Scotland Overturn the Odds In Rome.

The 2014 Six Nations made a brief, but compelling reappearance to the centre of the sporting stage over Friday night and Saturday afternoon. Three match weekends into a five weekend series has seen each of the six nations suffer at least one defeat. Although Ireland still hold a significant advantage by virtue of their points differential, they still have to travel to France on the final Super Saturday.

A comprehensive defeat for France in Wales and a much smaller one for Ireland at Twickenham leaves four of the six countries with ambitions to lift the trophy in mid March, but the most relieved coach will be an Australian born Scott.

Italy have gradually developed into worthy, if inconsistent members of Europe's premier international rugby competition, swapping occasional stunning wins against the top tier nations, with large margin defeats. However, they have become natural rivals with Scotland for the wooden spoon.

Since the competition grew from five sides to six in 2000, Italy have recorded 11 wins to Scotland's 18, well below the 37 win total posted by the next highest ranked side, Wales. So a match against Scotland, especially in Rome has increasingly become the game that Italy target to secure at Six Nations victory.

For much of the first half in the Stadio Olimpico, the narrow favouritism enjoyed by Italy, combined with the slight lack of overall quality throughout each team was reflected in a scoreboard that advanced only intermittently through penalty goals. An Italian try just before the interval appeared to give the home side the decisive score as they stretched their lead to 10 points. A deficit that almost always proves insurmountable. Not only does the trailing side require two at least two score to draw ahead, they must also prevent their opponents from adding to their score.

However, a flurry of second half try scoring from Scott Johnson's side edged Scotland in front, but they couldn't keep Italy off the scoreboard and as the clock reached the final minute they trailed 20-18 and heroic failure beckoned.

In the plot above, I've charted how the win/loss and draw probabilities fluctuated throughout the 80 minutes of the game. To add context and declutter the horizontal axis, I've listed the scoreline and various match events in the table below. As with football, scores are obviously the main factor in shifting in game probabilities, but pitch position also sways likelihood, although not as dramatically as in the NFL.

Time Elapsed.	Scoreline.	Comments.
0	0-0	Italy were 4 point favs at kickoff
3	0-0	Attacking lineout to Scotland
4	0-0
10	0-0
14	3-0	Penalty for Italy (Allan)
20	3-0
23	3-3	Penalty for Scotland (Laidlaw)
29	3-3
31	6-3	Penalty for Italy (Allan)
35	6-3	Scotland Attacking
36	6-3	Defensive Scrum to Italy
37	6-3	Attacking Scrum to Italy
38	6-3
40	13-3	Converted Try for Italy (Allan)
45	13-6	Penalty for Scotland (Laidlaw)
55	13-11	Unconverted Try for Scotland (Dunbar)
60	13-11
63	13-11	Scotland Attacking
65	13-11	Defensive scrum Italy
67	13-18	Converted Try for Scotland (Dunbar)
70	20-18	Converted Try for Italy (Furno)
75	20-18	Scotland Attacking
77	2018
79	20-18	Attacking Scrum Scotland
80	20-21	Drop Goal for Scotland (Duncan Weir)

Except for a brief few minutes late in the game when they took a five point lead, Scotland were underdogs right up until Duncan Weir's towering drop goal  16 seconds from the clock turning red. Although Scotland were well placed around the Italian 22 as they trailed with time expiring, the discipline of the Italian defence and a referee who was unlikely to penalise for anything but a blatant infringement, meant that they had to create their own score.

Two points down and with three on offer for a successful drop goal made their choice almost automatic. As they continually took the ball into contact, the chance of a fatal knock-on become all too real, so they had to trust to a kick that was further out than ideal.

Drop goals aren't successful anywhere near as often as comparable penalty kicks or conversions, a generic conversion rate of around 30% would be typical, although some are attempted under advantage when the player effectively has a shot to nothing.

