Goal And Shot Ratios: The Bundesliga Update

One of the notable features of Bundesliga play this season has been the relatively high goal to shot ratio in the league. This raises the question of which teams contribute to this trend, and which teams are underperforming. I also thought it might be interesting to look at the other shot ratios to see if we can pick up differences across teams in their patterns of accuracy and efficiency.

So here are the goal and shot ratios in the Bundesliga as of Oct.18, rank ordered by teams' goal to shot ratio.

We see that Wolfsburg, Mainz, and Hoffenheim lead the pack in terms of goal to shot ratios at close to .2. And surprisingly, Bayern Munich brings up the rear at well below .1. If you take a look at the maroon bars, you'll see at least one explanation for Mainz's magical season, and Bayern and Koeln's dismal campaigns so far: it's all about conversion! While Bayern and Cologne are generating reasonable accuracy ratios, they are not converting as well as they need to. Their conversion rates less than half of Mainz (at >.4). 

The data also show that Freiburg's success so far this year is in large part a function of conversion efficiency, not accuracy. In contrast, Moenchengladbach's accuracy is up there with the best of the league at about the same level as Mainz, but their conversion rates are more lower. Let's see if Mainz can hold on, and whether Bayern, Koeln, and Gladbach can bring up their efficiency rates. 

Finally, perhaps the most puzzling data points have to do with Schalke's performance. They shouldn't be where they are in the league table; and yet they are. I'm sure Felix Magath would like to know why, too!

Goal and Shot Ratios: The Big 4 Leagues Update

Here's another quick update on where the leagues stand roughly a quarter into the season, as of Oct.18, 2010. This time, let's take a look at goal and shot ratios.

Remember that the leagues typically are very similar in goal and shot ratios, with the exception that the Premier League tends to have more accurate shooters (the rate at which shots on goal, SOG, find their target), but lower conversion rates (the rate at which shots on target, SOT's, translate into goals).

We can see that play in the four best leagues continues to be roughly similar. As noted in a recent post, the goal to shot ratio continues to be roughly similar across the leagues this year, as it has in the recent past, with the one exception that Bundesliga shooters are finding their targets at a higher rate so far this year than in other years.

A couple of other notable features of trends so far this year: conversion rates (the goals/SOT ratios) are noticeably higher in the Bundesliga than in the other leagues, at well over .3, compared to roughly .25 in the Premier League, Serie A, and La Liga. In contrast, the EPL continues to stand out in shot accuracy, easily outpacing the other three leagues at about .5, indicating that one of every 2 shots finds the target. The reason the EPL goal/shot ratio is similar to the other leagues (not higher) is that the conversion ratio is the lowest among the four leagues. In contrast, the Bundesliga's goal/shot ratio is explained by the lower level of accuracy. So far this year, the Bundesliga and the Premiership offer the biggest contrasts in goal and shot ratios. Let's keep watching them to see if these will converge over the course of the year.

Goal To Shot Ratios: Comparing Teams Across Leagues in 2010-11

If you're a regular reader of this blog you will have noticed that one of the things I have been interested in for some time is to figure out how the leagues compare. That is, are there systematic differences across leagues in terms of style of play, offensive and defensive production, or fouls and cards? Of course, leagues are made up of teams, so another way to look at this is to compare teams across leagues. This will tell you which teams are really the best teams across Europe (well, at least across the leagues I look at). It also tells you how much variation there is across the leagues.

So following on the earlier posts about goal to shot ratios in the Premiership and across the big four leagues, here are g/s ratios for all teams so far this season.

If you ask me, what stands out is (a) how much variation there is, and (b) what a juggernaut Chelsea has been so far this year.

Regarding variation across the leagues, clearly some teams can't score a goal, even if you give them 20 shots on goal. This includes La Coruna and Osasuna who need about thirty - yes, 30! - shots to score a goal. In stark contrast, Chelsea has scored about 1 goal for every 5 shots they have taken.

