Monk Loses the Winning Habit.

At the end of August 2014, two sides, Swansea and Chelsea were vying for the lead in the Premier League table with a 100% record from three matches. Aston Villa were third.

So it represented business as usual for Mourinho and a validation of the soon to be written raft of complementary articles about the bright new manager in charge at Swansea, Garry Monk.

As of yesterday two of those three teams have seen managerial change and Mourinho's tenure hangs by a Champions League thread.

Monk's hot start to the season was prolonged enough to earn him a place on the Daily Telegraph's shortlist of six for manager of the season, along with the beleaguered Mourinho and the subsequently dispensed with Sam Alladyce.

A near 50% attrition rate in the blink of an eye.

It is becoming commonplace to increasingly acknowledge the role that luck plays in shaping a relatively short, skill based competition, such as a Premier League season.

More data hungry models in late 2014 were already suggesting that Swansea had been relatively shot shy and fortunate even as they remained buoyant, only slightly removed from their August heights,

An abundance of 1-0 wins, seven in total by May, further hinted at a solid mid table side inflated upwards by random, most likely non repeatable events.

Premier League managers, always looking over their shoulders.

Outsiders are never privy to the inner workings of the professional relationships with a football club that may drive change, but it was particularly unfortunate for Monk that an immediate see-sawing of narrowly contested 1-0 games fell so badly for him in 2015/16.

Five such league defeats and a cup exit since August 2015.

Extremes, such as Monk may have benefited from in 2014/15, tend to be less extreme in the future, but fueled by euphoria and congratulatory broadsheets, they tend to become the normal expectation from both the fan base and employer.

Swansea's 14 actual points through 15 games are around a win shy of their most likely total based on shot model simulations and they have created enough to have had a 1 in four chance of bettering the 20 or more points that would have invited a more prosperous New Year.

The reality is probably that, in part at least, a straight comparison has been made between the 0.9 points per game this term and the near 1.5 points per match in 2014/15 and knees have been jerked.

Random variation gives and it sometimes cruelly takes away.

What Chance Bradford City ?

Prior to last season, the average, end of season league position for Swansea since the 2000/01 season was 56th in the league pyramid. The comparable figure for Bradford, their Capitol One Cup opponents later next month was 58th. Despite this near identical average record, over the ten seasons or so since 2000, the respective fortunes of both sides have taken very different courses.

The Yorkshire side began the decade by quietly slipping out of the top flight, 16 points short of safety, after just two seasons of Premiership football. There then followed a descent into the lower leagues, punctuated by two spells in administration and culminating in relegation to the bottom flight at the end of the 2006/07 season.

Swansea have taken a mirror image trip in the opposite direction, climbing from the lower reaches of the football league, to briefly share playing time with Bradford in the League One. Most closely during the 2005/06 season, when they finished, respectively sixth and eleventh, before pushing onto Premiership promotion for the 2011/12 season.

                                     The Respective Rise & Fall of Swansea and Bradford.

If you want to check the league position of other sides over the decade check out this interactive tableau graph.

The League Cup has often provided the lesser clubs a route to silverware and European participation. Cardiff represented Wales last season, this time as underdogs to Kenny Dalglish's eventual winners, Liverpool and prior to that Birmingham denied Arsenal a trophy in the Blues' relegation season. However, this year provides one of the biggest mismatches for English domestic football's first trophy decider of the season.

The records of inter divisional games in such competitions as the FA and League Cups, as well as the minor lower league knockout competitions has provided a large amount of matches involving teams from different leagues.We can therefore, use the scorelines from this interlocking format to produce a numerical comparison of the relative qualities of side from vastly different positions from within the league pyramid.

But an alternative method can be used involving calculating how much the top of one league overlaps with the bottom of the next highest league. When teams are promoted or relegated between divisions we can compare their season long records in the two divisions to again quantify the difference in quality as we move either up or down the pyramid. For example, teams who have dropped out of the Premiership have, on average seen their goal difference improve by around a goal per game in the less challenging Championship.

It is therefore possible to related Swansea's currently goal difference per game to that of a typical relegated side, which in turn can be equated to an average goal difference when they revert to being a Championship side. The process can be continued down through the divisions until we reach League Two, where Bradford City currently reside. So instead of viewing each league as a separate entity, comprising 92 teams in total, we can look at the four divisions as 92 teams where there is varying amounts of overlap. Therefore, although there are currently 70 places between Swansea and Bradford, the effective gap from a quality standpoint is less because, for example teams at the bottom of the Premiership will occupy a similar standing as some of the teams at the head of the Championship.

Our final step to quantifying the actual difference in quality between Swansea and Bradford is to first determine the effective number of places between the sides, having accounted for league overlap and then use historical results to find the average difference in class in goals that a one place change in position in the league hierarchy represents.