Creating a goal expectancy model for drop goals follows the same route as those for goal expectation for shots in football. Matching the outcome of the attempt to the pitch coordinates from where the kick originated provides a baseline with which to measure any subsequent drop goal opportunities.

Weir was well outside the Italian 22 line, but shy of the 10 meters line and he had a nice line of backs innocently impeding any attempt by the Italians to charge the kick down. So his kicking action was relatively relaxed and although he was to the left of the posts, that aided the natural arc of his right footed kick.

As he caught Cusiter's pass and prepared to swing his boot, his and Scotland's chances of success probably hung around 26%. The odds favoured the hosts, but Weir provided a magnificent finish to a fine contest during one of the best overall weekends in Six Nations history.

Splitting Data At Home and Away.

Home advantage or the tendency of a team to produce consistent and significantly improved results at home compared to on their travels, is a recognized fact of virtually every professional sport. The existence of it in football is relatively easy to see. Depending upon the league, a team can expect to have an average goal difference per match at home that is around seven tenths of a goal superior to that that it records away, over the long term.

If its existence is a given, the reasons why a team performs less well away is more contentious. It's steady decline over time in leagues, such as the English top flight, implies that improvement in travel arrangements, that may have been major contributors in the past are having less of an effect currently. Also more detailed analysis has implicated potential factors, such as cowed referees and a desire to protect your home environment as a more primeval cause of home advantage. A factor that was particularly well recognized by home and visiting football fans, especially in the 1970's.

Another widely held cause is the partly synchronized approach where teams are naturally more adventurous at home causing their visiting opponents into a more measured defensive stance than they would usually employ. Even supporters of moderately successful sides eventually tire if their team appears to lack attacking intent on home turf.

If sides find themselves forced into adopting different tactical approaches at home compared to away, we should be able to see this effect in the game by game statistics, in much the same way as goal difference for home sides averages out at around 0.35 of a goal less than that recorded by the visitors.

To avoid one abnormal match skewing averages, for example if a tactically limited team tried to retrieve a situation by attempting cross after cross, I paired each Premiership teams matches by opponent from 2011/12. Therefore, in addition to looking at averages, we are also looking at a consistent tendency under relatively consistent conditions to produce above or below numbers of game events at home compared to away matches.

Stoke in 2011/12 had an inferior goal difference in away matches in 15 of their 19 paired matches compared to the corresponding home match. Three others were tied. For example, the Potters defeated Fulham 2-0 at home, but lost 2-1 in the reverse fixture. Turning a goal difference of +2 in the former into -1 in the latter. That the pattern continued for the great majority of their games makes it unlikely that Stoke were as adept at home as they were away, but the consistently under performing splits occurred through simple random fluctuations over the sample run.

In short, it was likely that the differences were real.

We can further break down the components of City's home field advantage in their last season on their legal, but extremely narrow playing surface. They scored significantly fewer goals away from the Britannia Stadium when comparing paired matches against the same opponent and they allowed significantly more scores on their travels.

For example, they conceded three goals at the Etihad, but just one when Manchester City visited the Brit and scored twice at home to Swansea, but failed to find the net at The Liberty.

Of more interest is if we apply this approach to each teams in game events data. Passes and other recorded events are the means a team attempts to use to create the ratio of goals scored and conceded and these may better describe their tactical approaches during matches. Be it through choice or because their course is partly dictated to them by their opponents.

For example, in 2011/12 (the only year I have this data), Arsenal, based on raw averages passed more frequently at home than away. 590 per match at home compared to 572 on the road. However, they passed more frequently against Norwich at Carrow Road than they had done at the Emirates and this wasn't an isolated event. It also occurred in paired matches against six other opponents.

So, although Arsenal may prefer to pass more often at home, that preference isn't so strong that we can say they do with a high degree of certainty based on this single season. An average of 18 more passes at home may be indicative of such a preference, but combined with nearly 40% of paired games when they attempted more passes in the away fixture, we could also put these splits down to random fluctuation.

