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| Champions' League Draw Probabilities | |
| Author: asbell
Date: 07-12-2006, 13:35 | What are the chances of each possible match-up in the 2nd round draw occurring? This isn't as simple as it sounds because you get two different results depending on which perspective you look at: e.g. Celtic v Valencia - Celtic can draw any of 7 teams = 1/7 - but Valencia can only draw one of 5 teams = 1/5 So how do you work it out? Any mathematicians out there? |
| Re: Champions' League Draw Probabilities | |
| Author: antonio62tr
Date: 07-12-2006, 13:56 | So you solved the problem, 20%... |
| Re: Champions' League Draw Probabilities | |
| Author: asbell
Date: 07-12-2006, 14:01 | No, that doesn't work, because by the same logic: Celtic v Chelsea = 14.3% (1/7) Celtic v Bayern = 14.3% Celtic v Liverpool = 14.3% Celtic v Valencia = 20.0% (1/5) Celtic v Lyon = 16.7% (1/6) Celtic v Arsenal = 14.3% (1/7) Celtic v Milan = 20.0% TOTAL = 113.8% (which must be wrong!) |
| Re: Champions' League Draw Probabilities | |
| Author: antonio62tr
Date: 07-12-2006, 14:06 | You are gonna make total 100 so: Celtic v Chelsea = 14.3% -->12.56% Celtic v Bayern = 14.3% -->12.56% Celtic v Liverpool = 14.3% -->12.56% Celtic v Valencia = 20.0% -->17.57% Celtic v Lyon = 16.7% -->14.67% Celtic v Arsenal = 14.3% -->12.56% Celtic v Milan = 20.0% -->17.57% TOTAL = 100% |
| Re: Champions' League Draw Probabilities | |
| Author: SHEV
Date: 07-12-2006, 14:07 Edited by: SHEV at: 07-12-2006, 14:08 | Last one looks quite right. |
| Re: Champions' League Draw Probabilities | |
| Author: asbell
Date: 07-12-2006, 14:17 | Yes, that straightens Celtic up to 100%. Trouble is, if you do it for all the possibilities, it makes Valencia 95.9% and Liverpool (for example) 103.0%!!! If you then correct those percentages in the same manner, you eventually get close to 100% for everybody (with Celtic v Valencia being 18.2%) but this still doesn't seem a very mathematically rigorous way of doing it - hence my appeal for help! |
| Re: Champions' League Draw Probabilities | |
| Author: badgerboy
Date: 07-12-2006, 14:18 | I have another question about the draw. Do they split teams from the same country into pairs so they play on different days as they do for the groups? Or do they do an "open" draw and decide the dates afterwards? There's nothing about this in the regulations but then I can't see anything about it for the group draw either. Also does anyone know exactly how the draw works? Logically of course you draw one group runner-up followed by one group winner or vice versa. But I have it in my head they might do something like for the groups. Draw say all the group winners (or runners-up - I'm not sure which) first and then once they have the order draw from the other pot. Can anyone remember from past years? |
| Re: Champions' League Draw Probabilities | |
| Author: Mikalobakus
Date: 07-12-2006, 18:55 Edited by: administrator at: 07-12-2006, 22:08 | If UEFA do the draw fairly, in the sense that every possible outcome of the draw process not prohibited by rules (same country, or same qualifying group) is equally likely, the following results show the probabilities of every possible match occurring. Total valid draws possible = 6655 R.Mad Barc Inter Roma Celtic PSV Lille Porto As Percentages: R.Mad Barc Inter Roma Celtic PSV Lille Porto Given the complexities of the draw conditions it is not particularly easy to generate a draw procedure that is totally fair in the above sense and can also be carried out semi-manually. However, the above should still be a reasonable approximation. |
| Re: Champions' League Draw Probabilities | |
| Author: Lyonnais
Date: 07-12-2006, 19:12 | Thank you very much Mikalobakus  There are maybe some very little discrepancies (if I look at Lille chances, I see that they have more chances to draw Chelsea than Bayern, whicch might need to be double checked) but as you said, it is a very very good working basis. And I truely believe you when you say that it's not easy to run such a simulation (i've tried almost all afternoon without having achieved 10% of what you've done). Thank you! |
| Re: Champions' League Draw Probabilities | |
| Author: asbell
Date: 07-12-2006, 19:17 | May I add my thanks! For comparison here are the full set of results from my "iterative" solution as discussed above - they agree very closely. Chelsea to play: Roma 16.4% R Madrid 15.7% Lille 15.7% Inter 15.2% PSV 12.4% Celtic 12.4% Porto 12.4% Bayern to play: Roma 16.4% R Madrid 15.7% Lille 15.7% Barcelona 15.2% PSV 12.4% Celtic 12.4% Porto 12.4% Liverpool to play: Roma 15.9% R Madrid 15.2% Lille 15.2% Barcelona 14.8% Inter 14.8% Celtic 12.0% Porto 12.0% Valencia to play: Lille 23.0% Inter 22.4% PSV 18.2% Celtic 18.2% Porto 18.2% Lyon to play: Roma 19.5% Barcelona 18.1% Inter 18.1% PSV 14.8% Celtic 14.8% Porto 14.8% Man Utd to play: Roma 15.9% R Madrid 15.2% Lille 15.2% Barcelona 14.8% Inter 14.8% PSV 12.0% Porto 12.0% Arsenal to play: Roma 15.9% R Madrid 15.2% Lille 15.2% Barcelona 14.8% Inter 14.8% PSV 12.0% Celtic 12.0% Milan to play: R Madrid 23.0% Barcelona 22.4% PSV 18.2% Celtic 18.2% Porto 18.2% |