The average difference between sides next to each other in the lower half of the Premiership and the rest of the Football league is around 0.05 of a goal and the number of places between Swansea and Bradford, once doubly occupied positions are allowed for is only half the actual difference in numerical order. Combining these figures, we find that the current difference between the two sides is 1.73 of a goal.

Swansea, well to the front to taste Cup glory in 2013.

Goals are an extremely useful measure of the relative abilities of teams, but on a single match basis, win, draw and loss probabilities convey more information. The Poisson distribution, where the likelihood of an event occurring, given that we know the average rate at which that event is expected to happen, can be used to model individual correct scores and ultimate the probability of match outcomes.

The limitations of the Poisson approach is well known, particularly the under estimation of the draw, but typically a side with an expected advantage in the region of 1.73 goals would win such a game 74% of the time, draw 18% and lose 8%.

All League Cup ties are currently decided on the day or night, first after 90 minutes, then over 30 extra minutes, if required and finally by penalties. So the 8% chance given to Bradford over normal time only accounts for one of the three routes by which they may lift the trophy at Wembley in a month's time.

To take the game into extra time, Bradford need to draw over ninety minutes, a 18% chance based on interlocking league form and applying a Poisson to the expected goal difference. Once the game reaches extra time, Swansea's pregame advantage will be a fraction of their initial supremacy, due to the now truncated nature of the contest, but they will still be the most likely winners by a considerable margin. The Swans would be about a coin toss to prevail in the extra 30 minutes, a draw would be about a 39% chance and Bradford would have a similar chance of winning as they had in the original 90 minute stretch.

The third possible route to victory for either side involves drawing at both full time and extra time and then winning a shootout, for which I've allowed each side a 50% chance of being successful, despite Bradford's apparent prowess from 12 yards.

Chances of Each Team Winning the League Cup By Every Available Route.

TEAM.	Win in 90 Minutes.	Win in ET.	Win on Penalties.
Swansea City.	74%	9.4%	3.5%
Bradford City.	8%	1.6%	3.5%

Overall, a magnificent feat by Bradford City to reach the first showcase final of the season, but their 13% overall chance means they are still long outsiders to parade the cup in February.

Are Championship Sides Coping Better in the EPL?

It's hardly inventing the wheel or the iPad to suggest that goal difference is a very powerful football statistic.The more goals you score as a team and the less you concede,then the greater your chances of winning in the low scoring environment that is football.We've seen here and here that average goal difference is both a very good indicator of past success and because it auto correlates strongly it is also an excellent predictor of future performance.

Goals are the currency of football.

The good early season showing of all three promoted sides has led to the predictable conclusion that the gap between the Championship and the EPL is steadily becoming more easily bridgeable.Both QPR and Norwich are currently in the top half of the table and the playoff  winning Swansea are only three points behind the duo.If the former Championship sides were hunting as a pack they would have amassed 33 points from a combined 27 games and be around seven points from safety with eleven games to play.An impressive performance all round,even when allowing for the natural tendency for over achievement in part of a season to be balanced out by slightly less impressive subsequent results.

Recent events naturally lead to a selective bias in the way people analyse events and information.East Anglians,even Ipswich Town followers will have Norwich's fine recent draw at Anfield at the fore front of their thoughts when discussing the EPL,rather than Ipswich's much more substantial achievement of winning playoff promotion in 1999/00 and following up with a fifth place finish in the EPL the following year.

The natural first step is to evaluate the quality of the sides making the journey between the two leagues and their average goal difference is a good tool.It quantifies a team's worth and is easily comparable to the goal difference they achieve in the higher league and although you won't be able to deduce much about the absolute quality of the team,the change in a team's goal difference will indicate how easily they made the jump up in class.

There have been just over fifty Championship sides promoted to the EPL since 1993,so I split the sample in half and compared the average goal difference per game recorded by teams in their promotion season in the Championship and their figures for their first season in the Premier League.

Average Goal Difference per Game Comparisons between the EPL and Championship. 

Season.	Average Goal Difference per Game in Championship.	Average Goal Difference per Game in EPL.
2003-2011	0.66	-0.57
1993-2002	0.67	-0.41

There is very little to chose between the goal difference per game of either group in their Championship phase,but promoted teams fared on average almost two tenths of a goal better in the initial seasons than they did in the most recent seasons in the highest tier.These numbers imply that on average the Championship sides found the transition to to EPL easier to make in the fledgling years of the Premiership.

