The advanced stats behind Rangers play-off failure

Nicky Law, courtesy of Andrew Milligan (PA)

written by – Rangers Report

This is the first part of a brief series looking back at Rangers failures last year through the lens of advanced statistics.  My goal for the upcoming season is to make Rangers Report a valued source for fans to gain access to a variety of statistical information on Rangers & on the rest of the Scottish Championship.  This is my initial foray in writing using analytics so your patience is requested.  Also, this is my first go-around with creating charts & graphs – so they’re going to be sloppy/experimental. 


Part of what I want to do in this project is to apply statistics being used in hockey analytics & apply it to football.  One of those hockey stats that is already being used in analyzing the performances of football teams is called PDO.  Clare Austin explains, in her 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 it’s ability to show how far away a particular team’s experience is from the average.”


Both save percentage & shooting percentage only apply to shots on target.

PDO isn’t necessarily meant to be used on a match-by-match basis & this is a very small sample size (six matches) but you can see that during the playoffs Rangers’ PDO of 0.868 is quite low & well below the mean of 1.000.  Conversely, the opponents exceeded the expectations of an average performance with a PDO of 1.132.

Even though this is a small sample size, we can predict how we may use PDO next season to evaluate what improvements/regressions the team may make over the course of the season.  Over those six matches, Rangers only actually won two games, drew one, & lost three.  If this was the regular season that would equate to Rangers collecting 7 points in 6 matches.  Those results are supported by the team’s low PDO.  The PDO would suggest that that rate of 1.2 points per match would improve as the team got closer to the mean.  If the team’s PDO was already close to 1.000, you would not expect the results to improve drastically.  That’s the value of PDO – as a way to make data-driven predictions about future results, whether they be in the coming weeks or in subsequent months or even seasons.  Additionally, next season we will be able to compare Rangers PDO to the rest of the clubs in the Scottish Championship.  Note:  you can see why PDO is popular for gambling.

Possession & actually doing something with that possession

We have all seen the possession numbers that are flashed on the screens during a match or printed in match reports that come after.  For the record, Rangers had the edge 51% to 49% over the course of the six matches – but so what?  What did they do with that possession?

That’s where we can begin to incorporate Total Shots Ratio (TSR) into the discussion to see if teams are actually turning possession into shots.  As Mike Goodman of Grantland, explains, “As with lots of analytics concepts, TSR is just a fancy set of letters for an incredibly simple idea: Let’s count shots.  Specifically, TSR is the ratio of how many shots a team takes versus the number of total shots (actual equation: shots for/(shots for + shots against).”

Nicky Clark, courtesy of Action Images/Reuters

During the play-offs, Rangers took 54 shots while conceding a total of 59.  That equates to Rangers having a TSR of 48%, proving that even though Rangers possessed the ball a majority of the time – they weren’t nearly as efficient as their opponents at creating offense with that possession.

The idea for measuring TSR is rooted in the transformative understanding that Corsi stats created for the National Hockey League.  Justin Azevedo of the Calgary Flames blog, Matchsticks & Gasoline, explains – “Corsi is the most popular advanced stat in the hockey blogosphere, Corsi is a possession metric developed by former Buffalo Sabres goaltending coach Jim Corsi. At its most basic level, Corsi is the plus/minus amount of shots directed at a net – blocked shots, shots high and wide, shots that hit, shots that get tipped, etc.”

The logic goes that the more a team possesses the puck & is putting pressure on the opponents’ goal, the more likely that they will experience success.  Conversely, if the opposition is not possessing the puck as much, they have less chance to create goals.

Like PDO, Corsi is a metric best assessed over the long haul.  TSR can function the same way.  In an individual match, a moment of brilliance from a forward or a few seconds of goalkeeping ineptitude (see: Cammy Bell) can break a match & go against the trends developing over 90 minutes.  However, if a team consistently has a positive TSR over a series of matches – logic dictates that they will win more often than not.