| Re: Champions' League Draw Probabilities | |
| Author: Arny
Date: 07-12-2006, 19:20 | Anyway why u all bother about this? Cuz it's 12% or 17% do u think it matters? It can be 90%-10% and still win the 10% thats why they are called precents. |
| Re: Champions' League Draw Probabilities | |
| Author: Mikalobakus
Date: 07-12-2006, 19:21 | The calculations are exact, apart from rounding in the percentages. I generated all 40320 possible draws, and eliminated those containing one or more of the 13 impossible matches (8 from group stages, 5 from country protection). That left 6655 possible draws, and I then counted the occurrences of each of the 51 possible matches in these 6655 draws. You will see that in the raw data, all rows and columns add up to 6655. By the way, does any helpful reader know how to make tables come out sensibly in these posts? My carefully spaced columns have been compacted so they are almost illegible (:-( |
| Re: Champions' League Draw Probabilities | |
| Author: Overgame
Date: 07-12-2006, 19:29 Edited by: Overgame at: 07-12-2006, 19:39 | The difference between Bayern and Chelsea (for Lille) is the same (and opposite) than the one for Madrid. If Lille plays against Bayern, there are more possibilities of 'impossible draws'. For the same reason, Milan has more chance to play against Madrid than Barcelona : if Milan plays against Barcelona, Lyon has 2 'impossible draws' (Lille and Madrid). |
| Re: Champions' League Draw Probabilities | |
| Author: panda
Date: 07-12-2006, 19:30 | Great thread - I nominate it for selected topics! |
| Re: Champions' League Draw Probabilities | |
| Author: Forza-AZ
Date: 07-12-2006, 20:17 | @badgerboy I have another question about the draw. Do they split teams from the same country into pairs so they play on different days as they do for the groups? Or do they do an "open" draw and decide the dates afterwards? What I can remember from the draws in recent years is that they did it this way: They picked a team from one pot (I'm not sure if it was the groupwinners or the runners-up; I think the latter because they play the 1st legs at home), and then they looked which teams they could draw (so not from the same country and not from the same group; and for the last pairs it could also be that a team can't be drawn because that will give problems in the last pair(s)). They then picked a ball from all possible opponents and put them in a bowl, from which they picked 1. I don't think there were pairs. I don't think it would be a problem to determine the matchdays afterwards with dividing the teams from 1 country over both days. They at least won't have to look at home/away, because these are already determined by the final groupstandings. |
| Re: Champions' League Draw Probabilities | |
| Author: moro
Date: 07-12-2006, 20:36 | looks like poker odds. Need some luck, but lots of cards are already returned, on the table. The river. |
| Re: Champions' League Draw Probabilities | |
| Author: MalcolmW
Date: 07-12-2006, 21:44 Edited by: MalcolmW at: 07-12-2006, 22:55 | I feel sure that the surviving pairs from the Group Stage draw will be retained for the same reason, without any impact on the draw possibilities because the English pairings (Chelsea + Arsenal and ManU + Liverpool) are all in group winners (first time all 4 have done so in the current format), and the Spanish pairing (Barca - Real M) are both in group runners-up. Only the italian pairing (AC Milan - Inter) is split, which actually helps the procedure as they will not be at home in the same week. What is not clear is whether Lyon will now be paired with Lille, but it does seem logical that this should happen. But if ManU play Lille and Liverpool play Barcelona a French pairing would prevent Lyon from playing Real Madrid. So the presence or absence of a French pairing affects the probabilities (the pairing would further reduce the 6655 options). How about this for a football festival: CL Tues Chelsea v Real Madrid CL Wed Arsenal v Barcelona UCR4 Thur Tottenham v Espanyol? |
| Re: Champions' League Draw Probabilities | |
| Author: bert.kassies