We are on much more solid ground in citing a more pass happy home approach for the likes of Villa, Chelsea, both Manchester sides, Newcastle and Norwich. To cite an example, Newcastle played more passes in home matches compared to the away return in 14 out of the 19 paired league games in 2011/12. Averaging 460 home passes against 380 away passes.

So there is perhaps stronger evidence for a different tactical approach in these cases.

Team	Longballs.	Touches in Opposing Box.	Big Chances Allowed.	Fouls Won in Danger Area.	Cards Shown.
Arsenal.	More away.	More home.	More away.	More home.	-
Man. U.	More away.	More home.	-	More home.	-
Everton.	More away.	-	-	More home.	More away.
Chelsea.	More away.	-	-	More home.	-
Man. C.	More away.	More home.	More away.	-	More away.
Liverpool.	More away.	More home.	-	-	-
Stoke.	-	More home.	-	-	-
Newcastle.	-	More home.	-	More home.	-
QPR.	-	More home.	More away.	More home.	-
Bolton.	More home.	More home.	-	-	-

This approach takes a season long view of the frequency at which sides attempt to do things on the pitch. By comparing matches against the same opponent, many variables remain relatively constant. The manger, playing staff, make up of the opposition, ageing curves of the players, all should remain fairly stable and the only major change involves the swapping of the venue. So, hopefully any significant change in the data, seen by an inflated or depressed average, occurring over most of the paired matches can be attributed, at least partly, to a different tactical approach being pursued on the road compared at home.

In the two tables, I've summarized significant tendencies for a group of teams and a variety of on field events from the 2011/12 season. A dash represents a difference in home and away data that didn't appear extreme enough for a preference to be attached to that particular side. Their tactical approach at home was broadly similar to the one they employed away for the stats under review.  
 

Team	Total Passes.	Forward Passes.	Final 3rd Passes.	Through Balls.	Key Passes.
Arsenal.	-	-	More home.	More home.	More home.
Man. U.	More home.	-	More home.	More home.	More home.
Everton.	-	-	-	-	-
Chelsea.	More home.	-	More home.	-	More home.
Man. C.	More home.	-	More home.	-	-
Liverpool.	-	More home.	More home.	-	More home.
Stoke.	More away!	-	-	-	More home.
Newcastle.	More home.	More home.	More home.	-	More home.
QPR.	-	-	More home.	-	-
Bolton.	-	-	More home.	-	-

Where tendencies possibly exist, they are generally shared by Premiership teams. A team that creates more touches in their opponents box, always does so at home (a sign of offensive pressure) and increased volume of long balls (to relive pressure) most often happens on away trips.

Inevitably, even with the uniqueness draining from their veins, Stoke managed one more surprise. They played significantly more passes away from the Brit than they did at home. A Stoke side with the ball, being considered by opponents less dangerous than one without it, perhaps.

I haven't listed crosses, but Manchester United supporters may be relived to know that every team, except their neighbours, City cross more frequently at home. Although their side's recent crossing obsession against Fulham was somewhat excessive. Of more concern may be United's apparent ability to diversify their passing options, by venue at least, under SAF, compared to Everton's much less varied repertoire, shown in the table above, under David Moyes,

Zidane, The Guardian, Pulisball and the Value of Statistics.

It this post I suggested that knowledge of the cumulative goal expectation for a side is insufficient to fully understand the connection between shots, goal expectation and the final outcome of match. A side that spreads its goal expectation out over many shots, extends the possible range of the number of goals it may score. But such a team is at a long term disadvantage compared to a side that creates the same goal expectancy, but does so over fewer, more clear cut opportunities. The example I used was deliberately extreme to highlight the effect, although it did persist when goal expectation was diced between just slightly more chances.

This blog is primarily based around statistical analysis of football. Therefore, apparently I should be excluded from experiencing the artistic delights of say a Zidane (see the Guardian/WSC's recent enlightened blog post on stats in football).

