Fun with shot percentages

While putting together some numbers for my previous post, I was a little curious to see what sorts of numbers were considered good, what was average, and what was not so good. I listed two different percentages, which I meant to explain a bit more, so I might as well do it here: SH % is the ratio of goals to shots taken. SG % is the ratio of goals to shots on target. A third ratio, we'll call SA % (for shot accuracy), relates the two - this is the percentage of total shots that ended up on target.


My suspicion was that SA % varies from player to player, while SG % is relatively constant. Whether or not a shot is on target is largely up to the shooter. Whether or not that shot goes in the net depends on much more - goalkeeper, the posts, defenders, etc. To find out, I added up the total number of goals, shots, and shots on target for every player in the Premier League over the past two seasons:

Season	G	SH	SG	SH %	SG %	SA %
2006/07	894	9133	4362	0.098	0.205	0.478
2007/08	924	8837	4547	0.105	0.203	0.515

The SG % didn't change much, but the SA % did. Pretty much what I expected. The league average save percentage for goalkeepers last season was just over 68%, which accounts for most of the non-goal scoring shots on target - the others being things like the posts/crossbar (especially when you hit it 3 times), blocks by other defenders, and referees who hate David Healy.


Now, if we look at individual players, the SG % actually does vary quite a bit. This suggests that some players shots are more difficult to save than others, which is definitely something I would expect, but the variance was more than I thought it would be. Below are all players who scored 5 or more goals in each of the past two seasons. In the interest of larger sample size, each player's numbers include seasons prior to 06/07, if available:

Name		SH %	SG %	SA %
McCarthy	0.250	0.422	0.593
Doyle		0.195	0.398	0.489
Viduka	0.243	0.396	0.615
Keane		0.231	0.385	0.600
Yakubu	0.202	0.368	0.550
Drogba	0.167	0.352	0.475
Adebayor	0.203	0.343	0.593
A. Johnson	0.219	0.342	0.641
Barry		0.149	0.326	0.455
Bent		0.188	0.321	0.586
Cahill	0.169	0.290	0.582
Agbonlahor	0.174	0.288	0.603
Kalou		0.163	0.280	0.581
Saha		0.145	0.265	0.547
Martins	0.127	0.256	0.497
Berbatov	0.151	0.255	0.592
Mwaruwari	0.153	0.247	0.618
Van Persie	0.133	0.246	0.540
Tevez		0.124	0.231	0.535
Defoe		0.143	0.231	0.618
Crouch	0.127	0.224	0.567
Anelka	0.136	0.223	0.611
Lampard	0.110	0.211	0.523
Ronaldo	0.101	0.203	0.499
Rooney	0.109	0.192	0.567
Gerrard	0.093	0.183	0.509

Most of these players are above the league average, but some are consistently far above that standard. Benni McCarthy, Robbie Keane, and Mark Viduka have been above 30% for just about all of their careers. Emmanuel Adebayor, Didier Drogba, Ayegbani Yakubu, and Kevin Doyle have been very close. Out of curiosity, I also looked at some leading strikers in foreign leagues. Luca Toni, Karim Benzema, Djibril Cisse, Daniel Güiza, David Villa, Alessandro Del Piero and David Trezeguet, as well as many others, are not only consistently above 30%, but have finished the season over 40% in most cases. In fact, even many of England's top scorers (Adebayor, Fernando Torres, Roque Santa Cruz, Robbie Keane) fell into this 30% or higher club. The league's top scorer, Cristiano Ronaldo, seems to suffer from a bit of Kobe Bryant syndrome - take a zillion shots regardless of quality, and you're bound to score a bunch. Interestingly, Man Utd's other leading scorers, Carlos Tevez and Wayne Rooney, seem to follow this strategy.


What is the point of all of this? I believe it can help in telling us which players are the best finishers, the best pure goal scorers. Not necessarily the best forwards - obviously, Dimitar Berbatov and Carlos Tevez are great players who excel at creating lots of their own chances - but this is a big part of the equation. We can see which players thrive when provided with quality service from the midfield. More or less, which players would do well for a team like Arsenal. With Fulham's growing stockpile of quality attacking midfield players, it would appear that this is the direction Roy is taking us. Signing players from this group would make a lot of sense.


