The Curious Case of Corners

In May of 2010 I attended a Seattle Sounders match where they were beat 4-0. In an attempt to find a silver lining to such a horrible loss, the one of the local commentators pointed out that the team had earned a franchise record 12 corners on that day. The obvious implication was that while the defense was porous that day and the offense unable to score any goals, the team was at least making progress by attacking the goal and getting corners.

Fast forward nearly a year, and we're now at the end of yet another EPL season. While Chelsea stumbled through the first two-thirds of the season, they have certainly come on strong over the last third and are now in the improbable position of challenging Manchester United for the championship. As part of this resurgence, Opta noted the following statistic:

220 - Chelsea have won the most corners (220) in the Premier League this season and conceded the fewest (110). Opposite.

What if all of this commentary on corners were wrong? What if the more corners a team got compared to their opponents, the less likely the team was to win a match? This is certainly the case in the EPL, and in fact the effect is even bigger than that identified in my previous post on the effects of shots. This post will quantify how much increasing corner differential lowers the average EPL team's odds of winning a match, and compare the effects of such corner differentials for the Big Six clubs.

The Data and League Model

As in previous posts, I am utilizing data from the 2005/06 through 2009/10 EPL seasons compiled by DogFace. The raw match data has been transformed into differentials for shots, shots-on-goal, corners, fouls, and fantasy points for yellow and red cards. Match venue (home/away) is also noted. Each of these variables is then placed into a binary logistic model (BLR) to assess their effect on the odds of winning a match. BLR's were created for the league, as well as each of the individual teams that played in the league during the years analyzed. In the case of the league, BLR terms with a p-value of 0.05 or less were kept in the model. When it came to individual teams, reduced sample sizes required the use of BLR terms with a p-value of 0.10 or less to ensure a significant number of terms were retained in each team's model.

Comparisons at the league and team level were made once the BLR's were created. The graph below represents the league average home and away performance for the range of recorded corner differentials in the data set and utilizing the average values for shot, shots-on-goal, and fantasy points by venue. The dashed lines represent the lower and upper bounds of the 95th percentile prediction interval for the BLR lines. Click on the image to enlarge it.

The slopes of the lines are remarkably similar. In the -5 to +5 corner differential range, where most of the data lies, a home or away team playing to their average form experiences about a 2% reduction in their odds of winning the match for every additional corner they earn versus the competition. Notice that the two lines are separated by about 0.3 at -5 and 0.25 by the time they reach +5. This means that given each additional corner earned by a home team playing to their average form closes the gap to the away team playing their average average form by about 0.04 in this region, or 13% to 16% of the gap.

Magnitude of Corners On Match Odds

In the last post I compared the effects of shots-on-goal to shots to demonstrate that while shot differential leads to lower odds of winning, it's effects on lower those odds are only 1/3 as strong as the power of shots-on-goal to raise a team's odds of winning. The table below plots a similar relationship for corners to shots-on-goal. Teams with significant BLR terms for corners were included in the table, and it has been sorted from lowest (best) to highest (worst) ratio of coefficients. All terms are negative given the positive coefficient for shots-on-goal and the negative coefficient for corners.

Take note of the number of teams in the table - 16. This represents a 60% increase from the number of teams included in the similar table for shots differential. Corner differential has the second highest team count of any predictor - only shots-on-goal has a greater number of teams. The league average effect is that shots-on-goal have nearly three times the effect on a team's odds of winning a match than do corners. To put it another way, for every three corners that a team has compared to the opposition they must record one additional shot on goal to not negatively impact their odds of winning a match.

How does this compare to the effect of shot differential? The table below summarizes just such a comparison. Readers of my last post on shot differentials will recognize the table from that post, which has had a column added it to capture the teams' corner differential coefficients.

What becomes immediately clear in studying the table is that on a league-wide basis corner differential is far more damaging to a team's odds than shot differential is - more than 2.5 times as damaging. Also note a few clubs take a bigger hit than others. Chelsea and Manchester United realize a lower benefit from shots-on-goal vs. corners than any of the teams in the table, and see the biggest falloff compared to their shots-on-goal to shots coefficient ratio. The other teams in the table stay relatively even or go up.



Impact on the Big Six's Odds

The graphs below are just like the first one in this blog post. They utilize each team's average home and away form in the other BLR variables to allow a sweep of each team's corner differential by venue. Click on either graph to enlarge it.

A few general conclusions can be drawn from the graphs:

• Arsenal and Liverpool pretty much follow each other's form on average, both home and away. They also represent the middle of the pack in both venues.
• In both cases Manchester City has the lowest overall odds of winning a match. This is likely due to lower average performance in the other BLR attributes that would drag down their overall odds regardless of the corner differential. Recall that in the first table in this post they also had the highest SOG-to-corner differential coefficient ratio of any team. This is due to their low BLR coefficient for corners, which provides their line with the shallowest slope of any team, home or away.
• Manchester United's convex curves both home and away represent relatively consistent odds at negative corner differentials with quickly diminishing ones as corner differential turns positive. Of all the teams when playing to their average form, Manchester United is the most sensitive to corner differential in their favor.
• Chelsea's odds of winning a match when they have positive corner differentials playing to their average form away from home is simply amazing. Their odds of winning a match are nearly double those of any other team as corner differentials approach 10 to 15 corners, and they still have the better than 1-in-3 random chance of winning a match. Their odds of winning still go down, but they are the most robust to the effects of corner differential. Perhaps the Opta tweet would have been far more insightful if they had mentioned that instead of the meaningless statistic regrading overall corner differential.

Overall Conclusions

The data above makes sense if we think about what corners represent within a match. It can be assumed that corners are generated one of two ways:

1. The goal keeper or a defender makes a play on a shot-on-goal that knocks the ball out of play.
2. Under intense pressure from the opposition, the goal keeper or defender intentionally knocks the ball out of play to stop the attack before a shot can be taken.

Either way, the defense has either stopped a shot-on-goal or play that had a high likelihood of generating a shot on goal. If we know that shots-on-goal are likely to generate goals, and goals generate wins, than denying the shot attempt in the first place is likely to lower the opposing team's chances of scoring a goal as well as their likelihood of winning a match.

The higher penalty for corner differential vs. shot differential may also make sense if we think of match play in this manner. Shots often represent attempts by a player to score a goal where the shot had little chance of resulting in such a goal as it was not on target (i.e. not a shot-on-goal). Thus, the opportunity lost from simply taking an errant shot may not be that large. But if most teams avoid knocking balls out of play and generating corners for the opposition because of the dangerous nature of set plays from the corner, it stands to reason that they will not look to put a ball out of play for a corner unless it is a defense of last resort or an unintentional consequence of their actions. Thus, a corner for a team represents a bigger deprivation of a scoring opportunity than a random shot does.