TSR has become very well established in the advanced stats world of football.  However, I plan to experiment with a new data point called Value TSR.  Let’s pretend this howler from Kris Boyd in the above clip went wide of the net (instead of backwards) & actually went out for a goal kick.  That would count as a shot & would count towards TSR.  Now Boyd’s miss, from the preseason against Sacramento, is an extreme example but let’s say he was able to tuck in that sitter for a goal – or that the goalie was forced into a Superman-like save – isn’t that more valuable then simply sending the ball flying into the stands?  Hence the motive to create Value TSR.  To figure out the data, you would add together total shots with shots on target for both teams & then follow the same formula for TSR.  It enhances the value of a shot on target (saved or for a goal) to be twice the value of a shot that goes astray of the goal.  (update:   I have since scrapped Value TSR & simply use Shots on Target Ratio instead).

In the six game snapshot of the playoffs, it is difficult to see a significant difference between Value TSR & actual TSR.  Rangers had 54 shots & 28 that were on target, while their opponents had 59 shots & 26 on target.  This means Rangers had a 49% Value TSR, which is only marginally better then their TSR of 48% & still below the 51% threshold which would be seen as slightly above average.

But the chart below shows how looking at Value TSR on a match-by-match basis can give you a better understanding if Rangers were actually creating legitimate scoring chances with their possession.


Opponent Poss For TSR ValueTSR TSR Cl ValTSR CL
Queen of the South 0.51 0.41 0.45 0.41 0.45
Queen of the South 0.54 0.55 0.57 0.55 0.57
Hibs 0.53 0.43 0.55 0.50 0.60
Hibs 0.43 0.22 0.22 0.22 0.22
Motherwell 0.49 0.50 0.56 0.43 0.21
Motherwell 0.57 0.61 0.59 0.67 0.65

As you can see – I have begun by posting the basic possession stats, followed by TSR & Value TSR.  Additionally, I have included TSR Close & Value TSR Close – which takes the score into account where shots are only calculated when the match is tied or within a goal either way.  Once a side goes up by two goals, there is little value to measuring their TSR because pressuring the other team is less of a priority then simply holding onto a lead.

For example, in the home loss to Motherwell if you only looked at the TSR or Value TSR it would look as if Rangers made the 3-1 loss closer then it really was.  However, if you look at the TSR CL & especially the ValTSR CL you can see that Rangers were dominated before Motherwell went up by two goals.  Motherwell’s TSR CL of 57% & ValTSR CL of 79% clearly support that.  Most of Rangers’ pressure on the opponents goal was because Motherwell were sitting on a two goal lead.

Additionally, you can carry that over to the second leg.  Rangers dominated possession because Motherwell came into the game with a two goal lead – they didn’t necessarily need to counter Rangers offensive efforts.  Of course, they still won the match 3-0 & we’ll look at that in the next post.

Also, you can see Rangers approach when sitting on a two goal lead of their own going into the second leg with Hibs.

Individual Game Charts

One of the most popular features of measuring Corsi in the National Hockey League is the development of live game charts, which illustrates the total shot attempts throughout the game.  Often you can see the exact moments in which teams swung momentum in their favor.

Hopefully, I can develop systems to replicate these charts in the upcoming season.

Here is an attempt to visually display TSR for both sides in the aforementioned first leg match with Motherwell in which Rangers only began to dominate TSR after they were losing by two goals.


The chart visually shows that Motherwell had the TSR advantage for the bulk of the match (hence the predominance of red in the chart) & the blue advantage for Rangers began to actually dwindle once Motherwell scored the opening goal in the 27th minute.  Additionally, half of Rangers shots came after the 70th minute – when the result for Motherwell had already been secured.

courtesy of Willie Vass

So, there’s an introduction to some of the advanced stats I hope to bring to the site in the upcoming season.  In the upcoming parts of this introductory series, we will look at individual players stats – beginning with the subpar play-off performance of Cammy Bell, followed by a look at the output of the rest of the Rangers players during the same stretch of matches.