Date: 07-12-2006, 22:12 | @Mikalobakus. Thanks, nice post. I hope you don't mind for me editing your post. For tables you can use the pre-format tags (see Codes above). Not so easy to explain because the tags cannot be used in a post without being interpreted. You may take a look by using the "Edit" button. |
| Re: Champions' League Draw Probabilities | |
| Author: Aliceag
Date: 07-12-2006, 22:40 Edited by: Aliceag at: 07-12-2006, 22:46 | I find one Odd thing. The single country teams: Celtic, PSV and Porto are the bottom teams to everybody else. Why do the teams that have no constraints at all, the less probable of being picked?? My intuition would tell me otherwise! That the teams that cause more constraints would prevent others to happen, so those should have less probabilities. Can anyone explain me this phenomena in simple english like I had 80 years old? |
| Re: Champions' League Draw Probabilities | |
| Author: MalcolmW
Date: 07-12-2006, 23:02 | Because those clubs with no national constraint have their 6655 possibilities spread between 7 possible opponents, whereas those with a national constraint have only 6 possible opponents, but the same total of 6655 possibilities. 6655/7 = 950.714285r714285 and 6655/6 = 1109.166666r6 |
| Re: Champions' League Draw Probabilities | |
| Author: Mikalobakus
Date: 08-12-2006, 14:53 | @bert - many thanks, I can see what to do now. On the wider issue, I was thinking about the possibilities of a genuinely fair draw, i.e. one that accurately reflects the chances calculated above. I can think of two ways. Method A: List the 6655 possible draws, and have the computer split them into five groups of 1331. Split each group of 1331 into 11 groups of 121. Then split each group of 121 into 11 groups of 11. Now make four bags with balls 1-5 in the first one, and balls 1-11 in the last three. The first ball selects a group of 1331, the second selects a group of 121 from the group of 1331, the third ball selects a group of 11 from the group of 121, and the last ball selects the actual draw from the group of 11. UEFA will not do this, because it is not exciting and progressive (nothing much is known until the last ball is drawn) and not transparent (it relies entirely on the computerised list of draws). Method B: Put all the teams into a completely free draw, and draw them until either the draw is complete, or a match is drawn that is not allowed. In that case, crucially to the fairness of it, put all the balls back and start again. UEFA will not do this, as it is not nice to have provisional matches, which don't get played if the balls all have to go back, and also it can take a long time. About 1 in 6 draws is legal, so imagine casting a single die every 5 minutes, and waiting for a 6. You might be there for 5 minutes, or 35, or 65, ... What UEFA will do is to force the draw to be legal by one or both of two strategies. The first is to pre-group teams so that illegal matches are prevented. This wildly skews the draw by arbitrarily eliminating a great many, often a majority, of perfectly legal outcomes. You can't say much about this until you know exactly what the system is, but it is often used to achieve results for commercial reasons such as television dates as well as pre-eliminating illegal matches from the draw. What is 100% certain is that what remains is not a fair draw, in any reasonable sense of the word. The second is to allow a computer to suggest the balls to be put into the bag for any individual selection. This can be perfectly harmless; if the first team is Chelsea, seven balls go into the bag, while if the first team is Valencia, only five teams go in. This saves a few moments and costs nothing. Later on, it can cause small biases in the outcomes. Consider the following situation where twelve teams have been drawn already, and let's say Chelsea, Liverpool, Barcelona, and Lille remain. Under method B above, a draw would be made, and if it was Chelsea v Lille, the draw would be completed - but if it was Chelsea v Barcelona, the draw would be rejected. As it is done by the computer, the latter result is prevented and the Chelsea is forced to play against Lille. No disrespect to anyone, it is just an example. The effect of this is to double the probability of the six matches already drawn forming part of the final draw on that particular branch of the draw tree. This has a tiny effect on the overall outcome (less than 0.1%) but there are hundreds if not thousands of these situations, where the computer pushes the outcome in one way or the other to avoid having to throw away the part of the draw already completed and start again. So total biases of a percent or two are perfectly possible over the whole process. Again, without knowing exactly what is done, it is impossible to analyse these outcomes. So my initial answer to your question, much improved by Bert's control thingies, depends heavily on the first line - "If UEFA do the draw fairly, ..." and without any suggestion of impropriety, it is almost inevitable that, at least in a mathematical sense, they won't. |