What this all says is that passing, pressing, and shots have some merit but they don't matter much in a match unless they translate into shots-on-goal. And if such pressure is met with a resistance that constantly puts the ball out of play when the club on defense is at most risk, the attacking is all for nought. If the attackers keep plugging away, ensuring that their shots are actually shots on goal and that any corners are coming from shots-on-goal and not random bad passes or ricochets from the defense they will break through. That is because for every shot-on-goal that results in a corner, the team's odds of winning the match go up in a "two-and-a-half steps forward, one step back" method according to the statistics.

Quantifying the Bias of Arsenal’s Referees vs. The Rest of the League’s Clubs

This post can also be found at Untold Arsenal.

Author’s Note: Special thanks to DogFace for his co-authorship on this post.  His voluminous data set, unending patience, invaluable insight and contribution, and constant editorial feedback throughout the creation of this article was invaluable. He’s a wonderful blogging partner with whom any Gooner or statistician would be lucky to work.

In my first post in this series I used DogFace’s match data to explain how Phil Dowd is the least desirable referee for Arsenal as he not only shows the most biased officiating in terms of fouls, yellow cards, and red cards, but he also shows the largest effect on Arsenal’s likelihood of winning a match. That analysis focused on the effects of all of Arsenal’s referees, but did not quantify how those referees officiated other teams’ matches. This post contains such an analysis, and the results are very interesting.

To aid in such an analysis, a binary logistic regression (BLR) model was created for each team’s likelihood of winning a match based upon a number of factors. Each BLR model includes terms that capture the effects of venue (home/away) and differentials of shots, shots-on-goal, corners, fouls, and fantasy points for yellow and red cards. Not every term was significant for each team – terms that had a p-value of 0.10 or less were eliminated from the team’s BLR and their coefficient for that term is set to zero. I know that may upset some stats geeks who would prefer p-values of <= 0.05, but the reduced sample size requires a lower p-value threshold or very few teams would have any significant terms. The resultant BLR’s allow a construction of each team’s odds of winning each match, and a study was constructed as to how each official impacts the odds of winning each match based upon their officiating versus the expected average officiating from the club’s total number of matches.

Background on the Data Used in the Analysis

Before diving in to any analysis, a few statements on the types of data used are in order.

The intuitive way to model bias in a referee would be from the fouls per booking and bookings per match figures – although DogFace has often found these to be counter intuitive in that, if a bias exists, it can be expressed within the game in different ways – these often depend on the styles of play of the teams involved.

The noise in these figures is further increased by the fact that the official statistics only reflect what the referee deemed to be a foul rather than the reality of a foul (according to the laws) and/or the consistency of the referee’s interpretation thereof. “Sins of omission”, where a referee should have called a foul but for some reason or another did not, are tough to quantify in an analysis that uses such statistics.

To combat this effect, Untold Arsenal utilises a professional referee (Walter Broeckx) to analyse matches and it is clear that what is recorded in the official statistics is often way off the mark. DogFace’s own data sets confirm this effect. The rise in popularity of statistical analysis in football has led him to notice a trend for parity in the fouls per booking figures that suggests that the referee is aware of his statistics in game – it could be said that this ‘trial by media’ has created the bias we see in these figures and that a referee himself has a conflict of interest in every call he makes or indeed does not make.

The ideal situation would be an independent body to record/analyse referee performance and provide an open source database for us to comb through though - this data would include the most important data of all i.e. the standard ‘human’ error. Alas, we do not have such research based on an independent body, and instead you will have to make do with the work of humble bloggers like Walter Broeckx, DogFace and me.

Quantifying How Arsenal’s Referees Officiate the Rest of the League

Just like the last post, each team’s average foul and fantasy point total was calculated. These variables represent the match attributes directly controlled by the referee. Each team’s actual odds of winning each match were compared to the odds that would be realized if the referee had given the team’s average foul or fantasy point differentials (different values were used based upon the team’s averages for home and away matches). This allows a calculation of an odds differential for each match.

Matches were then grouped by referee to allow an analysis of each referee’s overall bias vs. the average odds. In this case, the same referees as the first post were examined – Atkinson, Bennett, Dean, Dowd, Foy, Halsey, Webb, and Wiley – as they had officiated the greatest number of Arsenal matches and in general a large number of matches overall. Most importantly, they have officiated a range of home and away matches so the impact of home/away bias is minimized. Unfortunately, the limitations of the number of matches in a season and the availability of each of the referees prevents an analysis where each referee officiates an equal number of home and away matches, but the statistics used in the analysis take the effect of venue into account to minimize its effect on match outcome. The data used for this analysis was also isolated to the 2006/07 through 2009/10 seasons to ensure an adequate number of samples were available from each referee.

It should be noted that for the first part of the analysis, referee data from all four seasons was grouped together. This allows us to look at gross bias throughout the seasons, and keeps a pretty high sample size for the analysis. Later in the post key referees' data is broken out across seasons to show the effects of referee by season. Such a study by season helps us see any bias that may be dependent on club’s objectives (Premier League title, European competition qualification, avoiding relegation) and current quality of play (above, at, or below form). Inevitably, such seasonal analysis suffers from limited sample size and is saved for those referees whose overall bias is the most noteworthy.

One further adjustment to the data set had to be made. When creating BLR’s for each team, several of them showed no impact to their odds of winning a match due to foul or fantasy point differentials. That is to say that none of the two coefficients for those terms in a team’s BLR were statistically significant – the coefficient’s p-value was greater than 0.10. This means that we can’t evaluate the impact of officiating on those teams’ likelihoods of winning a match. Thus, teams that did not have a significant BLR term from the two associated with officiating bias – fouls or fantasy points – were eliminated from the analysis as they’d provide a zero impact and generate misleading results.

A general linear model (GLM) using referee and team officiated (Arsenal vs. not Arsenal) was created from the reduced data set to observe the resultant interactions. The results of the analysis are represented in the graph below which shows each referee’s average odds differential for Arsenal and the rest of the teams. The two plots in the graph show the same data in two different manners. The key plot is the one in the lower left (click to enlarge).

Before diving in to the plot, readers with a keen eye will note that the red line, which represents Arsenal’s average odds differential by referee, is a bit different from a similar line plotted in my previous post. This is due to the two different ways the data is analyzed. In the previous case, I was looking at the referee’s performance as a function of just Arsenal’s matches by year. That led to the grouping and averaging to be a bit different than this analysis, which simply looked at Arsenal versus the rest of the league regardless of season within the four analyzed. This latest analysis essentially ignores the effects of time.

Looking at the lower left hand corner of the plot, it’s clear that Dowd shows the largest gap between how he officiates the average match and how he calls an Arsenal match - about a 1.5% penalty for Arsenal. However, what’s different about this analysis is that it also clearly shows that Howard Webb is pretty biased too – also nearly a 1.5% penalty for Arsenal. Rounding out the top three are Wiley, Halsey, and Bennett each with a nearly 1% penalty for Arsenal. Atkinson and Foy seem to show the smallest gaps.