Delving into the Frenchman's back catalogue to investigate the effects of a headbutt on World Cup final results, may be allowed, but marrying an interest in stats to an enjoyment of the artistry of football is a step too far for the self appointed guardians of the beautiful game.

Fortunately, the proposed embargo on watching and enjoying football, while also writing about the statistical side hasn't extended to the Potteries, where Stoke under Pulis invariably put theory into practice in a compelling celebration of the diversity of the sport. Although the genius of his design was often obscured by a blinkered appraisal tied simply to artistic merit.

Overall, a Tony Pulis side was out shot every season, but inched their goal expectation upwards by trying to maximize their quantity of high value goal attempts and skewed their distribution to include as many such efforts as Delap's arms could willingly provide. Goals scored with every available body part from the area of the six yard box, in defeating Arsenal at home in their first year of Premiership football, was the norm rather than the exception.

Rather than depart in May with a patronizing pat on the head for "playing football the right way", Pulis, whether knowingly or not, eked out every possible advantage, both tactical and now it appears, statistical, to creep above the 40 point line. In doing so his side provides an ideal test case on the real life implications of creating fewer big chances (Pulis) or more frequent, lesser ones (Hughes).

The tactical delivery systems used by Stoke worked most effectively at the Britannia Stadium, where they were able to make the six yard box a realistic target from virtually everywhere in their opponents half, by legally narrowing and shortening the playing dimensions. So I've used every shot faced and taken by Stoke during the 2010/11 season at home, when Delap was still an almost ever present. He played in every league home match bar one.

The goal expectation values are derived from my usual model that primarily incorporates x,y co-ordinates for each attempt and also accounts for the mode of the strike, either by the boot or a header.

Spreadsheets for nerds, Dukla Prague away kits for purists. Stoke roll the statistical dice in Bolton's 6 yards box. 

Some league wide generalities were strong enough to topple even Pulis' stylistic tendencies and Stoke, as the home side, did narrowly out shot their opponents at the Brit in 2010/11. 270 attempts from the visitors were met with just over 300 from Stoke.

The distribution of opportunities were more extreme, over 20% of the chances created by Stoke carried an expected goal probability of 20% or greater, compared to below 10% of total efforts carrying such a high likelihood of success for visiting sides. Therefore, this combination would, quite naturally result in a formidable home record for Stoke and in fact only the Big Four plus Liverpool gained more home wins than Stoke in 2010/11.

To avoid the tedium of an algebraic meltdown, I have simulated the 2010/11 home season for Stoke based on my approximation of the goal expectancy of each actual shot from either side in those 19 games. I've then repeated the process, but spread Stoke's goal expectation over twice as many chances. They have the same goal expectation, both for and against in each game, but the skewed distribution of big chances created under the banner of Pulisball has been reduced.

Above, I've plotted the spread of home league points Stoke might have expected to get creating their chances, either evenly spread across more opportunities or in the more "big chance", shot shy method preferred by Pulis. And once again the distribution of chances matters.

An average of 37 points were gained at home using Pulisball, compared to 35 .5 points if goal expectation per attempt were more uniform and chances more frequent. Pulisball gained at least 30 points (three quarters of the way to guaranteed safety of 40 points) over 97% of the time, compared to 87% in the alternative. And most telling, in paired comparisons, the former approach gained more points 55% of the time compared to 38% wins for the less extreme distribution, with 7% tied.

So a combination of visual evidence and statistical analysis might have bought us to a better understanding of one of the more intriguing and on going spectacles of the recent Premiership. Statistics can enhance an appreciation of all sports.

If we rely entirely on visual evidence, gut feeling and the power of prose, commentators would still be peddling the old myth that headbutting an opponent and getting red carded makes your numerically disadvantaged side "more difficult to play against".

Twelve Shots Good, Two Shots Better.

