# Exploring the Chance Quality Index: Why more chances doesn’t necessarily mean more goals

**Karthik (KV) **seeks to establish why more chances don’t necessarily mean more goals.

How do you win a football game? The simplest answer would be to score more goals than the other team. So, how do you score more goals than the other team? Create more chances than the other team and you are likely to score more than them. How accurate is that statement? Not very accurate, in fact. What we can conclude with certainty is that, the team that creates chances of higher quality is likely to score more compared to the other team.

At every press conference that Arsene Wenger has had to attend in the past few years, he would respond to the customary question on possible transfers by stating that he always opts for ‘quality over quantity.’ Signing a player of top quality is more important than signing 3-4 players just to fill the void. We can apply the same principle to chances created. The probability of scoring from a chance of very high quality is more compared to scoring from three chances of mediocre quality. For better clarity, OPTA describes a chance as ‘assists plus key passes.’ Is it possible to measure the quality of a chance? Yes, that is what I have tried to do in the following lines.

The factors affecting the quality of a chance are:

- Distance from the goal
- The angle by which the goal is visible.
- The number of opponent players surrounding the player with the ball.

Based on this, we can say that Chance Quality is:

- Inversely proportional to the distance from goal.
- Inversely proportional to the number of opponent players surrounding the player taking the shot.
- Inversely proportional to angle A as shown.

Therefore,

### C.Q.I = cos(A)/D*P

Where, A is the angle between the line joining the centres of the two goals and the line joining the centre of the goal to the point from where the shot is taken. D is the distance between the centre of the goal and the point from where the shot is taken. P is the number of opposition players close to the player when the shot was taken. It is to be noted that Cos of the angle A is taken because, due to the property of the Cos function, as A increases, Cos(A) decreases and that is exactly what we need.

## The Ade”Can’t hit a barn door”bayor problem:

If you rewind a few seasons back to the 2008-09 season, you would realize that Arsenal lost 6 games, drew 12 and finished fourth. Teams that we lost to included Fulham, Hull City, Aston Villa and Manchester City. All of them won by a one goal margin (except for Man City) and all the games were dominated by Arsenal, in regards to possession. The number of shots taken by Arsenal also outnumbered the other teams, but the other teams just sat deep and chose the right moment to counter attack and create chances which had a high C.Q.I rating (statistics have shown that 43% of the chances created from transitions get converted to goals). At that time, everyone were busy criticizing the finishing of the Arsenal strikers like Emmanuel Adebayor and the inability of our defensive midfielders to stop perform better and not concede(Alex Song and Denilson), when the actual problem was that Arsenal lacked the creative firepower to breakdown teams and create high quality chances. A study on the recently concluded Barca-Milan game showed that, while Barca dominated possession(65%) and had 18 shots on target compared to Milan’s six, Milan had the best opportunity to score in the game, with a shot that had a C.Q.I rating of 0.08(which looks like a small number, but is actually higher than other shots).

## How can the C.Q.I be of help?

A higher C.Q.I pass means a better chance of scoring. So, players who create more number of C.Q.I passes are extremely valuable to the team. For example, in the Barca-Milan game, Xavi, Messi and Dani Alves created chances with high C.Q.I rating and they were also the best players on the pitch. It can also be used to analyse games and bring about changes. Iniesta wasn’t creating much, so Rodrigo Tello came on and immediately created a chance with a fairly high C.Q.I rating. It can even help develop tactics. For instance, we know that counter attacks tend to result in goals 43% of the time, so it makes sense to leave a player that creates high C.Q.I chances high up the pitch (like Messi). ‘The Invincibles’ Arsenal team had great players like Dennis Bergkamp, Thierry Henry and Robert Pires who created chances with high C.Q.I and won games playing counter attacking football.

## Conclusion

So often coaches have bemoaned the loss of a game which they felt they had deserved but succumbed because the other team just purely finished their chances. It happened last night with Barcelona claiming they should have won when in fact, they failed to create a better chance than Milan which was fired over by Robinho early on. Indeed, one article after the game questioned why Robinho regularly gets picked even though he hits the target with 44% of his shots and misses some great chances to boot (Ibrahimovic has 60%; El Shaarawy’s, Pato 52%). (As it turned out, the author concluded that goals are not everything as Robinho causes trouble with his movement – and that’s what creates chances for Milan).

While in it’s infancy (give us the funding!), Chance Quality Index has it’s merits if anything to challenge the established conceptions of chances and the likelihood of winning a game. Indeed, it was Wenger who once remarked, “the measure of football is the ratio of chances created to chances conceded” and that he concluded means Arsenal deserve to win the game as they have dominated. This is surely dependent on the quality of chances you create, is it not?

