Friday, 18 May 2012

How Costly Was The Woodwork To Liverpool?

The end of the season has recently spawned a cottage industry whereby the wrongs suffered by teams over the course of the year are righted and those sides are assigned their "rightful" place in the Premiership.Firstly we saw Arsenal's rash of unfavourable decisions charted,corrected and the Gunners elevated to runners up spot by a media eager to see conspiracy where there was simply randomly distributed errors of judgement.The press inevitably ran with the story even though the methodology was badly flawed and a big chunk of many team's rich  history comprises the result of miscalculations by both players and officials.For every piece of silverware there is an offside goal allowed to stand against you because the officials mistook a programme seller for the last line of defence.Reducing football to an endless visit to the television match official's replay booth merely serves up the punctuated spectacle that is rugby.

This year we have the saga of Liverpool's fondness for striking the frame of the goal.The average number of times an EPL side struck the post or bar in 2011/12 was around 15,so Liverpool's total of 33 was certainly excessive.Glen Johnson has come out in print with the view that had all of those shots counted as goals,then The Reds would have found themselves around 15 points better off,on the cusp of Champions League qualification and,one presumes,not currently seeking a new manager.

The number of times a team hits the woodwork is fairly strongly related the the amount of attacking they do,so we should expect Liverpool to be among the league leaders when it comes to striking the "woodwork".Stoke,for example attack rarely,but they do it with above average efficiency,realising that points are gained by goal difference rather than simply goals scored and as a consequence tallied just 7 such strikes last year.While the Premiership's top scorers,Manchester City's rate was three times that of The Potters.

If we are to indulge in the fad of revisionism,how should we go about it to remain fair to all teams in the division and not just realign the achievements of one team under the spotlight.Firstly,simply counting a woodwork strike as a goal and adding it to the final score is far too simplistic.Had Suarez scored in the 12th minute at home to QPR instead of striking the post,there is no guarantee that the game would have finished 2-0,comprising the early "goal" Liverpool should have scored and the later one they actually scored.Changing earlier events can only advance the team to a difference level of likelihood that they will eventually win the game.We have to include the small possibility that QPR spurred on by falling behind can pull off a remarkable come from behind they would do later in the year in the reverse fixture.

Twelve minutes in and scoreless,Liverpool would expect to take on average 2.4 points from QPR at Anfield,if we change Suarez's striking of the post to a score,their expect points jumps to 2.8.That's short of the 3 points they achieved for the actual 1-0 where they didn't lead early.So revisionism comes at a cost as well as a benefit.

Secondly,Liverpool are undoubtably outliers,but correcting this aberration by converting all their post and bar strikes to goals and making the team outliers at the other side of the line is wrong.The assumption being made by Johnson and others is that each shot that struck the woodwork was a"goal" that got unlucky.It could equally be a shot that was going to miss the target all together,but then got "lucky" and hit the frame instead.

The third problem is that Liverpool weren't the only team hitting the bar in their games.One of the most highly leveraged "woodwork" incidents happened in the 84th minute against Fulham when Downing hit the post with the game still scoreless.Liverpool's expected points prior to Downing's strike was 1.3,had he scored it would have jumped to 2.7.A difference of 1.4 longterm points in just one incident and comparable to the potential benefit Fulham would have gained three minutes earlier when Dempsey struck Liverpool's woodwork.

Lastly,although 33 strikes appears as though it should have a major effect on a team's final points tally,the raw numbers fail to identify that some games contained multiple hits and some even led instantly to goals.Liverpool were denied in this manner in less than half of their games.Above average without doubt,but a far cry from the near one event per game had each attempt been spread out more evenly.Over a quarter of their total woodwork hits came in four games against Everton,QPR,Villa and Chelsea,all games they went onto win anyway.

So if we are going to estimate a value for the amount of points Liverpool lost because of their bad shooting luck in 2011/12 we need to try to allow for all of these competing factors and we'll start by being unrealistically generous to the Carling Cup holders.Below I've listed all the games where Liverpool struck the bar or post and I've calculated the expected points just prior to the shot and immediately after,only I've assumed that the ball has hit the woodwork and gone in for a spectacular goal.Where games contain multiple events I've credited Liverpool with the event that would have been most advantageous to them in terms of advancing their expected points.Games are arranged with the highest leveraged situations listed first.