The proliferation of shot based models has lead to some excellent progress towards quantifying the primary talents of both strikers and goalkeepers. The importance of both shot type and shot location in determining the likelihood of success has been refined by the inclusion of important variables such as shot placement, as well as pace and power of the attempt. Small but steady progress is also being made towards adding defensive pressure to the mix along with keeper positioning and readiness.

Shot attempts and saves, when measured against a robust expected baseline can increasingly be used to identify striking and keeping talent, but the use of shot models to highlight potentially fortunate team wins or unlucky losses, may be more problematical. The fluid nature of the game inevitably means that a shot scored will inevitably alter the path a match takes compared to that same shot being saved. Not only do subsequent events inevitably take different courses in the two mutually exclusive scenarios, but the game state, a product of the score, relative abilities of each side and the time remaining will also meet of fork in the road, depending upon the success or otherwise of a single attempt.

Identifying problems is often halfway to a solution. for example, shots originating instantly from rebounds are the easiest to deal with. By allowing a side to score or concede just once from such intimately connected goal attempts, we can mitigate the problems of a second chance being dependent upon the first chance being missed.

However, even if we accept that goal attempts may quickly merge into the mundane ball recycling of the middle third of the pitch, before the desire is sufficient for another unrelated opportunity to be created, we may still be underplaying other factors, such as chance quality and quantity.

Late on Sunday afternoon, Fulham, were comprehensively out-shot, out-crossed, but not out scored on a visit to Old Trafford. United had 31 shots, nine on target for their two scores compared to Fulham's six attempts, three on target in claiming a share of the spoils. Even from shot location alone, it was apparent that Fulham scored from two exceptional chances.

Indeed Opta define their "Big Chances" as either a one on one situation with the keeper or an attempt from very close range and the opportunities that fell to Sidwell and Bent probably met both of those requirements. To further quote Opta both players could have "reasonably expected to score".

For all of United's gradual accumulation of large amounts of low grade chances and the goal expectation that went with it, Fulham created two high quality "one on one" chances from relatively close range.

Therefore, does a straight comparison of cumulative goal expectation give a realistic idea of what might/should have been, or is the spotting of "big chances" within the sample capable of skewing potential outcomes in a way that may not be apparent when simply looking at cumulative goal expectation.

To try to test the power of big chances, I simulated a match where two sides each accumulated a post game expectation of 1.2 goals based on the location of their chances. None of the attempts were as a result of rebounds, so we are looking at a simplified "shooting competition" , with equal goal expectation.

Team A created just two scoring chances, but each was of very high quality. They were both big chances and I've nominally assigned a 60% chance of scoring to each attempt. Team B, by contrast created 12 chances, but each of relatively poor quality. To maintain a goal expectation of 1.2 goals for each side, I gave each shot a 10% likelihood of success. So it is an artificial situation, but hopefully a test of the effect of goal expectation being unevenly spread among varying shot quantity.

Potentially, team A, based on just two goal attempts can only score a maximum of two goals in a shot based simulation, compared to a maximum, if highly unrealistic 12 goals should all of team B's lower probability attempts find the back of the net. The goal expectation based on their shots taken during this virtual game is the same for each side, but is there a long term advantage to creating a couple of guilt edged opportunities, instead of taking more numerous, but less likely to convert shots?

In short, do distributions matter, as well as raw goal expectation?

Running the simulation appears to show a distinct advantage for the team that creates isolated "big chances" compared to a side that steadily accumulates regular, good but not great opportunities. If a side generates more attempts in reaching the same post game goal expectation, their range of likely winning scorelines increases, but over the long stretch, in this artificially extreme example, a couple of big chances appear to get you more wins.

Simulating 20,000 Matches Between 2 Sides which Generated Identical Goal Expectations over widely Differing Shot Counts.