If that is true, however, then Arsenal should follow the route of Barcelona who believe possession is “nine-tenths” of the game. That should ensure Arsenal keep down the number of shots they concede which is currently at 10 per game in the league (and consequently, help them press better) – Barcelona’s is 7 despite both teams creating on average 17 shots per game. But that is patently not Arséne Wenger’s style as he says he’d rather a player who takes in a risk in their passing in the final third than play it safe – for Barcelona, it’s all about the quality of the chance. Wenger prefers urgency and while we are seeing a better drilled Arsenal this part of the season, the fact that they have gone down in half of the games recently, shows there’s gaps in the system.

It’s unfortunate Milan-Barcelona yielded no goals; it seemed the perfect encounter to experiment CQI because it carried with it, the old adage that possession (for Barcelona) should equal chances and consequently, a win – but that’s not necessarily the case. In fact, good chances are harder to come by when defences defend deep as Milan did because the attacking team is hindered by a lack of time and space. Milan on the other hand, had less chances but the best one on the night as Robinho fired over. Had the chance fell to Ibrahimovic, it might have gone in. That’s one of the issues with C.Q.I; it’s still subjective as much as it tries to quantify the art of the chance. Because some players are much more composed in front of goal. Take for instance, Thierry Henry’s goal against Leeds in the FA Cup; for some players, the chance may be harder due to the angle, the defender haring down on Henry’s back and not to mention the technique. But such was the familiarity of him in that position, it was almost a 10 out of 10 chance. It’s notable that in the game against Milan, coincidentally enough, Wenger altered the system so Henry could get into such situations. But it’s probably not the varying expertise of the player taking the shot that’s most important with the Henry chance; sometimes the angled shot IS the optimal way to score.

Back to the goalless draw at the San Siro, Pep Guardiola might have argued that his side deserved to win but Milan might have been the most aggrieved as a shot in the third minute flew over. It proved pivotal.

Filed under: Statistics

Tagged: adebayor, Barcelona, CQI, Statistics, Strikers

I’m intrigued about the use of CQI for more easily to qunatify chances i.e. free-kicks. The two by van Persie below – to the right, outside the box, are the only two he scored in 2011. Might the angle be the optimal way to score?

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kv Reply:

March 30th, 2012 at 7:31 am

@The Brain,

I read a statistic somewhere that said that only around two in 25 free kicks get converted to a goal. Free kicks are pretty tough to score from and even the specialists miss a lot of them. But they can be used to deliver high CQI crosses.

Regarding angle, I am not too sure. Some players like Henry and Walcott might prefer the angle, others might not be too adept at it. The logic I used is, if you are at a tight angle, the near post would be covered by the keeper, so the rest of the goal is the target. The keeper is going to try and dive in that direction and it also requires more ability to score from that angle. If you take that Henry goal against Leeds, the pass was good from Song, but it wouldn’t get the best rating from CQI as it was at the edge of the box, at an angle and Henry was surrounded by a few players. But the finishing would get a 10 on 10 because he converted a tough chance and made it look easy, whereas someone else like Gervinho wouldn’t have scored. It is important to segregate finishing from the quality of the pass.

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A few weeks ago I decided to use WhoScored.com to research the predictive value of statistics like possession, shots, shots on target and so on. A football match is seemingly a very random thing. For Arsenal this season, amount of possession explained about 15 % of the variation in results. Arsenal’s number of shots minus those of the opposition, explained equally much, while the best predictor was shots on target (minus opposition SoT), explaining 25 % of the variation.

When I however looked at the correlation between number of league points and those kinds of measures, the correlations were quite a bit larger. You had average possession explaining 44 % of variation, shots per game 47 %, shots conceded per game 46 %, dribbles per game 27 %. It was interesting to note that when I tried measuring chance quality by dividing shots on target with shots, I found that to explain 41 % of the variation as well. And the best predictor? Hands down number of shots on target per game, which explained 65 % of the variation.

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Really interesting post, i hope its okay for a Villa fan to contribute. Apart from wondering how you would get some of the numbers, like how many players surround the player when a shot is taken, I was wondering about the angle of the shot. Im not so strong on maths, especially the cos function, i think i copied the girl next to me most of the time, so bear with me and sorry for maybe asking very obvious questions:

Why do you choose not to draw two lines from the goal posts out to where the shot is taken? That should then give you an angle which would become tighter the closer the player was to the byline (of course this might be what the cosine function does for you), as well as a triangle.

