Reading vs Huddersfield, Championship Playoff Final.

The football match for the world's biggest prize takes place at Wembley on Bank Holiday Monday, when the two remaining Championship playoff teams meet to gain entry the the Premier League money mountain.

Much has been and will be written about the two sides, particularly about their less than impressive regular and advanced stats.

Reading, at least managed a positive goal difference of +4 compared to Huddersfield's -2, although the latter impressed more in the probabilistic, process driven world of expected goals.

There's a detailed preview being posted later in the weekend, but as a crib sheet for fans and neutrals alike, here's how the 46 game season looks for both teams through the lens of expected goals.

Each goal attempt has been assigned and expectation of of ending up in the net based on a variety of parameters and their historical contribution to a successful outcome.

Each individual attempt is then simulated along with all the others taken in each match and a scoreline emerges, based on the attempt events in each match.

Score effects will play a part in this partly artificial process and models will not capture every ingredient that goes into a complex team based sport, such as football.

Games have been "replayed" 10,000 times and the percentage of games which end in say a Reading win or a draw for Huddersfield have been counted.

Finally, the match have been arranged in descending order of how well the individual goal attempts and their associated expected goals reflect the actual reality of the result on the day.

Top of Reading's list for "slightly taking the liberty" is their 2-1 win at home to Wolves. The Royals' ExpG totals around 0.5 compared to 1.82 for Wolves. The home team scored with both of their only two shots of note and a simulation of all the attempts from the game suggest they win such a shooting contest 7 times from 100.

A match that kind of sums up the contrasting fortunes of both Reading and Wolves in 2016/17.

(click to enlarge).

Here's all of Reading's league matches, along with the simulated probabilities for each possible outcome. All of the top ten matches and 17 of the top 20 are Reading wins and are also games where the granular shot probabilities were initially skewed in favour of Reading's opponents.

Here's Huddersfield's season and a more mixed bag of game outcomes at the top of the table, perhaps implying that their season hasn't revolved around the Terriers pulling an Al-Habsi sized rabbit out of the hat on more than a few occasions. Unlike Reading.

Data is from the @InfogolApp which can be downloaded free and has historical Premier league, La Liga, Championship, Europa League and Champions League expected goal values for both teams and players.

The Ticking Premier League Clock.

With the 2016/17 Premier League season now a wrap there's inevitably a raft of season reviews, both statistical and narrative driven.

Already sides are scrambling to pick apart the squads of the three relegated teams and capture the talent that shone brightest amongst the mediocrity.

Improving your Premier League squad for the upcoming 2017/18 season is an obvious priority. The likely output from you current collection of talent does not stand still, principally through the ticking of the clock.

It has been well demonstrated that a player's output, as measured by simple metrics or the amount of playing time he is given first waxes and then wanes (desperately resists obvious pun).

Although there is some positional variations, as well as individuals who possibly fall outside the usual, the peak ages in general for Premier League players lies between the ages of 24 and 29.

It is a simple task the chart which teams are well set to enter 2017/18 with a squad that is likely to show an improvement, just because players who were deemed good enough to be given playing time in 2016/17 are either moving into  the sweet spot for age related peak of performance or are remaining within their peak years.

On the flip side, other teams may be anticipating the need to recruit new, younger talent to replace an ageing squad that may have produced results that are acceptable for the club's perceived status in the Premier League pecking order, but if left unresolved will likely see an age related decline.

In the table above, the weighted amount of playing time given to players has been grouped by age,

This makes it possible to see which teams have a comfortable buffer of young talent that was deemed good enough to play some part in 2016/17 and under normal development will be expected to pick up some of the shortfall from older squad members who may begin to show age related decline.

It's also possible to wind the clock forward to spot which sides are best placed to cope with these transitions in the absence of new signings.

Ominously, Chelsea will likely retain the highest proportion of peak age performers, narrowly followed by fellow Champions League participants, Liverpool and Spurs.

By contrast, Manchester City again find themselves with a dearth of peak age performers from their current squad in the upcoming season, suggesting a bout of major squad reconstruction is imminent.

Tony Pulis Is Not A Slacker

Tony Pulis is never short of narratives.

Since the diminutive Welshman announced his presence on the main Premiership stage, guiding an under funded Stoke team, lacking in top flight talent to perennial survival, he's attracted plaudits and brickbats as the master of squeezing the most from meagre resources.

He's acquired manager of the season awards, as well as acrimony for his dour, anti football, laced with innovation, for which all Stoke fans will forever forgive him, especially as it came with the added bonus of infuriating Arsene Wenger.

Slacker, however, is a term rarely associated with Pulis or his three Premier League charges.

Until now.

The results of every Premier League match played by a Tony Pulis team. The black line is where they hit 39pts. You'll notice the difference. pic.twitter.com/a8I7BOU4Hf

— Huw Davies (@thehuwdavies) May 21, 2017

Visually the evidence appears damning. In the 54 matches a Pulis led side has played after the black line in the graphic, only 45 points have been won.

That's relegation form in every season and the implication is that a manager who once infamously multi-tasked by cancelling Christmas, while also showering, has allowed his team to slacken when a likely survival target has been met.