| Re: Champions' League Draw Probabilities | |
| Author: badgerboy
Date: 08-12-2006, 15:37 | ""If UEFA do the draw fairly, ..." and without any suggestion of impropriety, it is almost inevitable that, at least in a mathematical sense, they won't." Great work on the maths for this Mikalobakus. But when you talk about the "fairness" or otherwise I'm not totally clear. Isn't it just the case that you can only ever list the probabilities before a ball is drawn and as soon as the draw starts each ball drawn changes the other likely outcomes? And that must be true of pretty much any draw ever undertaken? |
| Re: Champions' League Draw Probabilities | |
| Author: panda
Date: 08-12-2006, 15:40 | Any draw will have winners and losers in terms of who gets whom. The restrictions e.g. in pairing teams for the GS are part of the process of chance as to who happens to be involved. so like badgerboy, I see the maths point about fairness, but it isn't just about maths.... |
| Re: Champions' League Draw Probabilities | |
| Author: bert.kassies
Date: 08-12-2006, 16:14 | The draw could be made perfect if we let the computer identify all the 6655 possibilities. Now we organise a random draw of a number between 0 and 6655. For the media spectacle we hire some professional scenario writer, but the end result of all this should be a number between 0 and 6655. Then we look into the computer for the fixture list ... |
| Re: Champions' League Draw Probabilities | |
| Author: UncleSam
Date: 08-12-2006, 16:16 | There will be no pairing. But UEFA will divide the games up in such a way that we get maximum two English teams on the same match day. The same will happen for nations with more than one club - Spain, Italy, France. So we will get maximum two Spanish teams. The Italian and French teams will also be split. |
| Re: Champions' League Draw Probabilities | |
| Author: panda
Date: 08-12-2006, 16:24 | @bert hypothetically, some of those draw combinations are the same and could be published beforehand; then it can be like a lottery draw. and the winner is..... Draw No 3749 !!!! that could still be exciting. Y |
| Re: Champions' League Draw Probabilities | |
| Author: Mikalobakus
Date: 08-12-2006, 16:28 | 'Fairness' in a mathematical sense, means simply that every outcome allowed by the rules is equally likely. Of course, during a draw process, the remaining probabilities change as some things are decided. But the overall process should be fair as defined above. Additional rules, not publicised in advance, make a draw unfair mathematically, and, I think, morally as well. Teams and their supporters should know the competition rules, and be able to see that the authorities, as well as the participants, abide by them. Similarly, procedures which make one outcome more likely than the others are, at least mathematically, unfair. If they completely prevent a match being played which is possible in a fairly selected draw, I would say that makes the draw very unfair, and in fact morally wrong. If they just slightly adjust the probabilities to make the procedure more understandable and straightforward to operate, this can be justified. At the end of the day UEFA will do whatever they do, and the football will do the talking in the end. But the question was asked, and I have tried to answer it, both mathematically (in an ideal world) and in commenting on procedures UEFA has used in the past. In particular, I really don't like UEFA's pre-assigned groups. They may be effective in keeping teams who cannot play each other apart, but they also completely prevent a great many perfectly legal matches which should have their natural chances to occur. They should not be eliminated because UEFA, by a completely private and unspecified process, has chosen to put the teams concerned in different groups. But that's just an opinion, and we are only at the stage of the last 16. In the last 8 we have a completely unrestricted draw, and every game has an equal chance to occur. |
| Re: Champions' League Draw Probabilities | |
| Author: panda
Date: 08-12-2006, 16:34 | I agree, constraints have implications of moral fairness or unfairness. But essentially because some match-ups are more or less desirable for some sides. If non-maths constraints make such match-ups more or less likely, that can FEEL unfair. |
| Re: Champions' League Draw Probabilities | |
| Author: Ricardo
