Match 1:  Man U 49.9%, Liverpool 23.7%

Match 2: Liverpool 60.4%, Everton 15.6%

Match 3: Arsenal 41.3%, Liverpool 31.2%

Match 4: Arsenal 41.3%, Liverpool 31.2%

Match 5: Liverpool 47.2%, Arsenal 26.2%

Liverpool win all 5 matches: 0.7%

Liverpool lose all 5 matches: 0.3%

So, Liverpool are about twice as likely to win all five matches than lose all five matches. But neither is very likely.

Take a look at our Predictor for more of this sort of thing…

Let’s assume Liverpool go through. Manchester United will play one of 7 teams. 3 of them are English, and so the chance of Manchester United meeting an English club is 3/7 = 42.9%.

Actually we estimate that Liverpool have a 91% chance of qualifying for the Quarter Finals. So the best guess chance of Manchester United meeting an English Club is 2.95/7 = 42.1%.

OK, so Alec gets his maths GCSE, but would he be able to answer the following:

What is the chance of two all-English Quarter Finals (assuming Liverpool go through)?

Let’s look at one English club. There were 4 English clubs out of 8. There are 3 English clubs out of 7 that can be picked to play against one English club. Then we need the third English club to be picked against an English club. Now there is only 1 English club out of 5 that can be matched against the third club.

So the overall chance of two all-English quarter finals is (3/7) times (1/5) = 3/35 = 8.6%

What is the chance of zero all-English Quarter Finals (assuming Liverpool go through)?

Let’s look at one English club. They must be matched against one of the 4 non-English clubs (chance = 4/7). Now let’s look at the second English club. They also must be be matched against a non-English club. There are three out of five to choose from (chance = 3/5). The third English club must be matched against a non-English club – two out of three of the remaining clubs are non-English (chance = 2/3).

Phew. The good news is because we’ve dealt with three Quarter Finals the last (English V non-English) Quarter Final is fixed. So the chance of zero all-English quarter finals is (4/7) times (3/5) times (2/3) = 8/35 = 22.9%.

What is the chance of exactly one all-English Quarter Final (assuming Liverpool go through)?

Easy: Either there are zero, one or two all-English matches. We already calculated zero and two all-English Quarter Finals. The chance of exactly one all-English quarter final is simple 1 – 3/35 – 8/35 = 24/35 = 68.6%.

What is the chance of at least one all-English Quarter Final (assuming Liverpool go through)?

Again, that’s easy. If we want at least one all-English Quarter Final, that can either be exactly one all-English Quarter Final or exactly two all-English Quarter Finals. So the chance of at least one is 24/35 + 3/35 = 27/35 = 77.1%.

Now, do you think Alec has managed to do all those calculations? He probably didn’t bother because he wouldn’t like to assume Liverpool going through…

Thanks to Nagulan Saravanamuttu, who helped calculate the probabilities for a much easier problem last year when there were three English clubs left in the Champions League.

• Israel 24%
• Draw 25%
• England 51%

so things are looking pretty good for England. No analysis yet on the England squad, but perhaps I’ll put that up later. For interest, we rank England as 7th in the world, and Israel as 44th.

I’m also interested in the Ireland V Wales match. Here’s what we’re saying:

• Ireland 53%
• Draw 29%
• Wales 18%

Both sides have been looking pretty ropy over the past year or so – Ireland at 39, Wales at 53. Ireland have crashed since the World Cup, when we ranked them as 11th in the world.

On a brighter note, Scotland should beat Georgia. We give them a 66% chance of doing so.

That is all.

Ahh….

The BBC have now pointed out that if games end in a draw, the winner of the shootout would get 2 points, and the loser one point.  So that changes things somewhat… But the main points of what I wrote still apply (see below)

Original words:

The BBC is reporting that the football league is thinking about scrapping draws. Under the new scheme, matches ending all square after 90 minutes would be decided by a penalty shootout. It’s supposed to make the leagues more competitive, but the idea is clearly ridiculous.

First of all, 3 points for a win wouldn’t mean anything, since there would only be wins and losses. If a match ends all square, let’s say the chance of either team winning the shoot out is 1/2. (It might not be, since better teams tend to have better strikers and goalkeepers). So your expected number of points if it’s all level after 90 minutes is 1/2 times 3: You get 3 points with probability 1/2 (if you win the shootout), and zero points with probability 1/2 (if you lose the shootout).

So now we’ve got 3 points for a win, and 1 and 1/2 points for a draw. Remind you of anything? Basically we’ve gone back to the old system of “A win is worth double what a draw is worth” – or 2 points for a win.

The one thing the system would achieve is making the league look more competitive. That’s becuase instead of a guaranteed point for a draw, some teams would win lots of shootouts, and other teams would lose lots. But the competitiveness is only skin deep. The league isn’t really more competitive, it just looks like it because you’ve thrown a lot of chance into the points system.