Another way to look at in-match bias is to look for odd patterns in fouls-per-booking. A plot of four factors – Referee, Arsenal/Not Arsenal, Season, and Home/Away – and their impact on fouls-per-booking is shown below. Values on the left or right side of the plot represent the fouls per booking for the plots across that row. Values above and below the graph represent different levels of each factor expressed as text in one of the boxes in each column. The legends to the right of the graph explain what each color/shape combination represents in each row. Thus, if one wants to understand how each referee’s average fouls per booking for Arsenal compares to their fouls per booking for the rest of the league, one can look to the square in the 2nd row/1st column or the 1st row/2nd column. Each of those two plots shows the same data, but each is plotted in a different manner.  Click on the image below to enlarge it.

Looking at the plot of data in the 2nd row/1st column, one sees there is only one referee that has a higher fouls per booking for Arsenal than the rest of the league – Steve Bennett. Yet again, Howard Webb and Phil Dowd lead the pack with their differential of fouls per booking for Arsenal versus the greater numbers of fouls-per-booking they allow for the rest of the league. Surprisingly, the favorable Chris Foy also has a large gap between how he calls Arsenal matches vs. the rest of the league.

What’s especially disturbing is the fact that Dowd ends up with such a bias against Arsenal in fouls-per-booking given his disproportionate number of home matches he’s officiated for Arsenal (7 home matches to 2 away matches). Take a look at the plot in the lower left, which shows home (red) and away (black) fouls-per-booking by referee. Overall, Phil Dowd shows one of the largest gaps in favor of a higher fouls-per-booking average home versus away – nearly two fouls per booking. Yet such an advantage is not showing up in Arsenal’s numbers when Dowd is officiating their home matches. In fact, when looking for statistically significant factors in the GLM of fouls-per-booking vs. referee, club, season, and venue, the interaction of referee and venue is the only statistically significant term! Some referees are being consistent between home and away matches, while others are showing large gaps.

Comparison with Pre-Match Expectations via the Asian Handicap Swing

Does this comport with pre-match expectations? One loose measure of such expectations is the Asian Handicap assigned to a match. Luckily, DogFace has also been recording this statistic for each match. DogFace has also introduced the concept of the Asian Handicap Swing (AH swing) to readers of Untold Arsenal. The AH Swing is computed via the following equation:

AH Swing = Actual Goal Differential – Asian Handicap

The AH Swing represents the performance or deviation against the handicap in actual goal difference. The betting line data (or Asian Handicap) is an average calculated from around 30-50 bookmakers across Europe and Asia. We assume the average bookie handicap does not use corruption/bias as a significant factor in the markets – not only for the reasons stated below but also because referee driven match fixing would only affect the markets significantly in terms of an ‘upset’ against the odds.

If we were to take the stance that the betting line reflects referee corruption/bias then any deviation from that line in terms of an over/under performance would be understated i.e. we could say that any ‘noise’ in the original handicap from the bookies would actually understate the bias we are attempting to model. Luckily previous research does not indicate this case, but rather indicates that on the whole bookmakers may be creating a market that is essentially based on efficiency and competition. At the least, they are essentially hedging a gestalt metaphysical abstraction based on media disinformation and the credulous belief that “it all evens out at the end of the day”. However it is worth considering that, as perception of bias in referee performance becomes more ‘main stream’ and paradigms shift, we will see this effect in reflected in the markets of the future.

This post will instead focus on the reality of the results as it is a far more revealing stance to take. The Asian Handicap line is one that reflects, more or less, the illusion of an uncorrupted market. The swing from that line allows for an examination that a corrupted, or biased, market exists.

Just like odds differential, the AH swing has been calculated for each and every match in the database. A plot of four factors – Referee, Arsenal/Not Arsenal, Season, and Home/Away is shown below. Values on the left or right side of the plot represent the Asian Swing for the plots across that row; values above and below the graph represent different levels of each factor expressed as text in one of the boxes in each column. The legends to the right of the graph explain what each colour/shape combination represents in each row. Thus, if one wants to understand how each referee’s average AH swing for Arsenal compares to their AH swing for the rest of the league, one can look to the square in the 2nd row/1st column or the 1st row/2nd column. Each of those two plots shows the same data, but plotted in a different manner.  Click on the image to enlarge.

Looking at the plot in the 2nd row/1st column, it is shown that Mike Dean, Howard Webb, and Phil Dowd have the lowest average values for Arsenal’s AH Swing. This means they are consistently officiating Arsenal’s matches tighter than the other referee’s. Unlike the analysis of fouls-per-booking, the interaction between referee and venue is not statistically significant. Referees consistently provide a significant AH swing advantage to home teams compared to away teams.

It has now become clear that on multiple fronts that Dean, Dowd, and Webb appear to be the most biased against Arsenal. To get an even better understanding we must look at how each of the three officials impact each team and compare those matches to how bookies might expect them to turn out.

Quantifying How Arsenal’s Referees Officiate the Rest of the League

One way to visualize whether or not Arsenal is the most penalized when it comes to the officiating of Dean, Dowd, and Webb is to look at how each team’s average odds differential compares to their average Asian handicap swing when these three officials are present. The three graphs below represent just such a comparison for each referee. The x-axis represents the average Asian handicap swing. The y-axis represents the average odds differential.

The key to the graph is the lower left hand quadrant. Teams that end up there, especially those that end up further away from both of the lines along an imaginary diagonal line extending from the origin of the graph, are likely experiencing a higher amount of bias in officiating than the other teams the referee has officiated. The three graphs below show such plots for each team against each of the three referees. A summary of conclusions is found after the third graph.  Click on any of the graphs to enlarge.

Here are some conclusions that can be drawn from the three graphs:

• There is clearly a band around the ± 2% region of the odds differential where most teams cluster.
• It’s also clear that the top teams – Arsenal, Chelsea, Liverpool, and Manchester United – tend to do better on the AH swing than other teams. Indeed, teams that would generally have a more positive Asian Handicap tend to be to the positive on the swing.
• While Arsenal do seem to be experiencing some bias at the hands of the three referees, they don’t seem to be the worst off. Liverpool clearly pays a bigger penalty under these three referees.
• Of Arsenal’s main competition for league trophies the last half decade, Manchester United and Chelsea get a much better shake from the referees. Each has a vastly superior AH swing, while each of the two teams finishes much better in terms of odd differential than Arsenal for two out of the three referees. These advantages translate to an average of a 0.73 goal benefit in AH swing and a 1.6% benefit in odds of winning a match.
• Chelsea’s average odds differential is 1.6% better than Arsenal’s, while their average AH swing advantage is 0.78 goals.
• Manchester United’s average odds differential is 1.5% better than Arsenal’s, while their average AH swing advantage is 0.68 goals.
• Mike Dean is the only referee of the three to put both Chelsea and Manchester United to the positive. He’s also the referee demonstrating the highest bias against Arsenal in AH swing, both nominally and when compared to Chelsea and Manchester United (a 1.52 swing deficit to both).
• Perhaps Ryan Babel’s tweet with Howard Webb wearing a Manchester United jersey wasn’t too far off. It Manchester United is his most favored team by a mile both in terms of swing and odd differential.
• Of any referee who has officiated the Big Six, Mike Dean gives the most favorable treatment to Chelsea. Their average odds of winning a match are improved by nearly 1% when he officiates one of their matches, and they experience their best AH swing under him.
• Of Arsenal’s North London rivals, Spurs are treated about even by Dean and worse by Dowd and Webb.