Date: 08-12-2006, 16:43 | I wonder if (and if yes, how much) the drawprocedure influences the possibilities of the ties. I mean, all teams can be drawn first, chance 1/8, but which opponent is drawn influences the possibilites of the other teams. e.g. When Valencia is not drawn yet, the chance of the other groupwinners to play a not yet drawn Barca or Madrid increase. Or is this just all in the percentages given above? |
| Re: Champions' League Draw Probabilities | |
| Author: Mikalobakus
Date: 08-12-2006, 17:29 | @Ricardo: All the outcomes which obey the publicly stated rules (country protection, qualifying group exclusion) are included in the percentages. Obviously, once something has happened, the chances change - some things are certain, some now impossible, and all the relative probabilities of the unknowns change. But the chances before the draw starts are as shown above, if the draw procedure allows every outcome an equal chance. Bert's proposal above is one way to do this - it is effectively a procedural variation on my original method A above. But most of UEFA's procedures fail to a greater or lesser extent, which I think is a pity. |
| Re: Champions' League Draw Probabilities | |
| Author: badgerboy
Date: 08-12-2006, 17:45 | OK. So I wouldn't mind an example of the unpublished rules and/or procedures that make the draw "unfair". I understand the similar quibbles that affect the match schedules in the UEFA Cup groups for example. But not so much for the last 16 draw. So assuming the draw works as outlined by ForzaAZ above (and they draw the runners-up first). To simulate a totally random draw... Barcelona are drawn out first. They have six possibilities so these six balls are put in the "hat" Out comes Lyon. Sorry Lyonnais! Next - Roma. Obviously by now the probability of all the group winners left in the draw (except Chelsea and Valencia) to play Roma has increased but only because their possibility to play Barcelona has gone. Out comes Liverpool. Next comes PSV - all six remaining teams can play them without a problem. PSV v Valencia Next Porto - four possibilities left as they can't play Arsenal. Porto v Manchester United. Now the draw restrictions start to become more of a factor (and more complicated to follow). On the face of it Celtic and Real Madrid both have an equal chance of drawing any of the four remaining group winners. Chelsea & Arsenal an equal chance of drawing any of the runners-up. And when Celtic are the next ball out they do indeed have a one in four chance of drawing any of the other teams. But as soon as that ball is Chelsea the draw is over. Even if Real Madrid are drawn next and their own restrictions say they can play any of the group winners they must in fact play Milan. Why? Well Inter can't play Bayern or Milan so have to play Arsenal. Lille can't play Milan so have to play Bayern. So Real Madrid only have Milan left. It's a bit complicated to follow because you have to look at the possibilities for all the remaining teams - not just the one that comes out of the hat first. But all the rules and regulations that affect this are clearly available at the outset of the draw. The probabilities that these restrictions create can be worked out (at least they can if you have a mathematical brain like Mikalobakus - I'm not even going to try!) & these probabilities alter with each and every ball drawn until that draw is complete (after 5 games in my simulation). I can see that it's possible to dislike the restrictions. To say Liverpool v Man Utd or Barcelona v Chelsea should be possible in the last 16. But once the probabilities are calculated & set I don't see how the draw procedure affects them any differently than any draw anywhere. You put 64 teams in a hat. At the outset the probability of my team playing Chelsea is 62/1 against. But as soon as the first ball out is Stoke City the probability becomes 61/1. When there are four balls left including Brighton & Chelsea you don't say - hang on a minute the draws not fair. Stoke had a 62/1 chance of avoiding Chelsea but Brighton only have a 2/1 chance. Please put all the balls back in the hat to give Brighton the same chances as Stoke... |
| Re: Champions' League Draw Probabilities | |
| Author: Ricardo
Date: 08-12-2006, 20:23 | I had written a nice reply, but I lost it. The thing is that I woinder if the drawprocedure, as Uefa uses your second electronic procedure: first draw is free and then all limitation are entered in the computer to let always a possibility open. Can a first draw influence the rest of the draw? my sample, a simplified drawing of the CL draw: groupwinners: Valencia, Lyon, Milan, ManUtd and seconds: Barca, Madrid, PSV, Porto. Barca Madrid PSV PortoAnd my problem is this: First draw is free, so at that time ManUtd-Porto has the same probibility as Valencia-PSV. But after ManUtd-Porto, Valencia-PSV is forced, Lyon-Barca and Milan Madrid is left. After Valencia-PSV as first draw, Lyon can still draw Porto and Barcelona. Is this all in the percentages? |