Team	Av. Goals Scored.	Av. Goals Allowed.	% Wins.	% Draws.	% Losses.
1.2 Exp. Goals Spread Over Two Shots.	1.20	1.20	37.4	30.4	32.1
1.2 Exp. Goals Spread Over 12 Shots.	1.20	1.20	32.1	30.4	37.4

This result may simply be an artifact of my method. Although a less extreme example, where a goal expectation of 1.2 for each side was spread over 10 and 12 shot attempts respectively, gave a similar advantage for the side creating one clearer cut opportunity. Over 100,000 iterations, a side having 9 chances each with a goal expectation of 10% and one of 30% won the "game" 36% of the time compared to 35% for the team that created twelve 10% chances.

Accrued goal expectation may be the prime driver in evaluation if an actual result was deserved, but the ability to create a couple of outstanding chances (which may or may not be repeatable at team or player level) may also play a minor, yet important role. In certain circumstances, the benefit may be greater than simply the sum of the parts.

The whole concept of shot based models is developing at a rapid rate, so for further reading I strongly recommend you track these guys down on Twitter @colinttrainor, whose excellent work appears on StatsBomb, @footballfactman, who writes as Paul Riley about keeper evaluation, @11tegen11, who is pushing the use of expected goals models in an exciting predictive direction and @The_Woolster, who has must read views on Opta's big chance metric. Apologies to anyone I've omitted, feel free to post in the comments section.

The Value of an Extra Home Game in the Six Nations.

Often the format under which a tournament is played can have a considerable influence on the eventual outcome. Tennis provides a prime example. Five set matches enable the superior quality of a higher seeded player shine through compared to a best of three set sprint and, unlike the FA Cup, the best players are often seeded to meet in the final, rather than the earlier rounds.

A Seattle/Denver Super Bowl wouldn't have been possible prior to realignment in 2002, when the Seahawks moved from the AFC West to the NFC West. And their return to the NFL's showcase game also owes something to a playoff format that rewards the highest seeded teams with fewer post season matches and home field advantage all the way to the Super Bowl.

Another epic sporting occasion begins on Saturday with the first round of the Six Nation rugby and it also has a format that potentially aids certain sides in particular years. The four home nations, plus France and Italy play each other over five weekends. Therefore, each country alternates between playing two and three home matches from their total of five fixtures. This arrangement, not only creates alternate feast and famine markets for six nations tickets, but it also should logically give the teams with three home ties an advantage compared to seasons when they only host twice.

The home field advantage, in keeping with the NFL and rugby league, is worth around three points in union. So a switch in venue accounts for a swing of six points or very nearly a converted try.

At the start of the 2013 Six Nations, Wales hosted Ireland in Cardiff in the first match. Overall, Wales was considered the fourth most likely side to win the tournament with around an 18% chance of success, their visitors were slightly more favoured with a 22% chance. So Ireland was rated as a slightly superior side compared to the Welsh and that was reflected in the matchday predicted margin of victory. With the help of home field advantage, Wales were expected to win by an average of two points in repeated trials.

Had the game taken place at the Aviva Stadium, Ireland would have been four point favourites.

Expected margin of victory or defeat can be readily converted to win or loss probabilities. Wales as 2 point favourites in Cardiff are likely to win around 53% of the time, compared to just 36% of the time as 4 point underdogs in Dublin.

Similarly, England's expected 16 point margin of victory when hosting Scotland, equated to a near 90% chance of victory compared to a ten point average winning margin and a 78% chance of bringing the spoils back from north of the border.

Therefore, points spreads (assuming their accuracy) can be easily used to simulate not only recently completed tournaments, to gauge how likely was the actual outcome, but the venues for each match can also be reversed to test the impact of the unbalanced five game format.

Simulation of Six Nations 2013 Based on Points Spread for each Game.