There are some interesting interactions that go on between referees and managers as well. One could be referred to the Dean-Redknapp effect. When looking at matches where Dean is the official in matches involving Portsmouth and Tottenham, both teams do better in terms of AH swing with Redknapp at the helm than when he is not, bordering on statistically significant effects (odds differential was a wash). Interestingly enough, the interaction of manager and team is not significant, so Redknapp’s record under Dean is not unduly boosted or penalized by his record from either of the clubs. It stands on its own. Such a detailed analysis would have to be the focus of a subsequent post, and deserves a wider treatment of referees, to ensure that it’s not simply an effect of Redknapp’s superior coaching. Nonetheless, it provides intrigue when studying the effects of officiating.

A Comparison of The Big Six By Season

It has been shown that over the 2006/07 through 2009/10 seasons that Dean, Dowd, and Webb have given Arsenal a bit of the short end of the stick when it comes to fouls-per-booking, AH swing, and odds differential. One last bit of examination remains – what happens if we open up the examination to the entire six years of data in DogFace’s database, isolate for the Big Six for these three referees, and examine how a few of the trends may be changing over time?

The graph below provides a plot of such data. The solid lines represent the teams’ average AH swings under the three referees, the value of which can be found on the right hand side of the graph. The dashed lines represent the team’s average odds differentials under each of the referees, the value of which can be found on the left hand side of the graph (click to enlarge).

A few general trends can be observed:

• All teams except Manchester City have been on a general downward trend over time in terms of AH swing.
• Manchester City also is also the only team to demonstrate a steadily increasing odds differential over time.
• Arsenal started out with the third lowest swing in 2005/2006, and their decline has been consistent to the point of falling below 0 this season with the three referees. They are the only team of the Big Six to experience a negative swing.
• The dashed set of lines shows Chelsea and Manchester United hanging around neutral (i.e. 0%) odds differential over time.
• Again, Arsenal is on a steady downward trend to the point that their average odds differential under the three referees is on track to be greater than -2% this season. Only Tottenham has a worse odds differential.

So who’s driving this downward trend for Arsenal? The plot below shows the same data as the plot above, but it eliminates the other three teams and instead focuses on Arsenal’s referees (click to enlarge).

On the AH swing front, there’s been a steady erosion the last year. However, before that Mike Dean’s officiating showed a distinct downward path compared to the rest of the referees. His AH swing went negative in the 2009/10 season, and Webb has joined him now in 2010/11. It appears it’s a case of Dean pulling the rest of the average down with him, and the other two referees joining him this season.

As for odds differential, it’s Dean again that leads the pack. He started out as a neutral referee in 2005/2006, but then has steadily eroded that neutrality to a -2% differential by last season. Dean’s low average and the recent degradation in Phil Dowd’s officiating are what are leading to Arsenal’s precipitous drop in 2010/11.

Conclusions

Whether it’s actually poor form generating a higher number of fouls and cards or actual referee bias, it is clear that Arsenal pay a bigger referee penalty than all of the teams they’re competing against for the Premier League championship save for Liverpool. This might be combated by having the three highlighted referees – Dean, Dowd, and Webb – officiate fewer Arsenal matches. They officiated an average of ten matches, or 26% of Arsenal’s season, each of the last four years. Statistics would suggest that having a fewer number of referees officiate a greater number of matches for each squad would lessen the chance of a poorly officiated match impacting a team’s season point total. Such an assumption is based upon the idea that the official’s errors or bias are randomly distributed. The data above suggests otherwise.

Why Shot Differential Actually Hurts a Club's Chances of Winning a Match

Over several posts about Arsenal's odds of winning matches I have highlighted the fact that a club's increase in shot differential versus the opposition actually lowers that club's odds of winning the match.  This may seem a bit counterintuitive, but it actually makes sense upon a deeper dive into the data behind the binary logistic regression (BLR) model.  This post examines those details and provides the explanation.

The Effect of Shot Differential on Match Odds

Recall that the BLR model I have constructed for the wider league and individual teams consists of the following inputs:

• A constant term
• Venue (home/away)
• Shot differential
• Shots-on-goal differential
• Foul differential
• Red and yellow card fantasy point differential

It turns out that for the league, all terms in the BLR are statistically significant to a p-value of 0.05 except for foul differential.  When individual teams are examined the terms which are statistically significant vary by team, with statistical significance given to any term with a p-value < 0.10 to ensure a reasonable number of terms are included in each team's model.

To understand how shot differential impacts the average team's odds of winning a home or away match, the BLR values for shots-on-goal and fantasy point differentials were set to their averages by venue while the shots differential was varied from the minimum to the maximum value by venue.  The resultant plot of data is shown below (click on graph to enlarge it).

The graph shows the decreasing nature of the odds of winning as shot differential goes up both home and away.  The slope terms of each regression equation indicates that home teams pay a bigger penalty for increasing shots - only three additional shots are required to lower the odds of winning by 2%, while it takes four shots away to have the same effect.  The fact that the dashed lines, which represent the bounds of the 95% prediction intervals for the two venues, do not cross indicates the difference in odds between in home and away is statistically significant.  The average home team performance for a given shot differential is more likely to win than a similar shot differential for the average away team performance.  Similar relationships were seen for every team that had a statistically significant shots coefficient for their BLR model.

Some Binary Logistic Regression Nerdery

Before explaining why increased shot differential impacts the odds of winning a match negatively, a little digression into the basic theory of binary logistic regression is in order.  A BLR model based upon the data I have from DogFace is of the following form:

where:
p = odds of winning a match
C = constant
α = BLR coefficient associated with venue (home vs. away)
A = venue (1 = home, 0 = away)
β = BLR coefficient associated with shot differential
B = shot differential
δ = BLR coefficient associated with shot-on-goal differential
D = shot-on-goal differential
ε = BLR coefficient associated with corner differential
E = corner differential
φ = BLR coefficient associated with foul differential
F = foul differential
γ = BLR coefficient associated with fantasy point differential
G = fantasy point differential (red cards = 6 points, yellow cards = 3 points)

If the equation is re-arranged to eliminate the natural logarithm term on the left hand side of the equation, the relationship between p and the rest of the terms in the model becomes:

If the chain of exponentials on the left hand side of the equation is represented by the term x, and then the equation is re-arranged to isolate for p, the model becomes:

Thus, p increases as x increases (by the chain of exponentials increasing).  The inverse is also true - a lower x value produces a lower p value.