| Re: Champions' League Draw Probabilities | |
| Author: Aliceag
Date: 08-12-2006, 20:56 | I guess We will see a draw looked alike the one for GS, with both people taking off balls, and a computed saying "Where they should go", with green and red lights. (and then lots of people asking why??). The computer will follow the balls drawn, and will detect in advance which teams will lead to an impossible result, so giving only green light to the teams that can be drawn. Supose you pick up a ball with a team. In the other pot you still have 4 teams, but 2 of those would lead to an impossible draw. So computer highlight only the two, that still make the draw possible, and so only those 2 balls will be drawn against the one picked up. It seems the more logical procedure to me. |
| Re: Champions' League Draw Probabilities | |
| Author: Overgame
Date: 08-12-2006, 23:08 | badgerboy : everyone has the same chance to avoid Chelsea :p Chelsea is drawn first: you have 1/62 to play against Chelsea. But let's imagine another team is drawn, you have 0 chance to play against the team if you were in the same group (let's forget the country protection), and 1/62 if you weren't. If you are drawn, you avoid Chelsea ! So, you have 1/62 chance to avoid Chelsea 2nd pair : same calcul. 3rd pair ... . . . Last pair : 0 chance (if both teams are not drawn). Total : 61/62 to avoid chelsea |
| Re: Champions' League Draw Probabilities | |
| Author: Lyonnais
Date: 09-12-2006, 00:25 Edited by: Lyonnais at: 09-12-2006, 00:27 | There is a guy, teacher at the University of Lille and specialist in artifical intelligence, who has a website and makes statistical predictions about the French League here I sent him an email asking him if he could modelize probabilities and he replied to me. His results are consistent with yours! congratulations. |
| Re: Champions' League Draw Probabilities | |
| Author: spenk
Date: 10-12-2006, 12:49 | for the number of possibilities in this draw it is good that all english teams ended on the first place. If 1 of the 4 english teams ended 2nd, that would have added another 3 zeros to the scheme. That 2nd ranked team would have only 4 possible teams to be drawn against. Two english teams ending 2nd would have added 4 zeros to the scheme. Now I have a question for the guys with the maths in this thread. I'm wondering if there is a possibility (not with these teams but in general) that the complete draw is fixed, so there is only 1 possible draw. If that is not possible (which is likely I think), what is the minimum number of options? For this one should maximize the number of zeros in the draw scheme. With no country problems, the number of zeros is 8 out of 64 places, because of the nr's 1 and 2 not drawing against each other. I think it would be necessary to have as many teams from the same countries as possible. So 4 teams from the top 3 countries: 12 teams. To have as many zeros as possible to the scheme, for each of those countries two teams should end 1st and two 2nd. That would add 4 zeros for each country so 12 zeros in total. The last 4 teams can be divided over 2 countries 2and2 or 3and1. These would both add maximal 2 zeros to the scheme. So as far as I can see the maximum number of zeros is 22. The problem now is that I can't think of the number of zeros that is necessary for a draw to be possibly fixed... 57 to 64 zeros would mean an impossible draw for sure. With 56 zeros there are only a few ways to divide the zeros to have a possible draw, but there are a lot of ways to have impossible draws. this is where I get stuck, maybe somebody else? What is the minimum number of zeros that can provide a fixed draw with only 1 possible draw? And is this possible in the CL with the number of teams that can enter for each country? |
| Re: Champions' League Draw Probabilities | |
| Author: panda
Date: 10-12-2006, 18:50 | This is an awesome question; perhaps the people with the maths can all confirm a solution |
| Re: Champions' League Draw Probabilities | |
| Author: MartinW
Date: 12-12-2006, 09:50 | Yes the most restricted draw is 4 teams each from three countries and the remaining 4 teams from two countries (either 3+1 or 2+2). This will give 22 blanks which cannot happen in the draw, eg:A1 B1 C1 D1 E1 F1 G1 H1 As for the number of possible draws and the percentage chance of each opponent, I can't work this out myself! |
| Re: Champions' League Draw Probabilities | |
| Author: Ricardo
