Monday 28 January 2013

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.

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