Isolating for the two terms involving shots means examining the impacts of β, δ, B, and D.  If (β x B) > (δ x D), the net effect will be a shots metric contribution to x that is less than one, and thus lowers p.  If (β x B) < (δ x D), the net effect will be a shots metric contribution to x that is greater than on, and thus raises p.

Not All Shots Are Created Equal

How is it that increasing shot differential ends up lowering a club's odds of winning?  It is because all shots are not created equal, and that it is actually shots-on-goal differential that increases a club's odds of winning.

The β term in the BLR must be negative for a team's odds to decrease with increasing shot differential as observed in the first graph in this post.  Indeed, this is the case for the league and club models for which shot differential is statistically significant.  The key is that it must be offset by shots that are on goal.  It turns out that the δ term for the league and all teams for which it is statistically significant is positive.

Not only is the shots-on-goal term positive, its magnitude is much larger than the negative.  Thus, the impact of shots-on-goal is greater than that of shots.  One sign of a team's strength is the ratio of δ to β - a higher δ to β ratio means that they get a larger relative benefit from shots-on-goal relative to shots.

A table of such ratios for each team that has both statistically significant β and δ terms is shown below, as well as the league's ratio.  The table is arranged in descending order of magnitude (the negative values reflect the fact that the shots-on-goal coefficient is positive while the shots coefficient is negative).

The Impact of the Ratio of Shot Differential to Shots-on-Goal Differential on Match Odds

The plots below demonstrate the effects of the ratio of shot differential to shots-on-goal differential on match odds for the Big Four.  The first graph shows the impact on odds for a home match, while the second graph shows the impact for an away match.  Shots-on-goal differential is held constant at the average for each team by venue, while the shots differential is swept by a multiple of the average.  All other match statistics - differential for corners, fouls, and fantasy points - were also set to the average for each team by venue.

A few general conclusions can be drawn from the graphs:

• Liverpool and Manchester United experienced some of the highest negative ratios, where their odds of winning a match approach 100%.
• Arsenal's superior ratio shows up in the shallower slope of their line in both home and away matches, although they have a lower probability of winning a match at their average form compared to the other three clubs.
• Match odds are far more linear away than at home.
• Chelsea seems to be the most robust to positive ratios given their higher overall odds at ratios greater than 3:1, which is where clubs begin to wipe out any advantage from shots-on-goal.
• Manchester United and Liverpool have a very similar odds at home, while Manchester United has far superior odds away (~10% better odds regardless of ratio).

So, not all shots are created equal.  Every additional shot-on-goal that a club realizes versus the competition helps raise their odds of winning.  Indiscriminately taking a shot just to do so does nothing, presents a wasted opportunity as it never really had a chance at going in the goal, and statistically it actually lowers the team's odds of winning the match.  The key is getting the highest shots-on-goal differential to shots differential ratio as possible to gain the highest chances of winning the match.

Arsene Can Only Blame Himself, But He Can Fix It

"Ah, piss off!"

There was a time on Sunday when "King Kenny" and #PissOffWenger were trending on Twitter, demonstrating the reach of the global soccer community and the power of the Kop. Surely there are a lot of Wenger haters not aligned with Liverpool that jumped on the trend once it got going, but the phrase is symbolic of where the two clubs and their managers may be at this late point of the season. All the more fitting because of the fact that they started the season, literally, each at a different place. What a difference eight months makes.

The Match Statistics

Before diving into some thoughts on what ails my Gunners, I'll start with a statistical breakdown of each match - the first of the season at Anfield and this latest one at the Emirates. It provides some insight into what each side should have expected out of both matches, and provides some grounding in my later criticism of Wenger.

Just like this post, the tables below represent the odds of winning a match based upon a binary logistic regression (BLR) that looks at venue and differentials of shots, shots-on-goal, corners, fouls, and fantasy points for yellow and red cards. I've generated summaries of each match's statistics and the resultant odds based upon those statistics. Click on either table to enlarge it.

It wasn't just your eyes that told you Liverpool should have won the match at Anfield - the match statistics bear this out as well. Liverpool had the statistical advantage in every category - shots-on-goal, fouls, and fantasy points were in their favor, while total shots and corners were not (note: it turns out that teams want to have fewer corners and shots versus the opposition, a concept I will explain in a later post). Reina's muffing of Chamakh's shot truly was a gift of a point for the Gunners. Liverpool should have come away with a full three points that day.

Fast forward eight months, and the match at the Emirates was a little more even but still in favor of the Reds again. Arsene Wenger highlighted his team's "difficulty at creating chances" at his post-match news conference. Indeed! Even though Arsenal took 60% more shots than Liverpool, the Gunners had no advantage in shots-on-goal and had 7 more corners than the Reds - all adding up to a huge knock on the Gunners' chances of winning the match. All of this results in dropping Arsenal's odds of winning the match, which are only slightly raised by the two fewer yellow cards. Liverpool's oddity of being only one of three teams in the Premier League from 2005/06 through 2009/10 with a statistically insignificant constant term in their BLR model means that all of those statistical advantages added up to a 69% chance of winning the match, while Arsenal had a 34% chance of winning with such form. The odds were much closer than the first match, and perhaps a draw was warranted based on the statistics and what we all saw with our own eyes.

The bigger problem for Arsenal in the second match was their inability, yet again, to close out a match and take advantage of a lucky break. Statistically they may have been at a disadvantage for a win, but fortune broke their way late and they were a few minutes away from keeping pace with Manchester United. Instead, they walked away with what was a disappointing draw. Such collapses that snatch a loss or a draw from the jaws of victory has been all too common this season.

The Common Denominator - The Defense

What became immediately clear upon replay of the foul that enabled Dirk Kuyt's tying goal was the softness with which Lucas went down. Good for him, as drawing a foul is part of the game. What's more frustrating is how Emanuel Eboue put himself in position to have a foul called. This is symptomatic of wider defensive woes this season that have cost the Gunners a total of what should have been nine additional easy points that would have them top-of-the table right now, as well as the Carling Cup. Recall the following:

• Way back in September Arsenal drew Sunderland 1-1 at the Stadium of Light after leading for nearly 80 minutes. The stoppage time equalizer from Darren Bent came literally on the last play of the match, which was set up by a poor clearance from Gael Clichy.
• In November the Gunners conceded a two goal lead in the final 40 minutes of the match. I recounted here how rare an event that was. It was Tottenham's first win at Arsenal in 17 years.
• It was Abou Diaby providing the exact response for which Newcastle United were looking when they implemented their second half kick-them-off-the-pitch strategy while down by four goals in February. Diaby's sending off began Newcastle's comeback from four goals down, which was a first in the history of the Premier League and perhaps the best example of how Arsenal's defense can both make boneheaded mistakes and crumble under pressure at the same time.
• In the Carling Cup final, it was defensive miscommunication between Laurent Koscielny and Wojciech Szczesny that led the heavily favored Gunners to lose to Birmingham City. This loss, combined with the loss against Newcastle earlier in the month, set up an awful run in March and now April that has seen the Gunners fail to capitalize on any Manchester United stumble and now find them six points adrift of the Premiership title and only two points ahead of Chelsea.