Date: 12-12-2006, 12:39 | MartinW, Nice view. To calculate possibilites however, is this the most restrictive option? You placed the 2 German and 2 French teams all within the 4 English in the Groupstage. Maybe by dividing theses among all 3 (Eng, Esp, Ita) countries it has more restrictions? I don't know and wouldn't know how to calculate this. |
| Re: Champions' League Draw Probabilities | |
| Author: Mikalobakus
Date: 12-12-2006, 14:47 | MartinW is correct, but it is not the only possible layout, as Ricardo suggests. In fact as long as you have the MartinW's example teams as first and second (and the exclusion rules are obeyed throughout) any allocation of teams to groups has the same outcome in terms of exclusions. You just don't get the nice flag-like pattern in the exclusion table that MartinW has. As regards the percentage chances for the permitted games, I am not going to rerun all the calculations but they will be significantly less widely distributed than the values for the real draw shown above. This is simply based on the fact that everybody has 2 or 3 excluded opponents in this case, whereas in the real draw teams have 1, 2, or 3 excluded opponents - which is the cause of the varying percentages. |
| Re: Champions' League Draw Probabilities | |
| Author: mavano
Date: 12-12-2006, 18:37 Edited by: mavano at: 12-12-2006, 18:38 | What a great topic. These are the ones that made me come to this forum from the start. Just a pity that since the last 1,5 years these have become so scarce..... Last year we could have had a draw with 24 zero if i'm correct. A 5th entry from england would replace Ger1 and a 3rd from France Ger2. If the groupwinners would be the 1st and 2nd of all four countries. All second placed teams would have had 3 blanks. Now, for the whizzkids among us  what are the least amount of draws that could be made befor the rest of the draw becomes "fixed"? |
| Re: Champions' League Draw Probabilities | |
| Author: asbell
Date: 13-12-2006, 17:04 | Could you not have four teams from each of four countries, if the winner the previous year was not from one of the "big three" and had finished 4th or worse domestically? |
| Re: Champions' League Draw Probabilities | |
| Author: asbell
Date: 13-12-2006, 17:06 | mavano - I believe Liverpool were denied country protection last year, possibly partly because of the possibility that later draws could become quite forced. |
| Re: Champions' League Draw Probabilities | |
| Author: mavano
Date: 14-12-2006, 22:53 Edited by: mavano at: 14-12-2006, 23:35 | You're right, forgot about that. My bad. You're right though about countries 4,5,6 that could have 4 teams in cl. This would result in the same 24 blanks btw.... |
| Re: Champions' League Draw Probabilities | |
| Author: hooped
Date: 14-12-2006, 23:26 | have uefa announced yet how they will be carrying out the draw? also, is there a set system to decide which games are a tuesday and which are a wednesday, or is this decided after the draw? |
| Re: Champions' League Draw Probabilities | |
| Author: Mikalobakus
Date: 21-12-2006, 14:59 | The restrictions can result in quite early determination of the whole draw. Here is an entirely hypothetical example of some CL group results: Group A 1 Liverpool 2 Lyon Group B 1 Celtic 2 Man Utd Group C 1 Lille 2 Chelsea Group D 1 Arsenal 2 PSV and let us suppose that the teams from groups E-H draw against each other in the first 4 matches out of the hat. Now the draw is fixed: Liverpool must play PSV Arsenal must play Lyon Celtic must play Chelsea Lille is left with Man Utd With the following set of results: Group A 1 Liverpool 2 Lyon Group B 1 Bordeaux 2 Man Utd Group C 1 Lille 2 Chelsea Group D 1 PSG 2 Arsenal Group E 1 Barcelona 2 Juventus and if the teams from groups F-H draw against each other in the first three matches out of the pot, Liverpool must play Juventus - and Barcelona must play Lyon - but this just fixes two matches, not the whole draw. Each French team has a possibility of two English opponents, and vice versa. However, there are only two legal draws: Bordeaux v Chelsea PSG v Man Utd Lille v Arsenal or Bordeaux v Arsenal PSG v Chelsea Lille v Man Utd So the conclusion is: - after 3 matches are out of the hat there can be two fixed matches and only two possibilites for the other three - after 4 matches are out of the hat, the rest of the draw can be fixed Please accept that I have used teams that will hopefully be familiar to all and that I know how to spell . The examples are more alive than G1 v E2 etc, but are not an indication of my preferences in football, let alone any sort of prediction about anything. So please don't be offended if your favourite team isn't there. |