After that, the plan is to continue using the stats mentioned in this post to analyze the team’s output under each of the three managers the club had in 2014-15 season.

Since this a first attempt at presenting this kind of analysis – your feedback is very much appreciated.

You can follow Rangers Report on Twitter @TheGersReport

11 thoughts on “The advanced stats behind Rangers play-off failure

  1. Great start and very much appreciated a bit complicated for now but I am sure it will eventually become second nature.


  2. Thanks! I will continue making attempts to provide as straight forward a description as possible. I first started getting into hockey advanced stats a couple of years ago & felt the same way — now it truly has become a necessary narrative that accompanies each game.


  3. An excellent foray into the “dark art” of stats.

    I am looking forward to using your insight to educate myself and be able to more fully appreciate what is really happening rather than be deluded as to the depth of my knowledge.

    Keep up the good work, it is very much appreciated


  4. Thanks – I’m learning on the go as well. I have a pretty good understanding of NHL analytics (to an extent) but this is my first go around applying some of it to football. There will be growing pains for sure…


  5. Quite interesting , yeah . Can I ask about the raw data you collect . What is the source and correctness


  6. This is a very interesting format in breaking down the stats is if possible to award your top 3 players for best on ground in a 3-2-1 stat as they have in the AFL in australian rules football and at the end of the season the player with the most points wins the medal the 1 part if the player is suspended in the season he is not eligible to win the medal thankyou for your very hard work in putting this format together ……


  7. Interesting.
    Question for you. Into your analysis, can interventions from the management be somehow included.
    eg, in that last TSR graph, we see a switch of dominance from Rangers early on to Motherwell and then back to Rangers late on. Is there anything in particular that say influenced that measure? A substitution, A change in formation?, A goal? A game changing referee decision?


    1. If anything the chart supports what so many of us said about the match. The eyeball test told us that once Motherwell scored that first goal – Rangers buckled & Motherwell dominated form then out.

      Re: Rangers dominance at the end beyond the score – Motherwell made three substitutions in the final 20 minutes — signaling a change in tactics.


  8. I struggled to study statistics as part of my degree but I’m really interested in the application of stats to player recruitment, match preparation and training.

    I’m less sure of the value of statistics such as TSR and PDO which can only allow you to gauge performance after the fact. In what way are these useful/utilised by teams, gamblers etc?

    Looking at PDO for the NHL for instance there seems to be no strong relationship between this stat and the eventual outcomes of the last few seasons.

    Caveat: I know nothing of the NHL and, as mentioned, struggle with stats at times.


    1. Often you need to look at the bigger picture when it pertains to PDO & apply the ‘eyeball test’ as well.

      In 2012, Toronto was the further from the mean of 1.000 at the high end & made the play-offs. Nearly every person who followed analytics predicted that they would not replicate that success & have indeed been one of the worst teams over the past two seasons. The year before the same thing applied to Nashville

      In 2013-14, the two teams furthest from the mean were Boston & Colorado – both didn’t make the playoffs the next season. Everyone saw it coming with Colorado but Boston was the real surprise.

      TSR (or Corsi in hockey) can function as a great indicator of which teams will experience the most success.

      In 2012-13 Chicago, Pittsburgh, New York, Montreal & Boston were the top Corsi teams — Chicago beat Boston in the Stanley Cup

      2013-14 it was Boston, Anaheim, Los Angeles, Chicago, & St. Louis — LA won the Stanley Cup & Anaheim was the best team in the regular season

      Last season – Nashville, Tampa Bay, New York Rangers, LA, & St. Louis — Tampa Bay made it to the Stanley Cup & New York was the best team in the regular season.

      Like any advanced stats — it’s not perfect but they increase your probability of making predictions based on data driven evidence.


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