Rangers' regression has been halted as stunning graphics show van Bronckhorst effect

The problem seems to be rooted in the name and the misguided view that it attempts to predict scorelines. As if bookmakers haven't been trying to do the same thing for decades without the same level of noise.

In essence, a shot that has a ranking of 0.10 expected goals is comparable to a racehorse given 10/1 odds at the bookmakers.

Based on thousands of similar shots from that exact location on the pitch, a statistical model has decided that this shot at goal - or this horse in a specific race - should be successful once in every ten attempts. That's it, and it's a prediction but with a few caveats.

In most expected goals models, the player quality does not come into account. A penalty received an xG rating of 0.76xG, meaning that 76% of the time, it hits the back of the net. Would you bet on Kemar Roofe scoring more than 76% of his penalties? You probably would. Would you bet on Allan McGregor scoring more than 76% of his? Probably not. Therefore the 76% is the average of all players who have taken penalties in a specific timeframe. In other words, a penalty is converted in football roughly three times out of four.

You can query how long that timeframe for analysis is or which players and leagues are included in the calculation, and that's absolutely your right as a fan. But on the flip side, fans who try to predict results at a William Hill don't really know what bookmakers use to calculate their odds. Most of the time, it is a combination of things like team quality, previous results, form and more recently, advanced statistics such as Expected Goals.

READ MORE: Rangers' sudden improvement under Giovanni van Bronckhorst should have the rest running scared - Four Lads

When analysing a match, a shot will be assigned an xG rating, and the total of this will be the overall xG rating for that team in this game. In simple terms, if Rangers attempted ten shots that all had an xG rating of 0.5xG, then Rangers xG for that game would be 5. It attempts to measure how many good quality chances a team creates and, when compared to the goals scored in that game, indicates whether or not a team is performing as expected. As with all analyses, basing opinions on a single shot or even a single match can be flawed due to the limited evidence available. Therefore, a sample size of approximately ten games would be the minimum indicator to analyse any potential trends.

In the early part of this season, Rangers results were much more positive than their performances suggested. They scored goals from minimal chances whilst not playing anywhere near their best. The results contrasted to this, with the only defeat coming against Dundee United at Tannadice very early in the season - a sandwiched game between the Malmo doubleheader. The fans noted that Rangers couldn't continue playing as badly without slipping up. As the number of goals scored were significantly higher than the quality of chances being created, Rangers were primed for a 'regression' which means that the law of averages should kick in. Rangers could expect their luck in front of goal to run out unless overall performances improved.

In Match 6 of the league season, Rangers drew 1-1 with Motherwell at Ibrox and recorded an xG figure of 2.39, their highest of the season. For the first time this term, Rangers had created more frequent and higher quality chances than they had been able to convert. As you will be aware, they would draw three games in a row against Motherwell, Hearts and Aberdeen at Ibrox. This is the law of averages discussed earlier kicking in as Rangers should have beaten Hearts and Aberdeen based on the quality of chances created in both of these games. 

This is where probability and trends come into play again as far as analysis is concerned - not just in football. Suppose there is an overperformance in any field, from stock markets to sports. In that case, the expectation is that this should begin to average back out over a more extended period. Therefore if Rangers are consistently creating many good chances but are not converting them, it is unlikely that this will continue long term. Especially given the quality of players Rangers have in their attack and their control on most games. Since the last draw against Aberdeen, this has proven to be true. Rangers have since won four league games in a row.

As you can see by the graph above, they are enjoying their longest sustained period of high-quality chance creation since the campaign started. This four-game run included challenging away trips to Hibernian and Livingston, which should reassure that Rangers can maintain this throughout a hectic winter period.

In essence, the data above suggests that Rangers are currently in a period where they are creating higher quality chances than they have all season. The expectation is that this should continue, provided both team and individual performances remain at the same level.

Chances Conceded

Rangers have conceded 14 goals in 15 games this season, which is already higher a total of 13 conceded for the whole of last season. A large number of these chances have resulted from defensive errors. Still, many of these have also been conceded with an opponent's only shot on target. Similar to chances created, this would not be expected to continue throughout the season as the underlying data suggests.

It stands to reason that Rangers cannot be expected to continue to concede sloppy goals given their dominance in games. Since Rangers 1-1 draw with Hearts on Match 9 of the season, the quality of chances Rangers has conceded per game has reduced steadily. The goals conceded have not reduced at the same rate, which suggests that more regular clean sheets may not be too far away.

Interestingly in Giovanni Van Bronckhorsts first two league games - historically difficult away trips to Livingston and Hibernian - Rangers recorded their two lowest xG conceded figures of the season.

Even at this stage, this shows an improvement in how Rangers are defending and a reduction in the number of chances being allowed to the opposition. Should this continue, the expectation is that the defensive record will also start to improve.