So do the numbers support the view that a manager whose mantra is "work 'ard" actually relents during April and May.

"Can I have the month off, boss"?

Firstly, there is an element of selective cutoff points that do Pulis no favours in the graphic.

To surpass any target requires a side to either win or draw and in eight out of the nine seasons, Pulis' side reached the line set in the graphic with a win.

Therefore, just as "X has not won at Y since 2014/15, immediately tells you that they did actually win in 2013/14, each period of "rest and reflection" begins immediately after a positive result and that biases your perception of the ensuing games.

Secondly, gaining points is very difficult for mid to lower ranked teams, epitomised by those TP has managed.

It's quite easy to spot runs of 5 or 6 consecutive matches without a win during periods when Pulis was presumably cracking the whip (or wet towel).

Thirdly, the fixture list can get very unbalanced when broken down into segments of between 12 or just three matches, as has been done in the graphic.

Whether by quirk of the fixture list or design, Pulis has been sent more games against the Premier league's best and Arsenal in the latter phases of the season.

Rather than lounging on a deckchair, they've been taking on Arsenal (6 times), Man City (4 times, including once immediately after a FA Cup Final), Chelsea (3 times), Everton (3 times), Liverpool (3 times), and Manchester United and Spurs, twice each.

That's a disproportionately larger share of the current top 7 compared to a random draw.

The easiest way to quantify how a side has done over a range of games is to simulate the range of possible points won based around a probabilistic model that doesn't incorporate a "doesn't try when safe" variable.

This approach results in Pulis gaining the actual 45 points his sides accumulated or fewer in around 16% of trials.

So the return is an under performance, certainly, but one that might occur in 16% of simulations simply through the randomness of how points are won.

Here's an attempt to cherry pick a single season where the returns are so low compared to a odds based distribution of points that randomness is challenged as a possible contender for the actual points returned in the run in.

Seven out of the nine seasons are unremarkable, the two exceptions are the most recent campaigns at WBA, but even these two examples have respectively a 10 and 7% chance to just be random deviations from a bench line estimate of WBA's ability over the season.

And with a raft of sides hovering around WBA's performance expectation for points won going into April, the chances improve that someone, (not necessarily WBA), will appear to tank their season early.

Even if there is something in the tailing off of a Pulis side in two out of nine seasons, evidence must be presented for a possible cause, which could be plentiful.

Resting players carrying longterm injuries, experimenting with alternative tactical set ups, blooding inexperienced players, seeing your hot and unsustainable production from niche attacking methods regress towards less extreme levels each deserve scrutiny.

The list is nearly endless and almost universally laudable, but Tone giving the lads a breather would be way, way down my list, even if the data supported the claims.....which it doesn't.

Who's Made Their £Million Wage Earners "Put In A Shift"?

As soon as Omar Chaudhuri starts tweeting words like "bugbear", you know he's onto something that deserves a good going over.

£'s per point were deservedly in his sights as a way of determining over or under performance compared to league position following The Times perpetuating this nonsense.

I've outlined the fatal flaws in this approach in yesterday's blog, and Omar has also suggested improved methodologies on his Twitter timeline.

But it opens up a wider question about the simplified use of readily available data.

Just because something is relatively easy to calculate and appears to be intuitively sensible it doesn't make it immune from being a piece of pernicious hogwash.

In the NFL, strength of schedule prior to the season is regularly estimated by adding the win/loss record from the previous season of the upcoming opponents for each team. This seems sensible and excel & csv files are your friend.

However, this too is easily verified GIGO. Do you really think a multitude of easily identified factors that delivered a 2-14 record are going to perpetuate?

Note to the Racing Post, "stop using these numbers in your season preview".

No one minds flawed reasoning, but the greater the potential audience, the greater the responsibility to do some due diligence regarding methods and a willingness to make corrections if needed.

Here's the performance of Premier League teams over the last six, nearly complete seasons, using the proportion of resources outlaid in wages and the similarly weighted rewards in terms of wins and draws compared to the historical relationship between the two.

A couple of seasons may be missing because I couldn't find the data for a few sides.

Everton, Spurs & Southampton have had a more than fair return for handing out bulky pay packets as do Bournemouth, with more limited evidence.

Newcastle have managed just one, albeit a spectacular season of over performing against the splashed cash and Leicester's single over par was unsurprisingly the largest one in the whole six year sample.

Sunderland can at least attempt to eventually over perform in new surroundings in 2017/18.

Here's the individual under/over seasonal wages vs performance for the 11 ever presents over the six seasons.

Tottenham and Everton making a habit of beating expectation and Arsenal performing to similar relative levels as WBA and Stoke (whose managers names escape me for the moment).

Chelsea Win the Title By Efficient Use of Wages.

The Times is one of the pioneers of quality, statistically based football journalism, notably under their Fink Tank banner.

It's therefore no surprise when their sporting articles not only receive extensive coverage on Twitter and in other news outlets, but also carry a degree of authority based on the legacy of past departed star performers.

One such post appeared on twitter today and quickly spread via a raft of online newspapers and media, gaining many likes and re tweets.