How good has Chelsea been? One way to gauge this is to look at the x-axis to locate the "normal" goal to shot ratio  of .111. Clearly, a good number of teams cluster right around this long-term average value. Barca, Real Madrid, Schalke, Newcastle, or Napoli all fall into this category. But even lesser teams like Moenchengladbach or Stoke can be found here, and Bayern's mediocre season so far is clearly reflected in its ranking here. In contrast, Chelsea is (not quite but almost) twice as "good" in converting shots to goals (the average goal/shot ratio per match for Chelsea is .197 so far this year). Surprisingly, middling Wolfsburg (.184) and overachieving Mainz (.181) aren't all that far behind.

Feel free to print out the graph and ponder if over a beer or two with your friends. Let me know if you see something I missed.

Goal To Shot Ratios Across Leagues: The 2010-11 Season To Date

Here's a quick update on goal to shot ratios to date across the big leagues of European soccer. In an earlier post, I looked at these averages for the 2005-09 period. Across the Big 4 leagues, the goal/shot ratios were virtually identical and reminiscent of Charles Reep's ratio of 1 goal in nine shots on goal (.111). In fact, the picture of goal-shot ratios was so similar, you'd think these were identical leagues.

So far this year, there's a bit more differentiation. Below are the goal to shot ratios for the season so far. They show that the EPL is the league that comes closest to "Reepian" perfection. In contrast, La Liga and Serie A are significantly below, while the Bundesliga is above the historical averages. Substantively, this means that shooters in the Bundesliga are on fire - as evidenced by a number of high scoring matches (often involving Borussia Moenchengladbach for some reason) - while shooters in La Liga and Serie A are having a tougher go at it.

So, what's behind these early patterns? Some rummaging around in the data reveals that the typical home-away differences don't quite hold this year. Take a look.

Turns out that the away teams have a higher goal to shot ratio in the EPL and the Bundesliga so far this year. In contrast, home teams have a better goal to shot ratio in La Liga and Serie A, as would be expected. It's too early in the season to see if these patterns will hold (I suspect they won't), but it suggests that watching the Bundesliga this year has been a blast, offensively speaking, alongside the unexpected and exciting play of Mainz 05. Stay tuned for further updates in days to come.

EPL Goal To Shot Ratios: The Season So Far

I'm a little behind on some of my data collection for this season, but in case you were wondering where things stand so far this year on goal to shot ratios and other common metrics, I'll be providing some updates in the days ahead. So here's a first small installment to whet your appetite. This one is on goal to shot ratios (one of the stats we have Charles Reep to be thankful for).

Recall that, in the 2009-10 season, there was a fairly narrow distribution in goal/shot ratios across teams (these measure how often teams score, given the number of shots they take). In 2009-10, the EPL followed Charles Reep's 9 shot maxim (that, on average, one goal is scored for every nine shots) almost to the decimal. Reep's prediction would yield a goal to shot ratio of .111, whereas the 2009-10 EPL season yielded a .116 ratio.

Here's where we are so far this year (as of 18 October 2010).

Any surprises? Sure, if you ask me. So far Chelsea is way ahead of its pace from last year. This is something that will be hard to sustain and perhaps reflects their relatively easy schedule very early in the year. But Blackpool's record so far also stands out - who would have thought?! - along with West Brom's or Wolves. At the low end, Aston Villa and Liverpool are clearly below where they want to be and where they were last year. Over the course of the season, I'd expect a regression to the mean, with the top clubs moving closer to the .111 and for the lower ranked clubs to move up somewhat.

Stay tuned for more before too long!

Gaming the World: How Sports Are Reshaping Global Politics and Culture

Just finished reading Andrei Markovits and Lars Rensmann's Gaming the World: How Sports Are Reshaping Global Politics and Culture (Princeton University Press, 2010). I highly recommend it. It's a great read, and filled with lots of historical detail for soccer fans around the world. Fair warning: you may not agree with everything they say, but it'll make you think. My favorites: the chapters on women's soccer and on right-wing politics and hooliganism. If you want to take a sneak peek, you can find the first chapter here.

Enjoy!

Are One Goal Leads Better Than Two Goal Leads? Testing Alex Ferguson's Intuition With Some Data

After Man U gave up yet another two goal lead the other day, this time to West Bromwich, I was struck by Alex Ferguson's claim after the match that "Sometimes it is better to be one goal in front than two. You keep your focus a bit more." Well, I thought, is that really true? (and by "really" I mean "generally"). Assuming that Sir Alex's claim related to the Premiership and perhaps just his club, we can take a look at his intuition by examining the connection between halftime leads and full time results.

