Whose headers are better?

After watching Nadir Ciftci blaze several close-range headers off target during the first leg of Celtic's Champions League qualifier versus Stjarnan FC, I thought it would be interesting to take a closer look at headed shot attempts by strikers in the SPFL Premiership last season to answer the question, whose headers are better? (long story short, it ain't Ciftci)

The scatterplot below shows the relationships between total headed shots, headed shots on target and headed goals (all per 90 minutes played) for 41 strikers who played at least 500 minutes last season. All the data come from either BBC match reports (for shots) or Soccerway (for minutes played).

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The first thing to notice about the plot is that goals p90 (dot size) is only loosely correlated with total shots and shots on target. This is due to the fact that differences in shot conversion rate are mostly random in the short-term.

For example, if we just look at goals, we might conclude that 5'8" Leigh Griffiths (Celtic) is one of the best in the league at headed shot attempts. I don't know any Celtic fan who would agree with that statement. A better explanation is that he got lucky with the relatively few attempts he took last season. Thus, goals p90 is a not a very useful metric for judging whose headers are better.

Turning our attention to the more useful metrics, total shots and shots on target, we can see from the plot that three strikers really stand out: Josh Magennis (Kilmarnock), Brian Graham (formerly of St Johnstone) and Edward Ofere (formerly of Inverness Caledonian Thistle).

Ofere played relatively few minutes for ICT, so I don't consider his data to be very reliable. That leaves us with Graham and Magennis. Of the two, I would regard Magennis as the better header since his accuracy was much higher than Graham's. The latter got roughly as many headed shots on target as you would expect from the number of shot attempts (hence his dot is close to the regression line). Magennis, on the other hand, got many more headers on target than expected (hence his dot falls way above the line). I think it's safe to say the Northern Irishman was probably unlucky not to score more headed goals than he did last season.

So whose headers are better? In my opinion, the answer is Kilmarnock's Josh Magennis. Don't believe me? Just ask is team mate Jamie Hamill...

Josh Magennis demonstraing his excellent head shot accuracy

How long does it take conversion rate to stabilize?

Conversion rate (goals per shot attempt) is known to be a highly volatile aspect of performance that can fluctuate randomly within and between seasons. Conversion rate also tends to converge to a typical value over time (often called, regression to the mean).

This does not mean that conversion rate is soley luck based however. But the skill component may only be evident over a relatively long period of time. In other words, we may have to observe a lot of shot attempts before the skill component of conversion rate emerges. The question is how many?

In this post I will attempt to discover how many shots are needed before we can be confident that the skill component of conversion rate is evident. I will examine both conversion rate for and against using data from football-data.co.uk for the top division of Scottish football (SPL/SPFL) over ten seasons (2004-2014). My analysis is limited to six teams who played in the top division every season during this period, these are: Aberdeen, Celtic, Dundee United, Motherwell, Kilmarnock, Hearts, and Hibs.

My basic approach will be to plot cumulative conversion rate (for/against) vs cumulative shot totals at the match level, and to visually inspect these plots for a point or region where the volatililty seems to subside.

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The take home message from these charts is that it takes a looooooooong time for conversion rate to stablize to a point where we can reasonably argue for team differences in skill. We are talking about shot numbers in the thousands, not hundreds (2000-3000, depending on whether the shot is for or against).

The exception to this rule is Celtic's conversion rate for. Becaue they are the biggest club in Scotland with the biggest budget, they generally have much higher quality players. As such, their conversion rate for is distinctly high, even at relatively low shot numbers. This is clear evidence of a skill-based difference in conversion rate.

Celtic aside, these charts highlight the huge importance of random variance (luck) in short term football results. Given that the typical Scottish top flight team will attempt/concede 300-400 shots per season, it is possible that a team could be lucky/unlucky for several seasons in a row, despite common wisdom to the contrary. Also, we should not necessarily expect teams to fully regress to the mean within a single season. Regression to the mean may take many seasons.

Lastly, conversion rate against appears to take much longer to stabilze than conversion rate for, which may explain why goal-keeper performance is so hard to predict.