Best of all, there are players who may be available, and in our price range! In England, Kevin Doyle is the most realistic target. He had poor season in 07/08 after a very strong 06/07, but his past history for both Reading and the Republic of Ireland suggest that last season may have been a fluke. He's probably the biggest risk of the bunch, but also the cheapest. Benni McCarthy is getting older, but he's had two very good seasons since moving to England, and likely has a few more left in him. A few others who aren't on the above list include Man City's Rolando Bianchi (.229 SH/.500 SG split between City and Lazio) and Marlon Harewood (.238/.417 in 07/08; .181/.369 career), both of whom I believe to be obtainable.


One more note - a lot of this depends on how a player is used. It seems clear that Man Utd's coaches encourage players to shoot on sight. As such, a player like Louis Saha, who I would have expected to score better on this scale, varies quite a bit from year to year:

Season	SH %	SG %
02/03		0.135	0.227
04/05		0.059	0.111
05/06		0.167	0.412
06/07		0.123	0.195
07/08		0.278	0.556

Some players vary quite a bit when changing clubs. Take Darren Bent:

Season	SH %	SG %
05/06		0.247	0.450
06/07		0.212	0.412
07/08		0.167	0.286

Tottenham seems to do things in a similar fashion as Man Utd, so it make sense that Bent's numbers last season would look more like Berbatov and Defoe's numbers (and what does that say about Robbie Keane? One could make a strong case for him as one of the more underrated players in the league). Djibril Cisse is another who looked like a completely new player after moving from Liverpool to Marseille. Again, there are other key qualities that are important for strikers, but this tells us something about who the best pure finishers are. And more often than not, those players score a ton of goals.

Last night, I was laying in

Last night, I was laying in bed thinking about all of this, and how something just doesn't add up. So as a test, I took the 26 players in the list above, and calculated how many goals each would have scored if they all attempted 100 shots:

Name		SH %	SG %	SA %	ISO	SH	SG	G
McCarthy	0.250	0.422	0.593	0.172	100	59.3	25.025
Viduka		0.243	0.396	0.615	0.153	100	61.5	24.354
Keane		0.231	0.385	0.600	0.154	100	60	23.100
Johnson		0.219	0.342	0.641	0.123	100	64.1	21.922
Adebayor	0.203	0.343	0.593	0.140	100	59.3	20.340
Yakubu		0.202	0.368	0.550	0.166	100	55	20.240
Doyle		0.195	0.398	0.489	0.203	100	48.9	19.462
Bent		0.188	0.321	0.586	0.133	100	58.6	18.811
Agbonlahor	0.174	0.288	0.603	0.114	100	60.3	17.366
Cahill		0.169	0.290	0.582	0.121	100	58.2	16.878
Drogba		0.167	0.352	0.475	0.185	100	47.5	16.720
Kalou		0.163	0.280	0.581	0.117	100	58.1	16.268
Mwaruwari	0.153	0.247	0.618	0.094	100	61.8	15.265
Berbatov	0.151	0.255	0.592	0.104	100	59.2	15.096
Barry		0.149	0.326	0.455	0.177	100	45.5	14.833
Saha		0.145	0.265	0.547	0.120	100	54.7	14.496
Defoe		0.143	0.231	0.618	0.088	100	61.8	14.276
Anelka		0.136	0.223	0.611	0.087	100	61.1	13.625
Van Persie	0.133	0.246	0.540	0.113	100	54	13.284
Martins		0.127	0.256	0.497	0.129	100	49.7	12.723
Crouch		0.127	0.224	0.567	0.097	100	56.7	12.701
Tevez		0.124	0.231	0.535	0.107	100	53.5	12.359
Lampard		0.110	0.211	0.523	0.101	100	52.3	11.035
Rooney		0.109	0.192	0.567	0.083	100	56.7	10.886
Ronaldo		0.101	0.203	0.499	0.102	100	49.9	10.130
Gerrard		0.093	0.183	0.509	0.090	100	50.9	9.315

SG (total shots on target) is 100 multiplied by SA %, and G is the resulting number of goals. Same order and everything.

ronaldo really must have

ronaldo really must have shot a lot!