Below are win percentages as a function of halftime goal differences - being in front or behind - for the last five EPL seasons. Speaking generally, the data do not support Ferguson's claims. Between 2005/06 and 2009/10 the odds of winning the match are slightly greater than .7 when a team is ahead by one goal at the half, while the odds of winning the match are about .95 when a team is ahead by two goals. Thus, having a two goal lead is "better" than a one goal lead (of course, this does not deny the possibility that it is "sometimes" better).

On the flip side, the odds of winning the match are less than 10 percent for a team that is down by one goal at the half, and almost (but not quite) 0 when it is down by 2. Speaking Roughly, being up by two means an almost certain win and being down by two means almost certain defeat. This is what makes Man U's record of squandering yet another two goal lead last weekend so unusual, statistically speaking.

But perhaps Ferguson has something else in mind. Perhaps he merely meant his own club and its ability to hold a lead. So for that, I took a look at Man U's half time leads and full time results in 2009-10. Here's what the data tell us. In the 2009-10 season, Man U always won the match (the odds are 1) when the team was up at the half - by one, two, or three goals. So last season, it didn't matter whether the team was up by one or two goals - they always won the match. Moreover, even being tied still gave the team an almost 70 percent chance to winning at the end of the day. That's a remarkable set of facts and in stark contrast to this season.

Is Man U unusual in this regard? Let's take a look at the cross-town rivals Man City and the eventual league winner Chelsea for comparison purposes.

Who Got Punished? Yellow and Red Cards in 2009-10 By Teams

This post follows up on some earlier analyses of punishment in football and Wenger's hypothesis that bad teams foul more, especially when they play good teams. Because he is the manager of Arsenal, Wenger's comments are widely reported and discussed. And mind you, Wenger is a clever man, so much so that Sam Allardyce, the manager of Blackburn, accused him of trying to influence the referees. I have never met Arsene Wenger (he seems like a nice man), but I wouldn't put it past him to try and gain every advantage he can get, including subtle influences on those who are judging the game on the pitch.

As I've shown in a previous post, at least in the EPL, less successful teams indeed commit more fouls.   But do they also receive more red and yellow cards? It's one thing to be called for a foul - fouling can actually help the team by stopping a dangerous attacker, for example - but it's another to receive lots of yellow and red cards. Cumulatively, cards can put teams at a competitive disadvantage over the long haul of a season.

Below are the average numbers of red and yellow cards for the 2009-10 season across the Big Four leagues. From what I can make out, there is significant heterogeneity across teams and leagues; it is not the case that the best teams consistently receive fewer cards than the not so good ones. For every Bayern Munich that receives very few yellows there is a Leverkusen that does receive quite a few. Eyeballing the data, it seems that there is a slightly stronger tendency for less successful teams to receive more yellows in the Premier League, but this tendency is all that strong in the other leagues. Overall, Malaga and Zaragoza take the cake for the most number of yellows across the leagues (at well over 3 per match), while Fulham, Man City, Man United, Bayern, and M'Gladbach went relatively unscathed at around 1.3 yellow cards per match.

If you see a different pattern, let me know. In a future post, I'll be looking into referees and home/away differences in punishment some more. 

Are Some Leads Harder To Hold Than Others? Evidence From the English Premier League

As we head into a full weekend of fixtures after a week of international matches, a quick follow up on the question of whether leads are hard to hold. Specifically, given that leads don't seem to be all that hard to hold generally speaking, an interesting question is whether some leads are harder to hold than others. 

One way to measure how hard it is to hold leads of varying magnitude is to calculate the probability of a a team's match win, given different kinds of half-time leads. So, for example, are there differences in the probabilities of a win for a 2-1 v. a 3-2 lead, or a 2-0 v. a 4-2 lead? Let's take a look, again for the 2009-10 EPL season. Below are the win probabilities in a match as a function of halftime scores.