Country.	Number of Home Games in 2013.	Simulated % of Outright Title Wins.	Overall % of Title Wins (inc decided by points differential).
Wales	2	8.4	13.2
England	3	33.7	43.8
Scotland	3	0.7	1.6
Italy	3	0.4	0.7
Ireland	2	10.8	16.1
France	2	16.7	24.6

With the title decided over just 15 matches, it isn't uncommon for the top sides to end the championship level on points. Around 30% of the simulations for 2013 finished in at least ties and 4 out of the 14 tables (29%) since the competition was extended from five to six nations has seen the top sides level in terms of league points. So, points difference, akin to goal difference in football, now comes into play to decide the champions.Therefore, the second column denotes how frequently a side "won" the simulation without recourse to a tie breaking, points reckoning and the final column includes "wins" such a Wales' in 2013, where points differential across all five games was required to split teams at the top.

We can now reverse the venues and repeat "2013" using alternative probabilities that reflect the altered chances of each side winning or losing these virtual matches to see if the presumed advantage of playing three of the five matches at home is a significant factor.

Simulation of Six Nations 2013 Based on Points Spread for each Game, but with Venue Reversed.

Country.	Number of Virtual Home Games in Alternative 2013.	Simulated % of Outright Title Wins.	Overall % of Title Wins (inc decided by points differential).
Wales	3	7.4	12.4
England	2	33.2	44.0
Scotland	2	0.7	1.4
Italy	2	0.1	0.2
Ireland	3	8.8	14.8
France	3	18.7	27.4

Initially it appears that both simulations yield very similar results. The order in which each side was most likely to finish remains the same, whether a team had three or just two home matches. The chances of particularly England and Scotland are almost identical over 10,000's of iterations despite the reversal of venue.

Most interesting is that while the chances of France lifting the title improved for an extra home game, those of both Ireland and Wales declined slightly. There could be countless reasons for this apparent quirk, not least a faulty simulation or insufficient iterations.

An alternative explanation is that it is not just the number of home matches that impacts on  the likely number of points a Six Nations side may get, but also the relative ability of those opponents.

Based on the relative merits of the countries in 2013, Wales gain around an average of 18 extra wins per 100 matches when playing England at the Millenium compared to visiting Twickenham. As an extreme comparision, England's predicted 95 wins over Italy in the Stadio Olimpico has a very limited upside when the match takes place in TW2. Home field advantage in the latter case adds very few extra wins to England's cause.

Might home field advantage be a larger boon to teams facing similarly matched opponents, rather than taking on markedly inferior ones.

Both the Celtic nations each entertained two (on paper at least) strong rivals in their 2013 season with only two home matches. Wales hosted Ireland (3rd favs) and England (favs) and Ireland entertained France (2nd favs) and England (favs). France, by contrast had visits from Wales (4th favs) and Scotland (33/1 fifth favs).

So the interplay of two weakish (on paper) home opponents in one season for France, produces inferior expected returns compared to the reverse fixtures when they have three home matches. But the relative strength of the two home opponents for Wales and Ireland appears more advantageous than an extra home tie, but against markedly inferior countries.

In short, playing two very good teams at home and three,on average, less able ones away, may give you a better chance to win enough games to lift the title compared to the alternative of three home matches against overall weaker opposition and two really tough games on the road....Even though the latter alternative involving an extra home game superficially appears more attractive.

 Will Three Home Games Prove a Help or Hindrance to Wales in 2014?

Whatever the speculation, the way the unbalanced fixture list has evolved doesn't appear to unduly handicap any one side in the Six Nations and there may even be reasons to think that the complex interaction of matchups may actually slightly assist some "two home game" teams.

What the simulations do show is the scope for shock results to influence a competition decided over a relatively small numbers of matches. 2013's reality of Italy defeating both France and Ireland, Scotland finishing 3rd, Ireland on the opening weekend beating Wales, the eventual champions, before themselves nearly finishing bottom of the table, probably appears somewhere in the 10,000's of simulated championships, but it is a fairly unlikely one.