How Liverpool's Expected Points would have changed if their Woodwork Strikes had been Goals.

Opponent. Expected Points Prior to Woodwork Strike. Expected Points Had Goal Been Scored. Extra Points if Goal Had Resulted from Shot.
@ Fulham. 1.26 2.73 1.47
@ Arsenal. 1.27 2.28 1.01
Villa. 0.96 1.95 0.99
WBA. 1.87 2.76 0.89
@ Everton. 1.97 2.67 0.70
Newcastle. 2.06 2.67 0.61
Arsenal. 2.38 2.84 0.46
QPR. 2.39 2.83 0.44
@Bolton. 0.12 0.54 0.42
Swansea. 2.44 2.8 0.36
@QPR. 2.68 2.96 0.28
Sunderland. 2.66 2.92 0.26
Wolves. 2.78 2.98 0.20
Chelsea. 2.84 2.99 0.15
Norwich. 2.83 2.97 0.14
@Norwich. 2.87 2.99 0.12
@Villa. 2.9 2.98 0.08
@WBA. 3.0 3.0 0
Total. 39.3 47.8 8.6

So had Liverpool unrealistically converted the majority of their bar or post shots into goals instead of an Expected longterm average of 39 points,they would have taken nearly 48 points from those games.If we add that to the actual 21 points they tallied from games where they didn't strike the woodwork,Johnson's claim of challenging for UCL participation almost becomes a reality,as they now are level on points with 4th placed Spurs with 69 points.

However,the reality would almost certainly have been much less dramatic.Liverpool underperfomed all statistical models,the 39.3 Expected Points just prior to the shots hitting the post in reality yielded only 31 actual points.Events such as their failure to defend a two goal lead at QPR were much more the cause if this type of under performance than bad luck with the woodwork.Furthermore every team hits the woodwork sometimes during a season,Liverpool should expect some of their shots to hit the bar and bounce to safety.

We can simulate these more realistic expectations in such a way as to decrease the amount of rebounding shots whilst increasing the amount of goals Liverpool might have scored,such that they are no longer an extreme outlier.If we do this over a large number of iterations and also randomize the likelihood that Liverpool will receive either high or low leveraged extra goals,the average extra benefit Liverpool would have gained by being more normal in terms of hitting the bar or post,would have been around three points.

So rather than facing the agony of probably missing the chance of UCL football on goal difference to Spurs under The Glen Johnson Model,they suffer the agony of being pipped by Everton by a point for seventh under mine.


  1. Nice work ... couple of points to add ...

    1) I'm sure that teams hit the woodwork whilst playing AGAINST Liverpool and thus there flip side is that if those shots were counted as goals then their expected points would go up and Liverpool's down ... this means that the above is only HALF the story cuz as we know people (players, managers, fans etc.) really only look at the beneficial outcomes and never the negative outcomes :) ... therefore, nice to have a table that shows the woodwork shots against Liverpool.

    2) If we assume that the woodwork is infinitesimally small thus that the woodwork cannot be hit and thus that a shot becomes ONLY a Shot on Target (SoT) or a Shot (off target) we can use the shot stats in the following way ... a shot that hits the woodwork should fall under the Shots stat and not SoT.
    We know the percentage of shots that the team as a whole got on target (we can even calculate for individual players though their sample size is likely to be too small) thus we know the chance that a woodwork shot would be on or off target. Next we know the save% of the teams that Liverpool played against and thus the chance that a SoT would actually be a Goal.
    On average we know that a Shot has around 35-40% of being SoT and of those we know that the average goalie has a Save% or around 70% ... thus we know the %chance of a goal (not good at maths, but I'm sure readers can figure the average chance of a goal out form that). :) I believe it comes to around 2 goals from those 18 shots.

    Downing took 72 shots this season of which 19 were SoT ... 0.264 ... below average, unfortunately I don't know Mark Schwarzer's Save% (in 09 it was apparently 84%).

    cheers, b.

  2. Don't burst these people's collective bubble!
    Next they'll be saying Kenny's first part-seasonwas good on the basis of those results that came immediately after a below-expectation spell under Roy.