To read the graph, note that the numbers across the top of the panels are the goals a team scored by halftime, whereas the numbers down indicate the numbers of goals conceded by the time teams head to the locker room. So you can see and compare different kinds of half time scores: in the upper left hand corner, for example, the numbers show us that a 0-0 score yields a probability of a match win of about .25, whereas a team going into halftime at 0-1 has a win probability of only a slightly greater than 0. Once a team is down 0-2, the probability of winning is 0. Moving over one panel to the right, we can see that a team leading 1-0 has a win probability of roughly .7, whereas being tied 1-1 gives the team a win probability of about .35. 

Ok, enough about how to read this graph. Here's what stands out, if you ask me.

Are Leads Hard To Hold? Data from the 2009-10 Premier League Season

One of the things that people who don't know soccer very well sometimes ask me is why I care about a game in which scoring is so low. Never mind that score totals in American football are artificially inflated, but my answer typically is twofold. First, there's the elegance, athleticism, creativity, and sheer beauty of the game. And then there's the fact that the low scores actually make the game more exciting - since any one score, any one action or mistake on the field can make or break a team's day. This means that stakes are high, and a soccer match is like a constant dance underneath the Sword of Damocles. To me, that's pretty exciting stuff.

But back from Greek mythology to the real world of soccer. One empirical question I've been asked recently is whether leads in soccer are hard to hold. Since scoring is so low, the answer should be yes. So let's ask the data.

A good place to start is by comparing half time results with full time results. That is, what are the odds that teams with halftime leads will actually win the match? Here are the statistics for the connection between halftime leads (by number of goals - so 0 means the match is tied at halftime, 1 means that the team is up by one goal, etc.) and full time results (for wins, draws, and defeats) for all matches played during the 2009-10 Premier League season.

Turns out that leads aren't all that difficult to hold. When the match is tied at halftime, the odds of a draw in 2009-10 were about .42, while the odds of one of the two teams eventually winning were still greater at .58. But once a team is up by at least one goal, these odds change quickly and significantly. So once there's a goal difference at halftime of at least one goal, the odds of a team winning the match go from .29 to .72 (they more than double). Mind you, almost ten percent of teams 9.5%) managed to still lose the match after being up by a goal at halftime, and 18.4% managed merely a draw, but .72 are pretty good odds. And once a team is up by two at the half, the odds of winning become a prohibitive .935. What is more, not a single team that was up by two at the half eventually lost the match during the 2009-10 season (a small 6.5% of matches saw teams turning a two goal advantage into a draw). Finally, once a team is up by three at the half, the match is over. In 2009-10, not a single team lost a match when they were up by three or more at the half. So going from a tie to a lead by one or more goals increases a team's odds of winning from .29 to .72 to .93 and then to 1.

As a follow up, I have lots of questions: are these odds similar in other leagues? Are they similar for home and away teams? And are some kinds of leads harder to hold than others (say, a 3-1 v. a 2-0)? Lots of questions, and lots more to come on this.

Thanks to Don K.

Clean Sheets and Points Across the Big Four Leagues

In a recent post, I calculated the point values of goals conceded for the 2009-10 Premier League season. Keep in mind that a clean sheet guarantees a team at least one point from a match and potentially gives it three (in case the team scores a goal). For the EPL, the data showed that clean sheets were highly valuable to a team in 2009-10, producing about 2.5 points per match on average. And even only 1 goal allowed still gave a team slightly more than 1.5 points on average. But by the time teams conceded 2 goals, point value rapidly declined. And once the other team scored 3 or 4 on a team, the point value rapidly went to 0.

One question is whether this is a general pattern. That is, is the point value of goals conceded consistent when we look at data for several seasons? Another interesting question (well, interesting to me) is whether the Premiership is unique, as it is in some other ways (remember shot accuracy?).

To answer these questions, I took a look at data for the last five seasons and calculated the average amount of points associated with a clean sheet (and goals allowed per match generally) for the EPL as well as the other three big leagues (Bundesliga, La Liga, and Serie A). Here's what you see.