In some cases, it's been a lack of killer instinct (TottenhamSunderland, Birmingham, and Liverpool). Either way, it's clear that the defense has major holes when it comes to protecting leads. I agree with Tim at 7AM Kickoff - I think the goal keeper problem is largely solved via Szczesny. What we Gooners want to see is better play from the defense in front of him, and we want to see it next season.

The Transfer Policy Needs to Be Adapted, Arsene

I've written here and here about the impacts the squad and starting XI transfer cost can have on a team's likely finish position. I've also heaped praise on Wenger for grossly outperforming such a model - averaging a third place finish over the last six seasons when his transfer expenditures suggest he should finish 10th. What's also become clear over that time frame is that consistently finishing third isn't meeting the supporters' expectations.

The Swiss Ramble made an excellent post in September 2010 that provides an great summary to Arsenal's financial quandary. Their strategy of not taking on debt to finance transfers has generated tidy annual profits in the transfer market, which helps compensate for their lower commercial income when compared to Chelsea, Liverpool, and Manchester United. They also have match day income that is the envy of Chelsea and Liverpool, and surpassed only by Manchester United. However, they do have the third highest payroll in the Premier League, outstrip their next closest competitor (Liverpool) by £21M, and have a wage-to-turnover ratio (50%) the envy of everyone else but Manchester United. They may not be paying for transfers in the open market, but they are paying their players wages that are in line with winning championships. And that's the rub.

It's time for Arsene and the Arsenal board to admit the plan has failed. I know that they don't set out to finish third every year, have steadily earlier exits each year in Champions League, and go trophyless in FA Cup and Carling Cup. They set out to win, and they've tried to win in an anti-Chelsea manner. They've had a squad, transfer-wise, that barely maintains the league average transfer cost yet competes with the big boys every year. It also consistently fails to win a trophy. Arsenal has made some good deals (Walcott, Szczesny, Cesc, etc.) along the way, and have a few great academy players in the first team as well (Wilshere and Djourou being the brightest). Save for Djourou, none of those great deals and academy players starts between the goal and the midfield. The Gunners simply need a few more top quality defenders, and they'll have to pay to get them.

Which brings me back to the start of my post and #PissOffWenger. The man elicits such a response partly because he has been around so long, partly because he has been so successful in the past, partly because he's not English, partly because he's been in everyone else's face trying to explain that he's building a team differently, and partly because lately he's been a bit of an insufferable whiner. He may have a few legitimate gripes, but the sheer number of gaffes this season suggests there's more than bad officiating or a league conspiracy at work here. The public manner in which he has vented his frustrations during and after matches makes him seem like a sore loser, and plays right into the role within which the press want him to fit. If you're a defender looking to join a club fighting for the Premiership title, and you perceive that the manager is a bit of a complainer who seems to not be totally in touch with reality, do you take a pass on such a club? If you're Cesc Fabregas and looking at your manager's behavior and comparing it to the fun your Spanish national team squadmates are having playing for Barcelona, is their even a comparison? There's a time to get angry and harass the officials and opposite manager when officiating is biased or play is dirty. But when it seems to become your MO after each loss in the eyes of the public, you have to stop and wonder if that's the best way to build a positive atmosphere at a club expecting to compete for trophies each year.

Wenger is clearly a managerial and financial genius. Of that there is no doubt. Perhaps he needs to hear more people say it before he feels his approach vindicated. Whatever he feels, he needs to move on. He doesn't need to bust the bank and become a £300M transfer cost behemoth like Chelsea. The future of Financial Fair Play will prevent that. What he does need to do is stop having such an aversion to spending ANY money in the transfer market, and look to upgrade the defense this offseason. Finishing third with the cheapest squad to ever do so is no longer good enough. Only championships matter now.  This Arsenal team is his team - he owns it lock, stock, and barrel. It will be interesting to see if the old man can adapt his ways enough to get one more championship before he enjoys a well deserved retirement. As Tim at 7AM Kickoff said back in February,

"Wenger made this mess, and only Wenger can sort it out."

The Impact of Red and Yellow Cards on the Big Six

I am in the process of building a very large post that lays out how Arsenal is treated by officials versus other teams in the league.  To build such a case, I need to be able to show the impact of various match elements on the likelihood of a team winning the match.  The tool I am using to build such a case is a binary logistic regression (BLR) that looks at venue and differential of shots, shots-on-goal, corners, fouls, and fantasy points based upon yellow and red cards.

I am still working on the final analysis, but in the meantime I have analyzed the impact of red and yellow card differentials on each of the Big Six's chances of winning a match.  The plots below show the changing odds of winning a match as a function of red and yellow card fantasy point differential based upon data from the 2005/06 though 2009/10 seasons.  The first graph shows a plot of the changing odds at home, while the second graph shows a plot of the changing odds for away matches.  Both plots use the teams' average value for shots, shots-on-goal, corners, and fouls (broken out as home and away averages) as inputs to the model.  Click on either of the graphs to enlarge them.

Several conclusions can be drawn from the graphs:

• Manchester United clearly is the least sensitive to card differentials at home.  When playing to their average form, they win at least 75% of their matches.
• Chelsea is the most sensitive of the home teams in the Big Six.  They drop from nearly 90% odds of winning to 30% over the range of fantasy point differentials they see.
• Chelsea maintains the best form of the six teams when playing away from home.  This is due to the fact that the coefficient for the venue term of Chelsea's BLR was not statistically significant.
• Liverpool is the most sensitive of the Big Six when they are away from home.  They go from a 90% odds of winning with their most favorable fantasy point differential to a 10% chance of winning a match when at the opposite end of the fantasy point differential.
• Arsenal runs middle of the pack both home and away, and have a relatively linear relationship compared to the other teams.  This is due to Arsenal having the lowest magnitude coefficient in their fantasy point BLR term.
• Tottenham Hotspur and Manchester City maintain the worst overall form of the Big Six across the range of fantasy point differentials.

More to come on match statistics and their impact on Premier League teams' odds of winning a match  in subsequent posts.

A Personal Example of the The Garbage-In/Garbage-Out Principle

Clearly, my problem was with a "garbage model".