And look at the Championship, League 1 and League 2 tables: They’re already pretty competitive, for pity’s sake. It’s the Premiership that needs sorting out, not these lower leagues. There’s much more to say on this, and hopefully the subject will be mentioned in the Fink Tank soon.

It’s difficult, especially in Scotland, to decide whether a team is really declining under a manager, or whether a sequence of poor results is just a ‘blip’ in form. Scotland is usually even more difficult, because Rangers and Celtic are historically much stronger than other league teams (though that’s changed recently).

So I had a look at the European rankings given by our model for Scottish clubs in May 2006, when Le Guen was hired, and on New Year’s day, just before he was fired. Here are the results:

May 2006:

• Rangers ranked 2nd in Scotland and 53rd in Europe
• Attack is 60% of best team in Europe (Barcelona)
• Defence is 55% of best team in Europe (Barcelona)
• Rangers are 79% as good as Celtic, who rank 26th in Europe
• Hearts are catching up – they are 74% as good as Celtic

31st December 2006:

• Rangers ranked 2nd in Scotland and 86th in Europe
• Attack is 51% of best team in Europe (Barcelona)
• Defence is 48% of best team in Europe (Barcelona)
• Rangers are 74% as good as Celtic, who rank 43rd in Europe
• Hearts are 4th – they are 57% as good as Celtic. Aberdeen now ranked 3rd in Scotland

So Rangers rankings have gone down a bit. Celtic don’t have such a good Euro ranking this year either. But Rangers are about as far behind Celtic (in our model’s opinion rather than in League results) this year as they were last year.

Last year, Rangers only had Celtic and Hearts to compete with. This year, Aberdeen and Hibs are at about the same level as Hearts.

So there is some evidence that Le Guen has done a bad job, but it’s far from conclusive. At least there was a demonstrable decline in Rangers’ rankings though. I did some work on clubs sacking managers last year, and it was a painful piece of work, and it was difficult to come to any firm conclusions.

Sometimes, teams had declined before a manager was sacked. That wasn’t the case for many managers, though. My guess is that short term (less than 10 games) blips in form result in upset fans, and calls for the manager’s head. The directors duly comply… Rash decisions and short-termism seems to be behind a lot of manager sackings.

Oh well. C’est la vie, as Paul might say.

The current UEFA Champions League regulations (section 4, paragraph 5) state that:

If two or more teams are equal on points on completion of the group matches, the following criteria are applied to determine the rankings:

a) higher number of points obtained in the group matches played among the teams in question;

b) superior goal difference from the group matches played among the teams in question;

c) higher number of goals scored away from home in the group matches played among the teams in question;

d) superior goal difference from all group matches played;

… and so on and so forth. It’s obvious what the problem is: the group stage placing can often be determined before the final match leading to ridiculous matches and teams conspiring to generate a certain result.

Take group C in the Champion’s League last Tuesday: Liverpool had already won the group – they were only 3 points ahead of PSV but, having beaten them and drawn against them, couldn’t be toppled from top spot. Similarly, PSV would definitely finish second, and Bordeaux would definitely finish third – despite being only 3 points ahead of Galatasaray. The result was two pointless matches – indicated by Liverpool’s team selection – played out in front of half empty stadia.

What if we went back to the old rules and said that (d) – superior goal difference – determined the rankings? PSV would have gone all out to tonk Bordeaux, knowing that they had a chance to overturn Liverpool’s superior goal difference, and Liverpool would have needed at least a point to ensure finishing top. Who knows, Bordeaux and Galatasaray may even have wanted to ensure or snatch the UEFA cup place.

Even more galling was the group G fiasco in which Porto and Arsenal could ensure progress by drawing with one another in the final match, because previous results meant that if these two and CSKA finished on equal points then Porto and Arsenal would go through. Go back to the proper old version of goal difference and CSKA would be trying to score as many as possible against Hamburg, and Porto would have a lingering doubt that a draw might not be enough to see them through to the next stage. Much more exciting all around, yes?

I could go on. And I will go on. The rules meant that Chelsea could risk losing, in their fourth match, to Werder Bremen (as long as they beat Levski Sofia in the last round of matches they’d finish top) in order to increase Barcelona’s chances of finishing third in the group. Guess what? They lost. With old goal difference, that risk would not be worthwhile, since Barca could have still finished first after 4 matches.

What makes things worse is that I lost a packet backing Real Madrid on Tuesday, without realising that they had already finished second in the group, with no chance of finishing first. Guess what – they drew.

Old goal difference keeps things nice and uncertain until the final match. I’m not claiming that teams engineer particular results that are convenient for them, but anyone who’s looked at Game Theory can see that the rewards for sitting out a 0-0 draw – if it’s in the interests of you and your opponent – are great. The market knows it too. The price for a draw in the Arsenal-Porto match was 6/7 on. That would be unthinkable if it was the first group match. Similarly, the odds for Bremen to beat Chelsea were very low. The bookmakers know that something odd is going on – the prices would be a bit more realistic if we went back to old goal difference.

