PDO: To what extent did luck influence the Scottish Championship table last season?

courtesy of SNS

written by – Rangers Report

One of the most illuminating aspects of the recent analytic coverage of the National Hockey League  has been PDO.  This measure basically determines the extent in which luck is involved in a team’s results.  The accuracy of predicting teams’ downfalls over the past few seasons has helped analytics enter the mainstream of NHL coverage over the past few seasons.  Furthermore Vic Ferrari, the mastermind who created the PDO stat, was hired last year by the Washington Capitals to work with their management team.

So what is PDO, Clare Austin explains, in her hockey blog Puckology“What PDO does–the only thing that PDO does–is highlight those teams who are getting better or worse results than they ought to be given how skilled they are. That’s all it does. That’s all it’s meant to do. It does that very easily and very efficiently.”

You determine PDO by adding a team’s save percentage & their shooting percentage’s together.  The numbers naturally gravitate towards 1.000.

Austin continues – “The greater the distance from 1.000, the more likely there will be a change.  If it’s low, it will go up.  If it’s high, it will go down. This is called regression to the mean, and in the NHL (or any hockey league), the mean is exactly 1.000.  Always.  By definition.”

“Every shot (on target) in the league is either a goal or a save.  There aren’t any shots (on target) in the league that are not goals or saves.  Thus league save percentage plus league shooting percentage is always and invariably 1.000. The average, then, is mathematically defined.”

“The value of PDO lies in its ability to show how far away a particular team’s experience is from the average.”

Toronto Maple Leafs – 2013-14 PDO victims

PDO is now being heavily used to assess teams performances in football analytics.

Owain Thomas a financial journalist who covers the English lower leagues using advanced stats on his blog – The Only Statistic That Matterstook PDO even further by applying the work of Benjamin Pugsley to determine which teams were both lucky & good, while highlighting which ones were more lucky than good.  Conversely, which teams were unlucky & which ones were just really bad.

Shots on Target Ratio (SoTR) is considered one of the most effective measures of how well a team is performing.  The value of SoTR was explored in our recent post evaluating Rangers three managers last season. 

A basic definition of SoTR is that it is a ratio to explain how many shots on target a team is getting when compared to its opponents.  For example, if Rangers got five shots on target in a match against Hibs & Hibs managed two shots on target – that would equate to Rangers getting 71% of the shots on target in the match —- five  divided by total SoT (5+2).

Thomas applied PDO & SoTR & charted them in order to see which teams were lucky & good & so on.  I decided to apply the same concept to last season’s Scottish Championship data.

(Note:  The stats are courtesy of Fitba Fancy Statsan analytics site run by Celtalytics – an American based blogger who covers Celtic & the rest of Scottish football).

image (1)

Along the horizontal axis you have a team’s Shots on Target Ratio, while the vertical axis shows PDO.

Then we can divide this chart into four sections.  The first section being the upper right part of the chart – basically teams with a 0.50 SoT Ratio or better & a PDO of more than 1.000.  This section represents teams that were both good & lucky.  There is one team in this section & it’s Hearts.  The idea here is that good teams create their own luck.

The second section of the chart highlights teams that were good & unlucky – basically could & should have won a few more matches.  Teams with a better than a 0.50 SoTR & a PDO less than 1.000 – the bottom right section of the chart.  This includes Hibs, Rangers, & Falkirk.  The PDOs of Hibs  & Rangers are relatively close to the mean of 1.000 & it is safe to say their results were pretty close to what they deserved.  They really weren’t that unlucky.  Falkirk was the furthest of the three from 1.000 & the unluckiest team that had a strong SoTR.  That would make them a pretty safe bet to improve next season.

The bottom left section of the chart (PDOs less than 1.000 & SoTR less than 0.50)  represents teams that were not very good & unlucky.  These teams are Livingston, Raith Rovers, Dumbarton, Alloa & Cowdenbeath.  Cowdenbeath is the furthest left on the chart, which represents having the lowest SoTR.  Basically, the data supports that they were the worst team in the league & deserved to be relegated.  Of all of these teams Alloa sticks out.  While their SoTR wasn’t great, their PDO was the lowest of all of the teams last season.  While  their improvement next season isn’t guaranteed, you can make the argument that they will see their standing in the league improve from last year’s ninth place finish.  Chances are Dumbarton, Raith Rovers, & Livingston will see similar results next year given that they weren’t very good & their PDOs weren’t too far from the mean of 1.000.

The final section is the top left part of the chart (PDOs more than 1.000 & SoTR less than 0.50).  This section represents teams that were not very good & lucky.  Only one team features in this section – Queen of the South.  As you can see they had the second highest PDO in the league but a Shots on Target Ratio similar to Alloa, who finished second to last in the league.  It is safe to say that Queen of the South’s fourth place finish last season was a fluke.  Will they bottom out next season?  Maybe.  Will they make the play-offs again?  Probably not.  The evidence would determine that you could easily see Falkirk & Queen of the South swap spots in the table next season.

Queen of the South v Rangers

How do these numbers pertain to Rangers chances next year?  Given the extreme turnover in the squad – very little.

However, for the other teams in the Championship, whose squads won’t see as many players leaving as Rangers will, you can make some educated guesses on their fates next season.  Teams like Hibs, Livingston, Raith Rovers, & Dumbarton will likely have similar results next season.  Meanwhile, Falkirk is primed to improve from their fifth place finish & Alloa Athletic will likely finish higher than their 9th place finish.  Lastly, the safest bet is that Queen of the South will see a regression in their results from last season.

Based on that – here’s an attempt to predict the final table for next season.

1 Rangers
2 Hibs
3 St Mirren
4 Falkirk
5 Queen of the South
6 Alloa Athletic
7 Raith Rovers
8 Livingston
9 Morton
10 Dumbarton

Only Cowdenbeath had a worse Shots on Target Ratio & goal differential than Dumbarton, so it is safe to say that they will be battling to avoid relegation next season.

You can follow Rangers Report on Twitter @TheGersReport

11 thoughts on “PDO: To what extent did luck influence the Scottish Championship table last season?

  1. I do like this interesting way of using analyticals.
    I look forward to more of it during the season, when repetition will bring more accuracy



  2. Actually Rangers under McCoist was the only team close to Hearts in that upper right part of the chart. He had the team in second place – too bad he had no idea on how to build a team for the long term, like Hearts did


  3. whit a load of crap. we were not good enough.
    lets hope warburton nocks them into shape.
    oh for something more exciting than last season.


  4. I was really pleased when I saw the Rangers Report start up again but these repeated articles on stats are just boring !
    Hopefully when the season starts someone will start to post something worth reading .Until then… I`m out.


  5. William, don’t worry. Jordan & other writers will continue covering the team. For now, I’m dabbling in the dark arts of analytics. It’s something that has really proven invaluable to the coverage of both the sports I love – football & ice hockey.

    However, it is not for everyone. When it comes to hockey – I pick & choose the stats that I seek out to get a better understanding of the game. Maybe, you’ll find some that you’ll choose to follow & then discard the rest. Either way – I hope you stick with us.


  6. I think this is a hugely important aspect of football that, in the UK, we just can’t be bothered with (much like diet). We should be looking at every aspect to see where there is potential for improvement.
    It’s ignorance that leads to the constant statements that the EPL is the “best league in the world” when it clearly is not. If we start to consider where we are going wrong we can improve.
    Or we can bury our heads in the sand and think it’s all just down to bad luck!


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