Within that created triangle it would be fair to say that any players in its area would be capable of blocking a shot on goal, although maybe players just outside the triangle would need to be included as players have the potential to curl the ball outside the imaginary triangle.

As you say in the post, its a shame that there were no goals in the AC-Barca game which wouldve meant the maths couldve be seen working. Anyways, its very interesting premise. Best of luck, and sorry if my post makes you slap your forehead in frustration and say “What a plonker”, haha.

UpTheVilla 😉

Tom

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benhan Reply:

March 30th, 2012 at 4:53 am

@UTVilla,

Haven’t done the math yet but your idea is interesting.

By drawing line from both goal posts to the ball, we can form a triangle. The angle of the triangle from the ball side will increase when moving nearer to the goal line and decrease when moving to the byline. And the number of opponent players inside the triangle certainly a factor in quality of chances. It defines “surrounding players” better.

I think this could work better than the original post idea. Someone please do the math to see if this idea is workable.

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kv Reply:

March 30th, 2012 at 7:17 am

@UTVilla,

That is actually a brilliant way to measure the angle! It does exactly what the cos function does, without making the values small. Lets say the angle is 45, then using this method, you will get the numerator to be 45(the angle), then in mine it will be 0.707. I chose the cos function because, at that moment when I was trying to find a way to get angle to vary inversely with C.Q.I, the cos function was the only one that came to my mind. If you see the cos graph, you will note how the value decreases gradually from 0 degrees to 90 degrees. Of course, if you think cos function gives too much of a mathematical feel to the formula, you can ditch it for your method!

Regarding the number of players surrounding the player, I had lots of problems with deciding on the proper definition, but settled on deciding for each shot how many were in a position to limit his chances. Far from a clear definition, but the C.Q.I is still a work in progress!

Your comment definitely didn’t make me slap my forehead in frustration, it actually made me say, “Wow! That’s a great method!” Thanks for the appreciation, means a lot!

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UTVilla Reply:

March 30th, 2012 at 1:31 pm

@kv, Good to hear it was of some use. I was thinking about it more this morning. Once you have software to measure where shots are taken you would only need to transfer those onto a grid(representing the pitch), x as the width, y the vertical distance from the goal line, which would give you a coordinate (xy). With the two fixed points being the post it would be easy (i imagine), to write a formula to calculate the angle of the triangle at xy.

I worked out (i think its accurate) that the angle created from a penalty would be 38.86degrees. Obviously there would be just one player within that triangle when the penalty is taken (the keeper). Im not clear on how you would then use that to rate the chance though, i think a keeper would need to be given a special value as he can use his hands and it wouldnt be as accurate to class him as the same as a defender. It might be worth creating two extreme scenarios;

The easiest chance: A chance from <1yard with no players in the way.

Most difficult chance: A chance from the corner flag with 22players in the way.

The second scenario is very unlikely to happen but it will give you the two extremes from which a sliding scale could begin to take shape.

I do think you will have difficulties when it comes to headers for instance, or when a player shoots with his unfavoured foot. Also the proximity of the opposing players to the player taking the shot, especially the proximity of the keeper, as it will affect the chance, although you find something interesting, like a keeper can get too close.

Its fascinating though, best of luck going forward and keep us posted.

Tom

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kv Reply:

March 30th, 2012 at 8:08 pm

@UTVilla,

Thanks for the insight! Will get back to you if there are any further developments.

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UTVilla Reply:

March 31st, 2012 at 12:28 am

@kv, Remember me when you crack the formula for CQI and become rich 😉

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kv Reply:

March 31st, 2012 at 4:29 am

@UTVilla,

Haha! Yeah sure, but that is highly improbable I guess!

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yes, i agree with the analysis. but i would like to add, players who able to score when presented with low CQI point would be as valuable as those who create it. take van persie for example, his goal against barca last season & this season at liverpool. both were very difficult chances but he nailed it. another was against spurs where he turns 2 defenders and managed to avoid scoot parker to curl it home.

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kv Reply:

March 30th, 2012 at 8:13 pm

@g0on3r,

Sure, that was going to be one of the points I was going to write about, not sure how I missed that. Even the Henry goal against Leeds was a great finish as he converted a low CQI chance into a goal and made it look like child’s play.

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“But that is patently not Arséne Wenger’s style as he says he’d rather a player who takes in a risk in their passing in the final third than play it safe – for Barcelona, it’s all about the quality of the chance.”

