How Good is Liam Boyce?

Northern Ireland international Liam Boyce scored a hat-trick for Ross County Saturday in a 5-2 victory over Dundee in the Scottish Premiership. According to Soccerway, Boyce has 13 league goals in 1632 minutes so far this season, or 0.72 goals per 90.

In 2010, Boyce was on trial at Celtic but did not receive a contract. This is unfortunate because, as I will argue in this post, Boyce might be as good a goal scorer as any striker on Celtic's current roster.

FIGURE 1

Figure 1 shows the relationship between career goals scored and minutes played for Boyce, and Celtic's current strike force (data from soccerway.com). The black line represents the expected number of goals for a given number of minutes played. Most of Boyce's seasons fall on or above the line, indicating a relatively high level of goal scoring productivity compared to Celtic's strikers, In fact, Boyce's 0.84 goals per 90 at Cliftonville FC in 2012-13 is better than any single season performance by any of Celtic's current strikers, with the exception of Leigh Griffiths this season and last season.

Figure 2, shows the individual trend lines for each player's career. As you can see, Boyce's line has the most positive slope, indicating a higher goal scoring rate at 1500+ minutes played than any of Celtic's strikers, even Leigh Griffiths.

FIGURE 2

One could argue that most of Boyce's goals have come playing against part-timers in a "diddy" league, the NIFL Premiership. While this is an important caveat, in my opinion, Boyce is worth another look, even given the limited data presented here.

A related question is: what did Celtic see or not see in 2010 that turned them off? This seems an especially poignant question given the parade of disappointing strikers that have been given contracts by Celtic since 2010 (Mo Bangura anyone?).

The Problem with Group Stage Results

Celtic bombed out of the Europa League group stage last Thursday after a draw away to Fenerbahce. The Hoops finished last in Group A with a dismal 3 points from 6 matches. In the aftermath, manager Ronny Deila has been criticized harshly by fans and pundits alike.

However, as I will show in this post, 6 matches is not a big enough sample to judge a manager's results in any competition. This is because of the inherent randomness of football.

To illustrate this fact, I generated random distributions of points per game (PPG) and other metrics using bootstrap resampling in R with 100,000 replicates. The samples were drawn from Celtic's SPL/SPFL league matches over ten seasons between 2004 and 2014 (N=380).

Let's begin by looking at the bootstrap distribution of PPG after 36 matches, which is roughly equivalent to a full domestic league season, or 6 times the sample size of Europa League group stage.

As can see in Figure 1, the distribution is nearly bell-shaped and smooth. The center of the curve lines up nicely with the 10-season average for Celtic (2.321), as indicated by the vertical red line. Thus, PPG after 36 matches is a good representation of Celtic's long term results domestically.

Figure 1.

Now let's look at the distribution of PPG after 6 matches (Figure 2). The main thing to note is how different the 6 match and 36 match distributions are from each other. The 6 match distribution does not have a smooth, bell shape centered on the true historical average. Instead, it's spikey and wild looking, What this means is that, PPG after 6 matches is NOT a good representation of Celtic's long term results domestically.

The relatively high volatility of PPG after 6 matches observed in Celtic's domestic league matches is a pattern that would also apply to the Europa League group stage. However, it is important to note that this inherent volatility would be even greater in Europe, due to the overall similarity in quality between the teams compared to SPL/SPFL.

Figure 2.

So what alternative do we have to judge a team's performance after 6 matches? Figures 3 and 4 show two options, goal differential (GD) and total shot differential (TSD). 

As you can see in Figure 3, the distribution of GD after 6 matches is much more bell shaped than the 6 match distribution of PPG, and the former is more closely aligned with Celtic's 10-season average (1.416). However, the 6 match GD distribution is still very spikey, rather than smooth like the curve in Figure 1. Thus, 6 match GD is not a very good representation of Celtic's long term performance in domestic league competition.

Figure 3.

Finally, let's have a look at the bootstrap distribution of TSD after six matches. As you can see in Figure 4, the curve is remarkably similar in shape to the 36 match PPG distribution. It is smooth, bell shaped and centered nicely on the 10-season average (+6). Thus, 6 match TSD is a good representation of Celtic's long term performance domestically.

This is an important point because Celtic's TSD improved significantly this season in the Europa League group stage compared with last season, going from -22 to +2. Given the volatility of short term results, Celtic's abysmal PPG this season could be written off as a consequence of random variance. While the team's improvement in TSD is more likely a result of genuine and sustainable improvement under manager Ronny Deila.

Figure 4.