The 'value for money' league where Man Utd & Sunderland prop up a table led by Spurs and Bournemouth https://t.co/Enz500mDp2

— Martyn Ziegler (@martynziegler) May 16, 2017

The post was a long performed ritual come the end of the season, whereby a side's wage bill is divided by their points total to derive a "cost per point" number.

Following this intuitively comforting calculation, one team is deemed the most wasteful with their millions, in this case Manchester United (£3.6 million per point) and one is crowned the "value for money" team of the year. Spurs (£1.3 million per point).

Title winners, Chelsea came 12th out of 17 (the promoted teams were omitted), implying perhaps that they had won the title with a wasteful, inefficient splurging of the chequebook.

But is that really the case?

When Chelsea last won the league in 2014/15, the average wage bill for the 20 teams was around £100 million, ranging from £29 M at Burnley to £217 M at the title winners.

The Blues' wage bill was just under 2 standard deviations above the league average and for that outlay they gained 87 points or a success rate of 0.8 per game if you prefer to express draws as half a win.

The reward for Chelsea spending 2 SD above the league average wage bill was a success rate that was slightly greater than 2 SD above the average success rate for the Premier League.

This relationship holds for multiple seasons and for most teams.

Below is the plot for 2014/15.

The uncomfortable truth for a team wishing to gate crash the top of the Premier League, Leicester excepted, is that a typical title winning season requires a financial outlay in the region of 2 SD's above the league average.

Similarly, a stinting on the wage bill inevitably, with some variation throughout to account for luck, innovation, plagues of locusts etc pitches you into the bottom half of the table.

But the take away is that there is a strong relationship between how much you spend in comparison to the league average and the actual wage bills of the remaining teams in a Premier League season and your success rate again compared to the league average and that of your competitors.

Therefore, any under or over performance in a season should be compared to this historical relationship, rather than a perennial and flawed click bait ritual involving nothing more than long division.

Using the raw figures used by The Times (actually from 2015/16, but we're assuming 2016/17 will be similar), Chelsea spent 1.64 SD's above the league average this term.

 That "entitles" them, based on historical precedent to gain a success rate that is around 1.3 SD'a above the league average.

With a week to go their success rate ( (wins + draws/2)/Games played) is nearly 1.8 SD's above the league average success rate.

Whereas Chelsea languish two thirds of the way down The Times' value for money table, they've actually won the league, while also being this season's third best over performers in terms of share of money spent and success rate achieved.

Rather than being lambasted in a quality daily, Roman's bean counters, backroom staff and players deserve a huge pat on the back for being the best and efficiently so. Even if there was, as ever, an element of unsustainable good fortune, as well.

Bournemouth fall from 2nd to 4th, Watford from 4th to 8th, Stoke drop from 6th to 10th and Swansea also drop to 15th from 11th. Manchester City rise from 13th in The Times to 6th and Liverpool go from 15th to 9th.

Some teams remain relatively unchanged. Congratulations Spurs, sorry United fans, but consigning to the bin this self confessed "simplistic" method of ranking over or under achievement is long overdue.

Also check out Omar Chaudhuri's time line for his views on this "bugbear" & an alternate approach to quantifying inefficiency in wages.

Points per wages is a personal bugbear: @martynziegler's analysis vs adjustment for fact £1 extra spend is worth way more at bottom of table pic.twitter.com/n06pkw240F

— Omar Chaudhuri (@OmarChaudhuri) May 16, 2017

The Championship Playoff Defensive Kingpins.

The second leg of the Championship playoffs are played out over the next couple of days and while the headlines will inevitably be grabbed by the goalscorers I thought I'd spread a little love for the workhorses whose job it will be to prevent the net from bulging.

Analytics has unsurprisingly concentrated on attempting to quantify those involved in the actual act of scoring or not.

Expected goals, either from the perspective of the the player taking the chance, those who immediately set up the opportunity or the keeper trying to make the save, can begin to quantify the probabilistic based process between the singular outcome.

However, defensive actions are more problematical.

Mere counting actions, without context can lead to misleading if plausible conclusions.

My first ever blog gloriously demonstrated that the recently promoted Stoke City may have lead the league in fouls committed, but once possession and opportunity were factored in it was actually Arsenal that perhaps deserved the title of dirtiest team in the Premier league.

A simple tweak, that more reveals the importance of an individual to the defensive actions of his side is to look at the proportion of defensive actions a player has attempted compared to the proportion of playing time he has enjoyed.

These actions may range from attempted tackles to interceptions and clearances.

We can easily add a further layer of information to this gradual contextualisation of defensive stats by including the average position on the field from where each player carries out these actions, as well as how spread out these actions are from this average point on the field.

Here's the Defensive workload undertaken by the players who may lineup in this week's Championship playoff second legs.

A defensive quotient corrected for playing time of 1.0, suggests a player is participating in an average share of his side's defensive duties and the larger the average % distance his actions occur from his opponents goal, the more his mixing it in the muck and nettles of his own half.

So two predominately green bars denote lots of defensive actions, predominately in his own half. And red and red equates to a lightly defensively involved player, likely playing much higher up the field.

Great to see Deano still plying his deep lying defensive skills at a high level!