I’m a little confused about what you’re saying here. Wouldn’t a player who takes risks provide better CQI, since presumably they would play it before the defense are able to act? They may create fewer chances overall, but wouldn’t the quality be higher?

This is certainly a really interesting concept. I think that there hasn’t been enough work done in soccer statistics to determine the kind of predictive work that CQI seems to be. Obviously, you haven’t fleshed out all of the specifics, but things I would suggest looking at would include angle/speed of the pass needs to be taken into account (I would imagine faster is better on crosses, slower is better on ground passes, analyzing the angle of RVP’s volley vs Everton, etc), and perhaps being more specific on how the values for A, D, and P change based upon their own values as well as how it differs for the values of other players (i.e., perhaps more players around the player might increase the chance quality because the keeper can’t see the ball, etc, or is being 2 yards out really twice as bad as being 1 yard out). If possible, I’d also like to see something showing the CQI of various goals to see how well it correlates in a future article. But still, great work so far – it’s always nice to see innovation in analysis (speaking from someone who follows statistical analysis of American baseball as a hobby).

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kv Reply:

March 30th, 2012 at 7:47 am

@William,

Thanks for the comment!

Yes I do agree with you on risky passing producing greater quality passes in the final third. However, that will also lead to us conceding high C.Q.I chances on the counter attack.

I know, I haven’t really sketched out all the specifics properly. But aspects like angle and speed requires a lot of resources and statistics, which are not available right now. What I did was based on what I saw on TV, marking the shots on a paper and trying to scale them according to the real pitch dimensions. If we have access to more statistics, I’m sure we’ll be able to chalk out a better model which takes into account all the specifics you mention.

I tried to calculate the CQI for the Barca-Milan match, but was not entirely successful. I promise to do a proper one for the game against QPR and post it up. Tbh, calculating the C.Q.I without the statistics required is a bit of a pain.

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It is too simplistic to say that the only factors that define the quality of the chance are distance, angle and number of players in front of you. For example, even angle is not necessarily inversely proportional. Classic example is Walcott. You give it to him at an angle and he will usually stick it in. If you release him straight through on goal, he will almost definitely miss. Long range shots especially are easy to score at an angle.

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Great analysis. I was working on the same thing, but eventually reavhed the conclusion, that the measurement of the chance is far more complicated and many additional factors must be taken into consideration. For example here is some tips, that i stumbled upon while doing the same research:

1. The header is far more sensitive on the distance to the goal, than a shot. While the shot is altered greater by the number of blocking players, than the header. So I decided to try and put some weight on both of them, but ultimately failed.

2. The blocking players factor is great, but there is also a “putting pressure” player factor. A defender can be at the back of the player or sideways, but if hi is approaching him fast, it puts the striker under pressure and gives him less time to react.

3. I decided to evaluate the shots, rather than the chance, because the chance itself is kind of tricky. When the chance starts? If a payer frees himself with a feint and loses his mark, when actually the chance starts? At the beggining of the feint, or at the moment, the shot is fired?

Anyways, great work, keep it up :). By the way, I would like to know your twitter.

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kv Reply:

March 30th, 2012 at 8:33 pm

@Mishok,

Hi!

I don’t agree with you when you say that the blocking players factor doesn’t play a big role when it comes to headers. If you ask me, it plays a more important role, as heading is all about getting into the right position and timing your leap properly to head the ball before others. So more the players surrounding you, less space you have and tougher it is to get under the ball.

Other than that, I agree with all your points. But it’s important to keep the formula as simple as possible. It’s hard to accommodate everything into it. But that’s the challenge isn’t it?

I’m glad you enjoyed the article! Unfortunately, I don’t use my twitter account regularly(facebook is more popular where I live). Thanks!

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Good point all around, but I’m thinking if CQI does get implemented, a goals-per-game ratio for the one taking the chance should be taken into consideration as well (into the equation, making it something a little more complete).

Also, one thing that should be added (if it could) to the equation is the distance of the closest opposing player to the player who receives the key pass (probably hard to implement though).

And besides, I think the CQI’s ‘fallibility’ shouldn’t be taken too seriously, the way we don’t take Szczesny’s goalkeeping stats (worse than Friedel last time I read) too seriously when considering his ability as a goalkeeper.

And besides, Henry’s goal against Leeds was pure quality. For any striker at all, it would’ve been hard to score from there and you’ve got to give credit where it’s due, Henry was phenomenal at that moment. It’s a hard chance to convert, so should correspondingly be given a low CQI value. The equation is just about right at this moment and would really give a lot more perspective to the current stats flying around.