Yep, 181 to be exact! David

Yep, 181 to be exact! David Bentley was second with a mere 115. He's taken a ton ridiculous number of shots, but as more of a midfield player, those are bound to be rather low-percentage shots, so his percentages are still impressive. In 06/07, he scored 17 on 200 shots (and had a similar rate in 05/06), so he's either improved quite a bit, or was really lucky last year.

Aha, fantastic. I'd argue

Aha, fantastic.

I'd argue that SH is the most important, the goals per total shots, as if a player's going to shoot 3 times a game we need to know how many of those will go in, and, if that player is then upgraded, how much difference, all being equal, that will make.

You can't transpose like that, I don't think, but suppose Andy Johnson scores .219 per shot and your team are going to create three shots per game for him:

SH---shots-glpg---g-----total g
0.22 3 0.66 38 24.97
0.14 3 0.42 38 15.96

Technically, and this is too literal, the advantage of Andy Johnson over Jermain Defoe (.14) is about nine goals a season, which is probably worth nine points to a team like us (he says, making it up). Now we don't know if either SH% represents a true talent level, or how much falls under natural variance, but now we're onto something I think.

The thing here I guess is that we need to see what season on season reliability is for most players. Does it swing all over the place, or, as you've suggested, is it dependent on the club? And if we spot seasons that are unusual, are they flukes, a change in the player's teammates, an improvement in the player himself. And does this mean that Darren Bent's form is a result of the style of play, and that he should be shooting less?

There's a lot to think about here isn't there?!

Great stuff...
Rich

I was thinking kind of along

I was thinking kind of along the same lines at first, but then got a bit side-tracked and ended up in going in a different direction with this. I was hoping to find that shot accuracy (on target vs off target) was the important thing, and that most players had a similar percentage of shots on target that went in....kind of like what you said about BABIP. This is true to some extent, but it seems that the shooters do have more control over this than hitters in baseball. Consistency from year to year, I think, definitely can tell us something about the player. Most of these players weren't too far off from one year to the next, even when changing clubs. Viduka and Yakubu put in quality shots no matter who they play for. Darren Bent's weird season with Spurs may just be a result of small samples, but it also could have been a change in style or luck. I suppose Bent is one of those cases where an all-out Moneyball analysis won't work, and the numbers need to be supplemented with scouting. Other players, I think you can safely look at the stats and know just what you're going to get. It would be great to look at Ligue 1 and identify a Scott Hatteberg rotting on the bench at Saint-Étienne.

I'd also like to think that the relationship between the two shot percentages can tell us something about luck. I've been playing with it a bit, and I'm not entirely sure what to make of it all yet, but some calculations would indicate that Andy Johnson in 07/08 was the most unlucky of the bunch listed above. That makes me hopeful...but can a player be both overrated and underrated at the same time? On the other hand, all of those penalties could have messed things up quite a bit.

Those are some interesting

Those are some interesting numbers indeed. And great to see Johnson up there. How does Zamora look?

What the numbers don't capture is where the shots were taken from. So they don't really get at a player's "finishing" ability. The players low on your list like Ronaldo, Gerrard and Lampard are all edge of the box shooters, often creating goals out of nothing. To a large extent, those at the top of the list are strikers scoring from inside the box after being put through by someone else. If there was any way to distinguish where shots were taken from (e.g. six yard, penalty area not six yard, outside the box) you'd get a much better picture I reckon. Looking at those stats you may even be able to find midfielders who'd be better as strikers or to understand why certain goalscoring midfielders would never make good strikers (I'm thinking David Platt and Paul Scholes here). You could also use them to highlight strikers who are wasting their talent popping off shots from all angles when they should be conserving their energy and waiting for the right opportunity. (I remember this is something that Vialli told the other Chelsea strikers to do when he first arrived at Chelsea -- apparently they were always wasting their energy trying to do too much -- it would be interesting to see whether that is reflected in statistical form).

Ah yes, some very good

Ah yes, some very good observations. I've found that, with most football stats, it generally works best to compare players at the same position (and in some cases, its best to stay within a team). Like you said, the midfielders on the list take their shots from further outside the box - Ronaldo, as far down the list as he is, was actually quite good when compared with other midfielders. Gareth Barry might be one who would thrive as a striker.