To try to confirm this initial impression I then plotted  the individual  regression lines for each batch of games to confirm that there was a reasonable correlation between the Championship season and the EPL season and one or two particularly outstanding promotions weren't skewing the averages.Visually there does appear to be a correlation between seasons and the line of best fit is steeper in the earlier batch than in the later one.This appears to confirm that similar average goal differences in the 90's and early 2000's  translated into better goal differences in the first season in the EPL compared to the later batch.

As an example,the line of best fit in the early seasons of the EPL sees an average seasonal goal difference of 0.6 goals in the Championship translating into an average goal difference of -0.5 in the subsequent EPL season compared to  -0.6 goals in the later seasons.Once again earlier EPL years saw the promoted teams faring slightly better judged by the regression line's predictions.Also the average finishing position for promoted teams in their first year of Premiership soccer was 14th between 1993 and 2002,while from 2003-2011 they finished a place lower in 15th.

The goal difference from a team's promotion season would therefore appear to be a reasonable indicator of their likely performance in the higher league,so I then looked at how robust the relationship is for the different categories of promoted sides.The Champions could be expected to be the strongest contenders for future success as they have most likely proved themselves consistently superior to their fellow promoted sides over a 46 game period and if we use the EPL as a guide the most successful teams are also the most consistent.If you plot the goal difference comparison graphs for the Champions,the second placed sides and the sides promoted via the playoffs we find the correlation between seasons is much the strongest for the Champions and the strength of correlation falls for the second placed sides and is almost non existent for the teams emerging from the playoffs.

The correlation between goal difference gained in winning promotion to the EPL and subsequent performance is strongest for the Champions and weakest for those who had to win their Premiership passports at either Cardiff or Wembley.

It would be naive to believe that points gained in the previous season is the sole factor in determining subsequent points totals,there are mainly contributing factors,the most obvious one being money spent in the pre season transfer window.The shape of the points graph for Championship winners finely illustrates this missing factor.The linear fit for the points is relatively strong,however the best correlation is illustrated in the plot below.

The best fitting curve comparing goal difference pre and post a team's promotion to the EPL.



























Four teams who averaged a goal difference of around 0.8 performed relatively badly once in the EPL.A significant number of sides who averaged a goal difference of just 0.6 goals actually acquitted better when they made the leap forward .If we look at the individual teams involved the four 0.8,yet underperforming teams spent virtually nothing in preparation for their EPL campaign.Nottingham Forest,steeped in a tradition where Peter Taylor bought a million pound talent for peanuts from Long Eaton United,sold more players by worth than they bought in their EPL season(and were promptly relegated),Sunderland spent a net £130,000 (and were promptly relegated),Norwich spent £3 million (ditto) and WBA spent £4 million and were relegated by 3 points.

By contrast the group of teams who performed slightly worse in their promotion year than the yo yo group  spent a net average of £18 million and that outlay enabled them to put in a significantly better EPL performance.Charlton spent £18 million,Middlesbro' £16 million,Sunderland £40 million and even the lowest spenders,Sunderland back in 1996 invested £6 million.The high rolling group also outspent the more successful Championship winners,who appeared to reason that their higher quality squad required a slightly smaller outlay in order to survive their initial foray into the top flight and the graphical representation of thir campaigns confirms that their optimism was well founded.The best of the Championship Champions invested an average of £10 million,half the amount spend by the ambitious,but weakest of the champions.The lack of investment,especially early in the history of the EPL is understandably as the risk of instant relegation,high wage bills and potential bankruptcy was very real,but that threat receded with the introduction in 2006 of parachute payments to the demoted teams.

So for the Champions at least transfer money spent and previous goal difference are both significant indicators of first year EPL performance.It's not as significant for runners up and playoff winners,who are coming to the post season transfer scrum somewhat later and could possibly find themselves buying poorer quality players at unattractive and inflated prices.

A Championship champion's likely EPL goal difference is given by

0.01 * (millions spent) + 0.85 * (average goal difference in winning the Championship) - 1.344.

If we therefore bring the article full circle and use the average figures for our imaginary,composite promotion entity comprising the combined records of QPR,Norwich and Swansea.The teams finished 1st,2nd and 3rd and within 8 points of each other,so for this mild diversion I'm going to treat the teams as Champion class,even if only QPR have the silverware to prove it.We find that they would expect to end with a EPL goal difference of -0.71 given their outlay so far and past goal difference.Currently their combined goal difference measured over their combined 27 games is -0.48,so as a group they are finding the EPL marginally easier than their record and the record of all previous Champions would have expected them to.However,the smart money would be on their individual records falling back to earth come May,although almost certainly not as dramatically as the decline experienced by Hull in their 2008/09 season,when they joint topped the table,were unbeaten in all but one of their first nine games,won at the Emirates and White Hart Lane and yet ultimately escaped relegation on the last day of the season.