Rugby World Cup Simulation

World Cup's have been like London buses this year and the rugby union version kicks off in a week or so.

It's live and complete on terrestrial TV in the UK, with plenty of huge mismatches in the opening group games, before eight teams, (whom could be fairly accurately predicted beforehand) hold the really interesting knockout run to the Webb Ellis Trophy on November 2nd.

However, that's not to say that the group matches don't hold any intrigue. There are at least two tier one teams in each of the four groups and while they'll be expected to steamroller the lower grade group opponents, the outcomes of these elite matchup will have a huge bearing on how the pairings for the knockout phase pans out.

Therefore, if you want to chart the likelihood of a team's route to the final being paved with Southern hemisphere behemoths, a tournament simulation is the easiest method out there.

You'll need a ratings system to kickoff with, assuming you're shunning the merry-go-round that has been the world rankings. Ireland are the current leaders, having recently displaced Wales, who had just displaced New Zealand, who themselves had displaced South Africa....ten years ago.

So the world rankings, following a decade of stagnation have suddenly become volatile.

Let's make our own, instead.

I took the last 20 matches for all participants, and produced an attacking and defensive rating, based around match scores and opponent quality.

New Zealand are the tournament's most potent attack, they'll score around 14 more points against and average team than another average team would manage and Wales, courtesy of rugby league knowhow, has the best defence.

Next you need a way to simulate game outcomes.

The big clash of the group stages sees favourites New Zealand take on South Africa. After matching up the respective attacking and defensive ratings for each team, the model expects the All Blacks to average around 28.5 points and S Africa 23.5.

New Zealand are favoured by five points and there's likely to be 52 total points.

If we look at the spread of points scored and allowed by each side over the last year or so, we can produce a distribution of points that describes each team's likely scoring pattern in this game. We'll then draw a value randomly from this distribution for each team to simulate a single match scoreline and then repeat the process thousands of times.

After adding a few tweaks to mimic the largely redundant bonus points system rugby insists on employing and ensuring that each drawn score from the distributions is a "rugby score" (no scoring a grand total of four points etc), we just repeat for every group game, add up the total points won in the group, follow the draw format and find the winner.

This is how the simulations shake out.

Four sides with a double figure percentage chance of lifting the trophy, New Zealand, S Africa for the south and England and Wales for the north, with the former looking a vulnerable favourite.

Quantifying the Value of Every Pass

I've written about passing models over the last couple of years and posted passing maps for individual players and teams recently. So here's a quick overview the passing model upon which those maps are based, how it was developed and how they might be useful.

The model is derived from location and time stamped Opta data for every pass attempt. The model has been build in conjunction with Infogol, but as yet it isn't part of the data available on the Infogol app.

I was keen to use familiar units for the passing model, therefore all values for successful or unsuccessful passes are expressed in expected goals.

I've purposely avoided such things as distance gained, as this often leads to arbitrary definitions for "key passes".

It also breaks down entirely when you approach the penalty area, not only in terms of scaling, but also assigning value to a backward pass that actually adds value to a side if it is completed. (Think pull backs from the goal line, a "progressive" pass can easily go backwards).

The baseline values are the likelihood that possession at any position on the field will end with a goal and is taken from historical data.

Therefore, if passing from one point to another improves the likelihood of a goal, the successful pass is quantified as the change in this likelihood.

Because the unit of measurement is how likely historically, possession is to turn into a goal, it doesn't require a goal attempt to ultimately be made at the culmination of the move.

This is a huge advantage over passing models that are based solely around attempts being taken because every pass attempt is counted (a player is not reliant on success or failure further down the passing chain).

It also makes the calculation of speed of attack much more relevant to the actual threat present (advancing the ball ten yards in a couple of seconds from the final third causes much more of a threat than advancing the ball 20 yards in half the time from your own penalty area).

Finally, because the units relate to aggregated historical outcomes of possessions, we can quickly give a value to any point of the field, which is not the case if the point value is based on the expected goals of an actual goal attempt from that position.

And so because a goal attempt isn't required the units are designated as non shot expected goals to differentiate them from shot based xG.

To keep things simple, the following non shot xG passing maps omit other actions, such as carries or dribbles, take no account for time of possession or any likely passing skill differential.

The following maps simply record any successful, "progressive" pass (by which I mean any pass that advanced the likelihood of a team scoring) made by a player during the last Premier League season.

The maps are simply conditional formatting in excel, on a 10X10 grid, overlaid with a pitch. 10X10 is used for the convenience of Opta's x,y pitch locations which run from 0-100, lengthwise and widthwise.

The darker the conditional formatting the more NS xG has been gained from a successful pass from that location. Either by small gains, but large passing volume, large gains and fewer passing volume or a combination of the two.

It's easy to show the passing distribution through other plots.

Here's England's newly capped Declan Rice's successful progressive NS xG gains for WHU in 2018/19.

This represents the starting point of every successful pass.

The plot is best used in conjunction with video analysis, but you can quickly see that Rice's sphere of influence is concentrated broadly in front of the back four and across the line, but he also delivers an impressive range of threatening passing options mid way inside the opposition half and just leftfield.

The next thing we'd like to know is where these passes end up, so the following plot illustrates where on the field this improvement in NS xG production from Rice via his passes is distributed and received by a team mate.