I touched on this a bit in another commment, but I think that tactics and coaching instructions do play a big part here as well. A lot was made of Man Utd's 4-6-0 with Rooney and Tevez played in a more withdrawn role, and I think that shows up here. Another factor may be in coaches that employ a "shoot on sight" policy. It would appear that Spurs were doing this, and Chelsea seemed to shoot a lot more under Avram Grant - I can't find any team totals for shots at the moment, but I'll see if I can dig those up.

"It would be great to look

"It would be great to look at Ligue 1 and identify a Scott Hatteberg rotting on the bench at Saint-Étienne."

Surely his football equivalent would be someone who got all his shots on target (i.e. got on base) no matter what, but who rarely actually scores (i.e. hit for extra bases)!? Not quite what I'd be looking for in a striker. The football equivalent of Hatteberg would more likely be defensive midfielders like Makalele, Batty, or Carrick; players who keep it simple and keep the engine running with their incredible passing percentages from in front of the back-four.

Hmm, perhaps our own Danny

Hmm, perhaps our own Danny Murphy would fit the bill? Not necessarily a natural defensive player, but his passing in front of the back four was precise, dependable and often went unnoticed and unappreciated.

Exactly the kind of guy I'm

Exactly the kind of guy I'm talking about. Boring and unnoticed but solid and dependable. I reckon that Davis could turn into this type of player. Problem last season was he was largely just "boring and unnoticed" and crap.

Just returning to your

Just returning to your comment about luck. As someone who is just getting into baseball stats through fantasy there is something I've never understood about the supposed correlation between BABIP and luck. It strikes me that there are a bunch of reasons other than luck that a player would have a low BABIP (he's bad, is in bad form so struggles to find the gaps, struggles to hit lefties or righties, is called upon to bunt a lot) or a high BABIP (he hits with a lot of power, he doesn't hit with a lot of power but is a singles/doubles specialist, is in good form, etc.).

So I've never really understood why experts believe that all players trend towards a certain average (it's .285 or something right?). Certainly comparing a player's seasonal BABIP against his historical BABIP can yield an argument that a player has been unlucky. But that conclusion can only be drawn by taking into account a subjective analysis of his game to ensure that the player's not doing anything different to past seasons.

It is here that your stats are useful, and I don't think it matters that you haven't come up with a wholesale trend number for SG. Your stats are useful as a jumping off point for a focussed analysis of a player's game (what is Bent doing differently season by season? did he struggle? were most of his goals scored in bunches? if so, what was his SG% in those months/periods when he was scoring?). That's the advantage that stats give. They will never give the whole answer, but their objectivity can constrain and focus the qualitative analysis that is necessary to give the bigger picture.

I would suggest that you don't abandon SG% but rather try to deepen it with month-by-month historical analysis (if available) and then track a certain player through a season or two to see whether you are able to use periodic SG% variance to understand when and how the player improves his game.

Also, I'm no mathematician,

Also, I'm no mathematician, but surely if you wanted to come up with a trend number you could just take and average of the BABIPs of all the strikers each season and see if that average is reproduced season on season. I bet you'd find that it was.

I would agree with that. The

I would agree with that. The percentages across the league for all players was very consistent between seasons, and I've found that to be the case in other countries as well. I'd imagine that including only strikers would yield similar results, if not even more consistent.

You would expect that hitters

You would expect that hitters have more control over that, wouldn't you? I would. Voros McCracken (here is one of his early articles on this) is the guy behind some of the original studies, which show that defence and luck has the greatest effect on BABIP. There are tons of opinions on the matter though - some say that good line-drive hitters will always have a higher BABIP, others say that some pitches are better at preventing "good" contact. I think they're all right, to some extent. If a hitter consistently has a high BABIP, he's probably doing something right. If it varies from season to season, there is a good possibility that some luck is involved. Or, like you said, the player is doing something differently. Scouting is still important!

I was thinking about doing a more focused look at some of the stranger players I listed. Bent is a good one, and so is Saha. I'm very curious to see if these players do tend to more score in bunches, or in specific situations. Counting minutes between goals (and analyzing those) and month-by-month splits over multiple seasons seem like they may be a good start.

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