Cheers

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Good work Karthik,

Whilst trying to formulate my own model I was surveying the literature and Reep & Pollard (2002) “Measuring the effectiveness of playing strategies at soccer” also make a stab at a CQI that has some good features.

The people at StatDNA have also attempted a model that has some good features, heres the link.

http://blog.statdna.com/post/2011/03/29/What-determines-shot-quality.aspx

It seems to me though, that if the football community were to take up some form of CQI it would need to be (a) easy to use (b) not require too much input (c) yield clear and understandable ratings (3 out of 5 CQI sounds clearer than 58.45 CQI).

To be honest my CQI was gathering dust whilst I’ve been trying to find a way to measure how detrimental a fluctuating back line is (its impossible! lol), but you have inspired me to plough on, it would be great to share some ideas on the CQI if your up for it.

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kv Reply:

April 1st, 2012 at 9:18 am

Hi Joel!

I went through the StatDNA model, it’s good but they seem to have included too many features which makes it hard to put together into a formula. One important factor they have ignored is angle and I think angle plays a major role in quality of a shot.

One major flaw in my formula is the lack of a constant term. The formula without the constant doesn’t tell us exactly by how much CQI varies with angle, distance and players surrounding the shooter. Other drawback as you say is that the formula never gives a whole numbered value. So the next step would be to include a constant term and possibly another factor(if required). But then, that is the hard part, as we don’t have the stats to study the impact of the factors and come up with a constant term.

Is your model of CQI similar to this one? Maybe we can do a combined study for the updated version of CQI(if you are interested that is)… To tell you the truth, I started thinking about CQI only after AC and you had the discussion in one of the older posts, so thanks!

Btw, that bit on fluctuating back line sounds interesting. What is that about?

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Yeah the StatDNA one is needlessly convoluted.

“But then, that is the hard part, as we don’t have the stats to study the impact of the factors and come up with a constant term”

There us some work on this in the Pollard and Reep (1997) paper, they estimated that the scoring probability is 24% higher for every yard nearer goal and the scoring probability doubles when a player manages to be over 1 yard from an opponent when shooting the ball. I think they studied over a 1000 goals to get to these figures so the percentages can probably be trusted.

My model is a cross between the parameters I put forward in the earlier thread and Arsenal Columns more intuitive approach. The more simple the model the less precise it becomes, yet anything that differentiates the broad category of ‘shots on goal’ into some kind of spectrum is worthwhile, regardless of precision. Are you doing an updated version?

Oh yeah, perhaps ‘fluctuating’ was the wrong word. I suspected that some of Arsenal’s defensive problems stemmed from the lack of stability in the back four line-up, since arguably the most important feature of a defence is mutual understanding built up over time. I found that Arsenals back line had gone through 22 different combinations, whereas Manchester City had only used 13 different combinations. The problem is I couldn’t find a framework to ‘prove’ the correlation between defensive records and back line stability since defence is contingent on so many variables.

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[…] and a long-range effort. The areas where he is getting shots away from are not high on the chance quality index. Robin van Persie gets the ball in good shooting locations against Wigan, but is unable to get […]

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[…] What Wigan are able to do is limit his shooting from these areas on the left where he receives a lot of passes, blocking one of his shots and not allowing any others. Van Persie does get one shot away inside the area from the right side, but it goes wide. His other two strikes at goal in the game come from outside the box from a free-kick and a long-range effort. The areas where he is getting shots away from are not high on the chance quality index. […]

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Here’s OPTA’s study on chance quality. Have a looksie and tell me what you think: http://www.optasportspro.com/en/about/optapro-blog/posts/2012/blog-assessing-the-performance-of-premier-league-goalscorers.aspx

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kv Reply:

May 16th, 2012 at 2:14 pm

@Arsenal Column,

I think it’s a great article. However, I do feel they could have made it slightly simpler and it would have been better if they had specified the mechanics of the xG formula. It does confirm our analysis though, but it seems they haven’t used the number of players parameter, which can have a big impact on chance quality. For example, liverpool create shots that are very close to the goal, but still Luis Suarez fails to score, which could be because the penalty box is crowded at that point. But if OPTA can’t record those kind of stats, who else can?!

The challenge is to get the formula to give out whole numbers, which will make it an attractive stat to use. Their method seems to be better than ours at doing that, but I am sure even we could have done something similar, if we had access to data like them.

Do you really think liverpool’s attackers have been that bad or do you feel they haven’t created enough high quality chances?

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