To me, this is a beautiful picture of consistency. I find it almost incredible that the point value of a clean sheet is virtually identical across the four leagues at around 2.5 points per match. The consistency around this number is remarkable (so I'm remarking on it!). But it's not just clean sheets; look at the point values of conceding one or two goals. Here, too, we see plenty of consistency across the leagues. Conceding only one goal per match translates to an average of 1.5 points. Sure, there are slight differences across the leagues with the point value of one goal conceded slightly bigger in the Bundesliga, but overall, this is amazingly consistent. Finally, conceding two goals nets you slightly more than .5 points per match, and after that a team is pretty much done for the day.

In a few days I'll take a look at comparing offensive and defensive production values across the leagues as well as home and away. Stay tuned for more.

Crime and Punishment? The Connection Between Fouls Committed and Red and Yellow Cards

Do teams get punished for fouls? It matters, if you ask me. If teams know that they can get away with fouls, they may be more likely to use them tactically in a match. Think about it. Every time I see someone like Ricardo Carvalho foul the other team's midfielder in transition I think to myself "now that's a clever foul." These fouls are rarely egregious, but they interrupt the flow of the game and make it impossible for the team in possession to take advantage of the transitional moment.

But are fouls actually punished beyond a mere free kick? That is, do teams that foul more in a match also earn more warnings and ejections than others? The quick answer to the question is "yes", at least when it comes to yellow cards. Take a look.

Using data for the past five seasons (2005-6 to 2009-10), there is a tendency for fouls and cards to go together. There is a sizable positive correlation between fouls and yellow cards per match across the thousands of matches played in the four big leagues during this period. The table shows the correlation coefficient of fouls committed per match and yellow and red cards, respectively.

                       Yellow cards        Red cards

Bundesliga       .37                         .10

EPL                      .37                         .07

La Liga             .31                         .05

Serie A              .28                         .05

This tells us that more fouls committed by a team go with more yellow cards for that team in that match. The correlations are strongest in the Bundesliga and the Premiership, and somewhat weaker in La Liga and Serie A. The story for red cards is quite different; here, the correlations are positive, too, but they are much, much smaller. This tells us that more fouls increase the risk of a red slightly, but the connection is very weak. So, overall, fouls and yellow cards are connected, and this connection is strongest in the Bundesliga (ethnic stereotypes anyone?).

Fouling clearly comes at a cost. Losing a player after too many yellow cards or even a red is is not ideal for a team's continuity over the course of a season. But the results shown above imply that teams can commit fouls with slightly more impunity in Spain and Italy than in the Bundesliga and the EPL. So, one interesting question is which teams draw yellow and red cards most and least often?

Win, Lose, or Draw: How the Odds Change With Each Goal Conceded

In an earlier post, I provided the points value of goals conceded (or not). Clearly, clean sheets have enormous value for teams, and perhaps are more important than is commonly recognized. As a follow-up, here's another way to look at the value of goals conceded.

As before, the data are from the 2009-10 Premier League season. To assess how a team's chances change as a function of conceding goals, I calculated the percentages of outcomes (wins, draws, and losses) associated with varying numbers of goals conceded in a match. For example, with a clean sheet (0 goals conceded), two outcomes are possible: a win and a draw, whereas with one goal conceded, wins, draws, and losses are possible. So how common are these and which are most common at every level of defensive production? Take a look.

The numbers tell the story. Teams with clean sheets won 71% of their matches in 2009-10 and drew 29% of the time (hence the roughly 2.5 points value of a clean sheet). And wins remain the most common outcome when a team conceded only one goal (at 43% of the time), but this is no longer a majority of outcomes. Yet, conceding 1 goal still means that a defeat is the least likely outcome at 24.6%.

In contrast, the outcomes tip quite quickly once a team concedes 2 goals: now the odds of losing the match are about 64%, while the frequency of wins is only 12%. Unsurprisingly, teams that conceded more than 3 goals in a match in 2009-10 did not win.

Taken together, looking at the numbers and the graph, it's clear that a clean sheet or conceding only 1 goal is qualitatively different from conceding more than 1 goal. One way to see this is that the odds of a draw don't change all that much, regardless of whether a team concedes 0, 1, or 2 goals, but the odds of winning and losing change radically. So make sure you cheer on your favorite team's goalies and defensive players this weekend and don't give up on them if they concede a goal. It's conceding that second goal that will do them in.

Thanks to Graham M.