Overall Rice's progressive passes are received around 10% further upfield than their points of origin. He spreads the ball wide, as noted by the darker areas on the flanks either side of halfway and towards the final third. And he finds a team mate on the edge of the box, but doesn't appear to be a predominate passer of the ball into the box (particularly if we strip away set plays).

Rice appears to be an active and productive passer over around three quarters of the playing area, but may not be fully appreciated because he rarely plays a pass that may be considered an assist.

By contrast, here's a much more attacking NS xG passing profile from Manchester City's midfielder, David Silva. A darling of the highlights reel.

 Unlike Rice, Silva rarely ventures into his own half to begin build up play. The starting point for his progressive passing is a hot spot just outside the left edge of the opposition penalty area, although he does occasionally drift to the opposite side of the box.

The end point of his passing is again strongly centred around the left side of the field, but deep into the opposition box. He sticks rigorously to the left sided channels and relatively shuns pass attempts to the right side of the box from his team's perspective.

Finally, for now, we can also show where a player is showing up as the recipient of a progressive pass.

Once again his fondness for linking up with a team mate in the dangerous left hand side of the area is shown, firstly by the darker formatted green area just inside the left flank of the area on the plot and secondly in an actual example from a game.

This just scratches the surface of how these plots, maps and quantified valuing of passes can be useful in assessing a side, or a player. It is particularly welcome because it removes the highlight reel aspect that blights player assessment (particularly on youtube immediately following a transfer). We can see from the heat maps if creative passing into particular areas of the field is a largely consistent player trait....or if the exceptional pass, that perhaps resulted in a goal was a once in a lifetime fluke.

This post has concentrated on progressive, NS xG gaining successful passes, but it can also be applied to unsuccessful attempts to measure risk reward, the probability of a pass being completed can also be added and we can also look at ball retention plots to see which players excel at retaining the ball for others to make the decisive progressive deliveries.

Rice and Silva obviously play different midfield roles in widely differing teams, but their respective importance and discipline in playing a role it those two systems becomes much more apparent once we look at their passing contribution as a whole.

The Best & Worst Passers in the 2018/19 Premier League.

This is essentially just a data drop of the passing abilities for every player who made at least 600 pass attempts in the last Premier League season, based on a non shot passing model.

Here's our approach.

Every inch of the pitch has a non shot expected goal value associated with it based on the likelihood a side will eventually score from that field position.

So it's very low if you have possession near your own goal, much higher if you possess the ball inside the opposition box.

Successfully passing the ball from one point to another leads to a change in NS xG.

If you have the ball on the edge of your own box and roll a pass five yards forward to a defensive midfielder, you get credited for improving the side's NS xG, but not by much. Repeat the move on the edge of the opponent's box and you'll get a fair bit more.

Knock the ball backwards and your side "loses" NSxG, but at least you keep the ball.

Give away possession, either as a defender accidently passing to an opponent near your goal and you lose a combination of the NS xG you had and the NS xG your opponent gains.

Similarly, try and fail with a tricky pass inside the opponent's final third and you lose the fairly substantial NS xG your side had, along with the much smaller NS xG the opposition has gained.

This has led to three definitions for types of passes, two successful and one not.

Firstly, successful, creative passes that improve a team's NS xG.

Then, successful, backward passes that retain the ball, but "loses" NS xG

And finally unsuccessful passes that turnover possession.

These are further normalised for position played.

A defender will have a very different average profile in each category, compared to an attacking midfielder and the metric is also normalised to 100 passing attempts to put players who play for a possession poor team on a more level footing with Manchester City.

Here's an example.

From left to right. The average Premier League full back adds 0.64 non shot xG per 100 passing attempts by way of successful, creative passes. TA-A added 1.026 NS xG/100, an improvement of 0.386 on the average full back.

Backward, successful passes where NS xG was "lost", but possession was retained mirrored the average experience of a full back.

An average full back actually lost 0.8 NS xG / 100 via turnovers, TA-A did slightly worse, losing 0.894, but this is a function of the risk/reward balance. He is given free rein to get into advance positions, but the reward is well worth the extra risks taken.

Here's the differentials for every player who made at least 600 passing attempts for all 20 clubs last season.

They've been normalised for position, but many are a product of the role they are asked to play and the stylistic approach of the team they represent.

Figures such as these cannot tell the entire story, pass volume in particular will be hugely relevant, but we can take a lot from the tables.

For instance, there's the different roles of goal keepers. Those who play out from the back, such as Alisson & Ederson added below average creativity, but are well above average when preventing turnovers.

Similarly, van Dijk is no more than an averagely creative passing centre back, but again the systematic demands of the team do not require him to be more adventurous. His main aim is to largely play unadventurous ball to slightly advanced players and again, not turn the ball over, which is reflected in his well above average turnover numbers.

Manchester City's adherence to keeping the ball is shown again by the turnover figures, with the perhaps significant exception of Sane, who is poor at retaining the ball, with little above creativity to compensate.

Passing volume ensures that their relatively unexceptional creativity, De Bruyne aside, invariably overwhelms an opponent.

And finally, the departing Hazard is a rare beast, who not only is above average creatively for his position, but also avoids the often boom or bust cycle by looking after the ball exceptionally well.

There are plenty of players who show above average creativity, but pay a relatively high price with turnovers.