A few weeks ago I quantified the epic scale of Arsenal's second half collapse against Tottenham Hotspur, and I couldn't help but harken back to that data set during Arsenal's match against Birmingham. Arsenal headed into halftime with a 1-0 lead, and I noted that they had a 64.7% chance of winning the match. After the third goal, and deep into the second half, I called for a clean sheet. After the match I went back to the 2005-2010 results to study the odds of all such outcomes, and the results are presented below.
My previous post on this topic focused on an ever-narrowing case of circumstances - first on halftime leads, then on home halftime leads, and then home halftime leads that are also clean sheets. In this analysis, both home and away leads and clean sheets are studied. Of special interest in this study is whether or not increasing goal differences at the half increase the likelihood of victory and/or maintaining a clean sheet. To judge this, a Z-test for two proportions was used via this online calculator.
The two proportion test is used to compare the percentage of an outcome - let's say wins - given a goal differential at the half - let's say two - versus the next lowest goal differential - in this case one. This is done for each goal differential to determine if there is a statistically significant change in the likelihood of an outcome given each increase in goal differential. Throughout each table a red highlight indicates a statistically significant reduction in the likelihood of an outcome and green a statistically significant increase in its likelihood. Logic would dictate that as goal differential at the half increases, we'd expect to see more green in the win column and more red in the draw and loss columns. One could see the colors going either way when it comes to clean sheets.
The Effect of Goal Differential on Match Outcome
The first effect that is examined is the extent to which increasing goal differential at the half helps home and away teams translate matches to victories. A baseline must be established before any comparisons can be made. The table below summarizes the overall outcome of matches from the 2005/06 to 2009/10 seasons in the English Premier League (click to enlarge).
Readers paying close attention will notice that the Home and Away wins and loses are inverses of each other. Here one begins to understand the home pitch advantage in the EPL. Not only does the home team have a nearly 80% better chance of earning the full 3 points, they also have a 41% better chance of earning at least a single point via a draw. These baseline percentages - regardless of halftime lead, regardless of half time clean sheet - are now used to study whether such halftime advantages produce statistically significant advantages in winning a match.
The table below summarizes the effects of goal differential on match outcome for both home and away teams (click to enlarge).
There are a few critical points to be made based upon the table above:
- The expected patterns of increased chance of winning the match, and decreased chances of drawing or losing the match, apply to all differentials except Away teams with a single goal differential. In this case, the likelihood of winning goes up but the likelihood of drawing does not. The likelihood of losing does go down by a statistically significant amount. This likely means that a single goal differential is enough to guarantee nearly nine in ten away teams a single point by greatly reducing the chances of a loss, but is not enough to move enough teams to the full three points.
- Interestingly, a one goal differential is the last point where the home team has an advantage over an away squad with the similar goal differential. By the time an away team has a two goal advantage, their likelihood of a win or a draw is statistically indistinguishable from a home team with the same advantage.
The Effect of Halftime Goal Differential on Maintaining a Clean Sheet
The table below summarizes the likelihood of a team maintaining a clean sheet with increasinging goal differentials.
There appears to be very little correlation to halftime goal differential and the ability to maintain a clean sheet for away teams. This seems a bit intuitive, as all it takes is a single goal to upset a clean sheet, and teams that are up by several goals may be happy to come away with the rare away win and resultant three points. Part of this also stems from the natural advantage a home team has in scoring goals - while the away team may go on to win the match they they seem to concede at least one goal 50% of the time.
The impact on the home side is much more interesting. When a home side goes up by two goals at the half they have a statistically significant 69% chance of finishing with a clean sheet - the highest percentage outside of the four goal scenario. However, when they reach a three goal halftime lead they see their chances for a clean sheet drop to 43.8% - the lowest of any differential home or away. Perhaps there is something psychological about a three goal halftime lead that makes the team that is on the wrong side of that lead come out of the half with more desire to score a goal quickly. Perhaps they see a three goal differntial necessitating quicker scoring than a two goal differential. Perhaps it makes the team on the right side of that lead more lazy. Whatever the cause, it generates a statistically significant drop in the likelihood of maintaining the clean sheet.
Whether a team is home or away, they should not lose a match when they have a two goal halftime lead. Beyond that, they can truly hang their head in shame if they lose after having a three goal or better lead at the half, as they would be the first team to have not won a match in the last five and a half years with such a lead. The likelihood of a clean sheet for an away team with a halftime lead is no better than a coin flip, while fans who desire a clean sheet of their team at home should root for a two goal lead at the half but nothing more. Keep these likelihoods in mind the next time your team is down or up by as many goals at the half.