The other night I was checking a few figures for an upcoming post that were based upon my binary logistic models (BLR) built from EPL match data, and I saw a number of counter intuitive trends.  That got me to check my data for a fourth time, and sure enough... I had fat fingered a formula!  It turns out that formula was used throughout the data set, and thus all of my analysis using DogFace's data had been using incorrect numbers.  In terms of my blog's header quote, my model was really wrong and wasn't really useful.  My post-match analysis of Arsenal/Blackburn and my quantification of Phil Dowd's officiating of Arsenal's matches were now both in question.  I had to re-run the analysis, which totaled several hours of statistical work and about twice as long checking my numbers.

It's a bit frustrating, as my blog relies on the accuracy of my numbers to drive its content.  I am very systematic in making sure they are right, and this is the first time I have found such an error.  However, more important than being right the first time is correcting mistakes when I find them.  This post is such a correction.

The Impact of Cards and Phil Dowd on Arsenal


After re-crunching the numbers, I found that the significant factors in the binary logistic regressions (BLR) turned out to be a bit better.  My erroneous calculations had resulted in my elimination of fantasy league points for cards from consideration in the BLR.  This was unfortunate because I had already done several posts on officiating at Arsenal's matches using that metric, and had hoped to re-use it here.  It turns out that when the numbers are correctly calculated, such a term is statistically significant.  Note that I have used Yahoo's Fantasy Premier League scoring system, which gives 3 points for a yellow card and 6 points for a red card.  All other terms from the BLR in the previous post - venues and differentials of shots, shots-on-goal, corners, and fouls - were included in the analysis.  The graphs below show the true relationship between those terms and fantasy point differential.

The updated models show that Arsenal is less impacted by cards at home than the average team in the Premier League, while they are impacted nearly identically as the average team when they are away from home.  Quite a different conclusion than my previous post that had erroneous data!  It turns out a number of the general conclusions regarding their overall odds, especially regarding their best away odds not even matching their odds of a home match where they experienced a fantasy point deficit of 5 points, didn't change much from the original post with bad data.

What about the affect of referees on Arsenal's matches?  The plots below show the impact each referee has on the odd's Arsenal wins a match compared to the odds of Arsenal winning the match had the referee handed out the average number of fouls and cards Arsenal saw over the five year period.  Only data from the 2006/07 through 2009/10 seasons was used as those were the four years where each of the eight referees had officiated at least one match.

Again, we see Phil Dowd lead the pack in odds differential penalty, although it is smaller than originally estimated (3% now vs. 4% with erroneous data).  Webb and Halsey's numbers round out those who have the greatest impact on Arsenal's odds of winning.  These corrected numbers will become more valuable in my next post on this topic, where I will compare the bias of Dowd, Webb, and Halsey to their records officiating other clubs' matches.

Finally, there's the small matter of Phil Dowd's officiating at Arsenal's recent match against Blackburn.  We Gooners still can't blame the loss on Phil Dowd - his officiating certainly helped the Gunners odds.  But their play didn't help nearly as much as my original post indicated, and in fact played into Balckburn's statistics a good bit.  The table below summarizes the match statistics, and shows the likelihood of winning by each club.

That's not a typo - Blackburn did actually have a higher odds of winning the match based upon the way the statistical models work.  Let me explain:

• Arsenal's coefficient for the constant term in the BLR is significant, and it is negative.  This means that before anything else is known about Arsenal's match, they start out with less than a 50% chance of winning.  This is not the case with Blackburn, whose constant term for their BLR is non-signficant and thus gives a coefficient of zero for no effect on their odds of winning.
• Arsenal's odds certainly increase playing at home and having a greater number of shots on goal, but their BLR coefficient for shots is not statistically significant so their is no significant contribution to their odds of winning from their 15 shot advantage.
• Blackburn, on the other hand, does have a statistically significant coefficient for the shots term of the BLR, but it is negative.  That means as the opposition's shot differential increases, Blackburn's odds of winning go up.  This can make some sense, if one thinks in terms of accuracy.  A shot doesn't really matter unless it is on target.  Blackburn's coefficient for SOG is statistically significant as well, and is positive, which makes sense.  This means the more SOG's the opposition gets, the more Blackburn's odds of winning go down.  However, they actually benefit when team's take wild shots with little likelihood of scoring a goal.  This is all reflected in Arsenal's need to take so many shots to get roughly the same percentage of shots on goal as Blackburn.  Had they had better accuracy, Blackburn's odds would have been much lower.
• Arsenal's odds suffer, and Blackburn's benefit, from Arsenal's corner differential.  This is a trend seen throughout the data set, both in the total league data and individual team data.  This possibly counter-intuitive trend will be explored in a later post.
• The foul differential is zero, but even if it weren't it would not matter.  Neither team's BLR coefficient for fouls is statistically significant.
• Clearly Arsenal benefits from only having a single yellow card vs. two and a red card for Blackburn.  This raises Arsenal's odds and lowers Blackburn's due to their statistically significant coefficients for fantasy points.

In all, it gives both teams high odds of winning the match.  Perhaps a draw was the most appropriate outcome according to the statistics.

Conclusion

The beautiful thing about blogging is that mistakes can be corrected instantly, unlike books where one must wait months or years until th enext edition is published or magazines where a retraction can be made next month.  The instantaneous nature doesn't negate the challenges associated with errors, but it does make the communication more honest and more open in a quicker manner.  I hope that in being honest with my mistake that it reassures you that I am always striving for quality data.  I'm redoubling my efforts to check all my numbers before I post any new material.  Catching the error and correcting it has turned out for the better when it comes to the flexibility of the data set and the conclusions that can be drawn.  Most importantly I have shown that fantasy points for yellow and red cards are statistically significant, which will enable the use of a single metric to capture the effect of two related, but one especially rare, events in a match.  Stay tuned for the follow up post...

You Can't Blame This Arsenal Draw On Dowd

I've done my best lately to highlight the bias of Phil Dowd when it has come to officiating Arsenal matches.  Today he did the best to bust up my theory (at least statistically) by tossing my Gunners a wonderful opportunity to earn three points via some favorable officiating.  Unfortunately, Arsenal did their best to not take the opportunity to keep pace with Manchester United.  In fact, it was a massive missed opportunity.  Let me explain...

In generating data for an upcoming post on Premier League officiating, I created binary logistic regression (BLR) analyses for each team over the 2005/06 through 2010 seasons.  Similar factors were considered in these BLR's as in my last post on officiating, but significant factors were set at p-values <=  0.10.  I know that may upset some stats geeks who would prefer p-values of <= 0.05, but the reduced sample size requires it or very few teams would have any significant terms.  Creating a BLR for each team allows for the study of how sensitive a team's chances of winning are in regards to each match statistic.  Thus, having a match's statistics allows us to retroactively examine the odds of either team winning the match.

Which terms are significant in each team's BLR provide some insight into how each team wins and loses.

