## Goal Value – An Alternative Top Scorer Chart

September 26, 2017 5 Comments

Each summer, every manager in the Scottish Premiership craves a 20-goal-a-season striker. Perceived wisdom says that a regular goalscorer is worth a couple of places in the Scottish Premiership table, enough to drag relegation battlers towards mid-table safety, or safe mid-table sides towards a spot in Europe. It is certainly true that having a regular goalscorer is never a bad thing, but a striker’s value to their team depends not only on how many goals they score, but also when they score them.

One last minute winner is surely worth more than five late consolation goals in heavy defeats. Scoring 20 goals isn’t quite as important if they are all just putting the figurative icing on the metaphorical cake of a comfortable victory. Rather than judging players purely by the number of goals they score, perhaps it would be better to measure them by the overall importance of their goals.

### The Value of a Goal

Here, we propose a new method for doing exactly that. The concept is simple; we estimate how many points a team earned as a result of a player’s goals. A naïve way to do this would be to remove the goals scored by a player from each result, and then recalculate their points tally based on these new results. For example, scoring the only goal in a 1-0 win, would be worth 2 points to the team, while scoring twice in a 2-1 win would be worth 3 points.

However, this method is too simplistic, since it fails to consider each goal within the context of the match. If a player scores the opening goal in a 3-0 win, then that goal still has a considerable value to his team, since it completely changes the tactical dynamic of the match. However, scoring the third goal in the same match has a lot less value, since the outcome was probably already decided by then. Under the naïve method outlined above, both goals would be worth 0 points to their team.

### Expected Points

We therefore propose a more realistic method which considers each goal within the greater context of the match. This method is based on a quantity which we will call expected points (xPts). The xPts is a measure of the number of points a team would expect to earn given the current scoreline and time played. This is calculated by looking the final results in a set of previous matches which had the same scoreline after the same amount of time.

For example, if a team is leading 1-0 after 65 minutes, we can calculate their xPts by identifying previous games which were 1-0 after 65 minutes and looking at how many of those were won, drawn and lost. The xPts is then given by totalling up the number of points earned by teams in those positions, divided by the total number of matches. Suppose we looked at 20 such matches, with 15 resulting in victories, 3 in draws and 2 in defeats. The total number of points earned would be 15×3 + 3×1 + 2×0 = 48. The xPts in that scenario would be 48/20 = 2.4.

Our xPts values are produced using data from all 912 Scottish Premiership matches between 2013/14 and 2016/17, which was kindly supplied by the SPFL. The time of each goal is provided in minutes and seconds, and therefore our xPts values are computed down to the nearest second. To simplify our calculations, we base the xPts simply on the size of lead rather than than exact scoreline – a 1-0 lead is treated as being the same as a 2-1 lead.

### Goal Value

We can measure the importance of each individual goal by computing the effect which it has on a team’s xPts. If a team had an xPts of 2.4 before a goal, and 2.8 afterwards, then that goal is worth 0.4 points to the team. We will call this the goal value (GV).

Some additional consideration must be given to goals scored from penalties. The traditional goalscoring charts include these, but many newer analytical exclude penalty goals since they can artificially inflate a player’s tally. We take an approach which lies somewhere in between.

Thanks to fellow statto Thom Watt, we know that in the period covered by our data, there were 241 penalties awarded, and 195 of those were scored (80.9%). We use this 80.9% value as the baseline for an “average” penalty taker. When a team scores a penalty, 80.9% of the value of the goal comes from the act of winning the penalty, but the other 19.1% comes from the player who actually puts it away. Therefore, we calculate the GV for a penalty goal as being 19.1% of the difference in xPts. If a team had an xPts of 2.4 before a penalty goal, and 2.8 afterwards, then the GV is given by 0.191 x 0.4 = 0.0764.

### An example – Motherwell 2-0 Kilmarnock

To illustrate the GV statistic, I will outline the calculations for both Motherwell goals in their 2-0 victory over Kilmarnock on 9^{th} September (this match was chosen since there was one regular goal and one penalty).

Ryan Bowman opened the scoring for Motherwell after 64:38. The xPts for a side who are level after 64:38 is 1.226, while the xPts for a side who are a goal ahead after 64:38 is 2.452. This goal was not a penalty, therefore the GV is 2.452 – 1.226 = 1.186. Bowman’s goal was worth 1.186 points to Motherwell.

Louis Moult scored Motherwell’s second goal with a penalty on 87:29. The xPts for a side who are a goal ahead after 87:29 is 2.807, while the xPts for a side who are two goals ahead after 87:29 is 2.989. Moult’s goal was a penalty, so it only receives 19.1% weight, and the GV is given by 0.191*(2.989-2.807), which is 0.035. Moult therefore only earned Motherwell 0.035 points by scoring his penalty.

### The Goal Value Data

The GV for every goal in the 2017/18 Scottish Premiership, along with the relevant calculation, is outlined in this Google Docs spreadsheet, which I will keep updated every week. https://docs.google.com/spreadsheets/d/1fPPj8PmuZf-S4MlJH2nrsgG2TSwsCGVVmMT8xU3eCBQ/edit?usp=sharing

### Alternative Top Scorer Chart

We can produce an alternative top scorer chart for the Premiership by adding together the goal values for each individual player. This is not an attempt to replace the traditional goalscoring chart, but rather to provide some additional information and context.

The table below shows the current top 10, as of 25th January 2018.

The full alternative goalscorer chart can be found at the following link, which will also be updated every week. https://docs.google.com/spreadsheets/d/1Ez_kSEz81IK_hpP40GfDbqomRNXly1LzM_kOUDV0dPo/edit?usp=sharing