversaire le plus probable du PSG en 8emes de finale de Ligue des champions (19.4%). Voici le tableau complet des VRAIES probabilites (400 000 simulations du tirage suivant la procedure officielle UEFA, erreur < 0.1%)
@lequipedusoir
Happy to share my new article Dispersion-Constrained Martingale Schrödinger Problems and the Exact Joint S&P 500/VIX Smile Calibration Puzzle. A follow-up on my Risk 2020 article with new theorems, proofs, and analysis.
#SP500
#VIX
#derivatives
#quant
"From Black-Scholes to Path-Dependent Volatility: A Brief History of Volatility Modeling". I'm very happy to give this talk at Fundação Getulio Vargas, Rio de Janeiro, Nov 22, 6pm. Please share to anyone who may be interested!
@fgv
@fgv_emap
Very happy to give a talk at the MIT Sloan Sports Analytics Conference this Friday at 11am ET. I'll be talking about the risk of collusion in the new World Cup format with groups of 3 that FIFA plans to use in 2026. Hope to see some sports nerds there! :)
#ssac21
#showmethedata
Here are the *correct*
#draw
#probabilities
of the round of 16 of the
@UEFA
@ChampionsLeague
🤓 NEW: play with the draw simulator and use the live probability calculator during the actual draw!
After my
@nytimes
article on the risk of
#collusion
in the new
#WorldCup
format (16 groups of 3, in 2026), readers have suggested solutions.
@MonkovicNYT
compiled them, I comment on their feasibility & propose another one. What do you think?
@united2026
Si j'etais
#ENG
ou
#BEL
je prefererais finir 2e du groupe G. Le 2e du groupe aura un parcours beaucoup plus facile que le 1er ! L'Angleterre se mord peut-etre les doigts d'avoir marque autant de buts contre le Panama...
#Mondial2018
@ggaretier
Final
#standings
of the English
#PremierLeague
? Here was my suggestion. It removes bias of current rankings due to strength of remaining opponents & remaining home/away games. Note: it does NOT pretend to be predictive.
@martynziegler
@OliverKay
Here are the CORRECT
#draw
#probabilities
for the round of 16 of the
#ChampionsLeague
, based on 4,000,000 simulations of the OFFICIAL DRAW PROCEDURE (which is quite complicated). Watch how likely Barcelona-Chelsea is: 41.3%! Then PSG-CHE & BES-CHE at 29.4%
Here are the CORRECT
#draw
#probabilities
for the round of 16 of the
#ChampionsLeague
based on 400K simulations of the REAL draw procedure (up to sampling error). Real-Leipzig most likely (30.5%). Liverpool or Chelsea-Porto least likely (10.6%).
@ManuBojan
@FourFourTwo
2) Of course you need good rankings for building pots by level. I had also urged FIFA to adopt Elo ratings for their FIFA rankings at the time, which they did in August 2018.
Comment décider du classement final de la
#Ligue1
si elle ne pouvait pas reprendre ? Il faut bien sûr tenir compte des calendriers plus ou moins difficiles des équipes. Voici ce que je propose. MHSC serait 6e. Merci
@lemondefr
!
@ggaretier
@ManuBojan
Poland first ever relegated team in the UEFA Nations League. They were a seed at the World Cup in June (after avoiding playing friendlies), now they’re in the second division of Europe...
#POLITA
#NationsLeague
Si Donetsk & l'Atletico se qualifient demain, voici les
#probas
du
#tirage
au sort des 8e de finale de la
#liguedeschampions
sur la base de 1M simulations (+/- erreur statistique). Valence & Barca sont les 2 adversaires les + probables de l'
@OL
, la Juve le - prob
@ggaretier
#OL
On me demande souvent pourquoi les
#probabilit
és du
#tirage
des 8e de finale de la
#liguedeschampions
peuvent varier autant (pas tellement cette année) et comment je fais pour les calculer. J'ai donc écrit ça. Merci
@lemondefr
!
Here the
#draw
#probabilities
of the
#EuropaLeague
Ro32 now based on 200K simulations of the OFFICIAL PROCEDURE (up to small sampling error). Prob is quite uniform. Sporting vs Espanyol, ManU, Sevilla, Celtic most likely (~8.7%). Salzburg vs Lev, Shak, Olimp least likely (~5.5%)
I was interviewed by
@RiskDotNet
about volatility modeling and football in the latest episode of their podcast
@Quantcast
. We talked option pricing, path-dependent volatility, SPX-VIX, and World Cup draws and formats. Enjoy!
With Mathieu Rosenbaum, Prof. Ecole polytechnique; Patrick Drahi, pres. of Altice; Asher Cohen, pres. of The Hebrew University of Jerusalem; Myron Scholes, Prof. Stanford, Nobel Prize of Economics 1997; Paul Glasserman, Prof. Columbia; Alex Lipton, Quant of the year 2000
#FIFA
finally announced
#WorldCupDraw
procedure. Here are the draw
#probabilities
for
#Brazil
, based on 100,000 simulations using the official rules. Small fluctuations due to finite nb of simulations. Watch the impact of geographic constraints
#Russia2018
What a fairer 24 team UEFA Euro could look like. My new article was just published in Journal of Sports Analytics (open access to all). UEFA has adopted my "Suggestion 6" (see Table 5) for the new bracket of the
#Euro2020
!
Many people have asked me why the
#draw
#probabilities
of the
#ChampionsLeague
round of 16 can vary so much and how I computed them. So I wrote this. Hope this helps! I'm happy to answer questions if some things remain unclear :) Thank you
@FourFourTwo
!