I’m not out of vitriol yet: These new rules apply to international matches. You hear managers spouting tripe like “there are no easy games at this level any more”. Why? Goal difference. No one cares about crushing Andorra 18-0 when they know full well the goal difference from that result is very unlikely to count if there’s a tie for Euro 2008 qualification. Bring back the old goal difference and I bet that kind of result will become more common – because goals against any team are worth something.

Oh, and changing teams’ incentives by bringing back old goal difference makes matches easier to predict too.

Here endeth the lesson.

But you can view a pared-down version of our predictions, which use a model that isn’t quite so funky, on line.

Take a look at The Predictor. You’ll need flash installed.

 Football manager rage

Here’s a look at what I did to see where West Ham are going wrong, in a bit more detail:

Team Ranking

We have a model that ranks all English league teams on their attack and defence, taking into account shots, shots on target and goals. There are other details, such as the fact that recent results influence the ratings more heavily, and the observation that the goal scoring rate increases as the game goes on.

Anyhow, we have an objective way of rating teams and the first thing to do if we want to see if a team is doing badly is to take a look at their rating:

The graph shows that we never rated them that highly: When they were promoted in May 2005, we ranked them 26th. They were a reasonably good Championship club, and no one expected them to do well in the Premiership. We didn’t either. In fact, last season the highest they were ranked by our model was 16th, and yet they finished 9th in the Premiership! Why the discrepancy?

West Ham’s real problems

Let’s take a look at the attack and defence ranks, to see where West Ham were going wrong:

This season, their attack and defence have declined, but last season defence seemed to be more of a problem than attack. Neither rating was spectacular, and we still haven’t explained why our model ranked West Ham as 16th best club (at best), when they finished 9th in the Premiership.

The problems in the team are caused by shots: They don’t create enough and they allow far too many. Last season, that didn’t matter because they converted chances into goals very well, and their keepers kept out all of those shots. We can take a look at how their rankings of shots, shots on target and goals have changed from the 05/06 season to the 06/07 season. This graph shows West Ham’s ranking compared to other Premiership clubs:

West Ham conceded 509 shots last season, more than any other Premiership team. They created only 354, with only Charlton Athletic creating less. But it didn’t matter because they ranked 6th on goals scored and 13th on goals conceded, and that was enough for them to register a 9th place finish.

It might be the case that West Ham’s strikers are so good, it really doesn’t matter about the low number of shots created, but that doesn’t seem to be the case. This season those low numbers of shots aren’t being turned into goals, suggesting West Ham’s strikers aren’t good enough to dig them out of their shots hole.

In fairness to the defence, they’ve been better at stopping shots and shots on target this season, but that hasn’t seen a payoff in their goals conceded ranking. Well, goals involve luck, and West Ham don’t have any at the moment. Their current league-wide rankings from our model are:

• Shots created: 56th
• Shots on target conversion: 39th
• Goals conversion: 10th
• Shots allowed: 26th
• Shots-to-shots on target allowed: 4th
• Goals-to-shots on target allowed: 31st

• Overall attack: 37th
• Overall defence: 19th
• Overall: 26th

(Hmm, I’ve just noticed that they’ve beaten Arsenal 1-0, so perhaps their luck is changing…)

The Players

So, who’s to blame? Well, we have a player model that looks at all player actions, correlates them with goals scored and goals conceded, and so works out how valuable a players’ actions are in terms of changing the team’s chances of wining a game. We measure a player’s value in ‘Premiership points per season’. If that player wasn’t playing, how many points would their team drop?

Here are the heroes of West Ham in the 05/06 season:

• Daniel Gabbidon is worth 8.45 points per season
• James Collins is worth 8.19 points per season
• Marlon Harewood is worth 4.06 points per season
• Yossi Benayoun is worth 3.10 points per season
• Shaka Hislop is worth 2.81 points per season

and the villains…

• Paul Konchesky costs 7.64 points per season
• Lionel Scaloni costs 5.59 points per season
• Shaun Newton costs 5.58 points per season
• Roy Carroll costs 5.42 points per season
• Christian Dailly costs 5.34 points per season

We rate Harewood and Benayoun highly because of the goals and assists they provide. They haven’t been doing that this season. Collins has also been injured for most of the season, and Hislop’s gone to Dallas. 6th ranked was Dean Ashton, and he’s been injured too. Carroll’s played more often this season, and he was poor last season. It’s too early to say whether their new keeper, Robert Green, will do as well as Hislop did last season.

In Conclusion

Danny summed it up well in his article. I’ll paraphrase: 1) Create more shots, and allow less because you won’t always be as lucky as you were last season, 2) Hope that Tevez and Mascherano start providing the quality that Harewood and Benayoun did last season, 3) Get James Collins and Dean Ashton back from injury: They’ll help solve your shots problems.