For Arsenal, differentials in shots, corners, and fouls seem to not have a statistically significant effect on their odds of winning, while venue and differentials in shots-on-goal, yellow cards, and red cards do have a statistically significant impact.  Each of the four statistically significant terms comports with expectations - playing at home and a greater number of shots on goal are positively correlated with odds of winning, while yellow and red cards are negatively correlated.

For Blackburn, shots and red cards are not statistically significant.  Venue, shots-on-goal, corners, fouls, and yellow cards are statistically significant.  The coefficient for the corners term is negative, which indicates that an increasing differential in corners lowers Rovers' chances of winning a match.  There may be a rational reason for such a relationship - a greater number of corner kicks means more of Rovers' shots may be getting knocked out, indicating fewer shots on goal and fewer goal scoring opportunities.  The rest of Rover's terms correlate to expectations.

Now that BLR's have been created and their rationality checked, it's time to apply them to the match statistics.  The table below summarizes the match statistics according to ESPN.com.  Differentials for each match statistic for each team were calculated, and then applied to each team's BLR model.  This allowed the calculation of the likelihood of each team winning the match, shown in the far right of the table.

You're reading the table correctly - Arsenal led in every major category except fouls (dead even) and had a five-in-six chance of winning such a match.  Arsenal's failure to win the match is a one-in-six occurrence, one that cost them two points and may end up costing them the title race in the Premier League.  Notice that Blackburn's chances of winning were only 31%, but that's the odds of winning and not the odds of drawing. Somewhere between Arsenal's and Blackburn's odds of winning is the odds of a draw, something that a BLR can't quantify.

I still think Dowd is a bit biased against Arsenal - you'll all see why next week when I publish the second part of my study.  It is clear, however, that biased officiating is not what is costing Arsenal this seasons' championship.  It's an inability to score when given opportunities like those in the Blackburn match, or second half collapses due to defensive lapses like those seen against Tottenham, Newcastle, and Sunderland, that's costing them the championship.

An Indictment of the MLS Playoff Structure, Part 4: Quantifying the Impact of Game Differential on First Round Odds

In my last post I used binary logistic regression (BLR) to show the impact of various EPL match attributes on the likelihood of winning a match.  Soon after beginning the work I thought of another good use for a BLR model - identifying the factors that truly matter in predicting (as compared to retrospectively assessing) first round MLS playoff success.  Regular readers know I am no fan of MLS's playoff system that seems to buck the trend of most leagues using a top-of-the-table format to determine their champion.  I took a pass at explaining the phenomenon of teams with fewer games played winning a disproportionate share of first round series since 2003, but at the time could not prove that it was one of the few statistically significant predictors from the many identified by Climbing the Ladder (CTL).  Since then I have used CTL's lineup database to construct a BLR model of the major factors identified by CTL and isolated the statistically significant factors.  The results suggest that MLS has a lot of changes to make to continue to improve their playoff format they seem to love so much.

The Data Set and a Few Summary Statistics

I utilized CTL's lineup database to create the following statistics:

• Difference in the number of games played
• Overall goal difference
• Difference in coach experience (MLS games only)
• Difference in seeds
• Home record difference
• Away record difference
• Regular season goal differential between the two teams

Here are a few interesting summary statistics regarding several of the attributes above for the 2003 through 2010 seasons:

• Games played difference: The maximum difference came in the 2008 NY/Columbus series where the Crew played 14 more games than the Red Bulls.  This was due to the Crew playing in both the old and new format for CONCACAF Champions League (CCL).  The median differential is 2 games.
• Overall goal difference: 2005 through 2007 saw some of the highest overall goal differentials between first round playoff participants - one series each with 22 and 23 goals, and two series with 27.  The median goal differential was 9 goals.
• Difference in coach experience: Sigi Schmid is the king of mismatches in manager experience with the largest gap of 196 games realized when his 2008 Columbus Crew defeated the Kansas City Wizards.  The median difference is 68 matches.
• Regular season goal differential between the two teams: The peak of regular season goal differential between two teams was witnessed in the 2006 through 2008 seasons, when an unbalanced schedule saw teams play each other up to four times during the regular season.  Chicago's 2008 first round series versus New England witnessed the largest such goal differential - 8 from four regular season games.  Chicago went on to win that first round series, while the median value for the first round series is 2. 

The Results of the BLR

After compiling the data for every first round playoff series from 2003 through 2010, a BLR was constructed to predict the likelihood of a team winning the series.  Dummy variables for each year were constructed to ensure no special causes were missed.  Terms having a p-value greater than 0.05 were successfully eliminated until only two terms remained: manager experience differential and games played differential.  All other terms - overall goal difference, difference in seeds, home record difference, away record difference, and regular season goal difference - were not significant by a mile (most p-values were equal to or greater than 0.40).

Plots of the the changing odds with various manager experience and game differentials is shown below.

The plot of manager experience differential is counter intuitive, but is born out by the statistics.  Apparently having a less experienced manager actually bodes well for a team in the first round.  Perhaps it is that long term managers have more data points in the MLS playoffs, increasing the likelihood that the random nature of the playoffs will lead to their increased number of losses.  Perhaps newer, less experienced managers can take a team by surprise, or are managing teams that do not perform well the prior season and thus align with the teams with fewer matches.  Whatever the cause, it seems that fewer games for a manager, relative to the opposition team's manager, bodes well for the team with the less experienced manager.

More interesting is the intuitive relationship between the game played differential and the likelihood of winning the first round playoff series.  The equation provides a very clear relationship between the game played differential and resultant odds.  The relationship is largely linear from -5 to 5, meaning that it's about a 7.5% change in odds for each incremental game difference.  As game differential approaches more than five matches, the incremental benefit of increased or reduced game differential is minimal.

What does this mean for the 2011 playoffs?  The most direct assessment is that MLS missed a golden opportunity to correct this imbalance by not going to a two game series in the first round of the playoffs.  I commented here how I would have liked to have seen such a re-balancing prior to MLS's announcement of the 2011 format, as well as my reaction to the announcement that the first round would be a single match while the second round will have the usual two-match series.  If history is any indication, MLS essentially gave the lower seeds a 7.5% advantage in odds of advancing to the conference final by not making them play an extra game in the opening round.

We'll see how things play out in the 2011 playoffs and will update this study once they're complete, but I am not holding out hope.  With my Sounders having one of the league's more experience managers and their desire to go deep in the US Open Cup and CCL, I think it will be another year without an MLS Cup.

Perhaps MLS really does like this parity that borders on complete unpredictability.  Allowing MLS clubs to buy championships like Chelsea is not what I want, but the fact that no prior rational metric correlates to first round playoff success suggests MLS has some major adjustments to make.  It seems as if MLS has swung the pendulum so far to the side of parity that no club's supporters know what to expect from regular to post-season, let alone year-in and year-out.  Ultimately, this holds back the professional game's success and growth in this country.