The question posted in the title of this article seems to deserve a rather simple and straightforward answer, doesn’t it? Compile a simple list of the amount of goals scored by each player and, voilà… N.E.C.’s Björn Vleminckx managed to score 23 goals during the past Eredivisie season, outscoring ADO’s Dimitry Bulykin by two goals and the Belgian striker is rewarded with the trophy.

However, here comes the tricky part: imagine that not all goals are worth the same. Vleminckx’ fourth goal against Roda at home settled the score at 5-0 in the 93^{rd} minute, but he also opened the score in the 18^{th} minute. Gut feeling tells you that these goals are never equal in terms of utility to his team N.E.C.

**How do we quantify the value of each goal scored? **

Let’s list the factors that influence the value of a goal. There’s of course the timing within a match. An ideal opening goal would be a 94^{th} minute 1-0 as it’s almost certain that that goal will change the perspective of drawing the match into winning. Should the same goal have been scored in the first minute, there would have been enough time for the opposing team to score an equalizer.

A second factor to take into account is of course the goal differential at the time the goal is scored. Opening the score, or equalizing is definitely of more value than increasing an already comfortable lead.

Another factor to consider is the quality of the opponent you’re playing. Opening the score for a mid-table team against the league leaders would be much more valuable than it would be against the relegation favorites. Chances are that the team would win the match against the relegation favorites anyway, while against the league leaders an opening goal has more potential to influence the final outcome of the match. This is also true for the difference between home and away matches, as scoring away from home can be considered a more rare event than scoring in a home match.

But these factors are also related to each other. Should the league leaders have a tough time against a team they are expected to beat easily and the striker rescues them by scoring a dying seconds winner, that goal would change the expected amount of points taken from that match from one to three, regardless of the quality of the opposition.

**Now, how do we express all these factors into one score? **

We begin by looking at the match odds. Data on the pre-match odds can be extracted from the football-data.co.uk website. For the present analysis I’ve computed the average match odds of all betting companies in the data set (Bet365, Blue Square, Bet&Win, Gamebookers, Interwetten, Ladbrokes, Sporting Odds, Sportingbet, Stan James, Stanleybet, VC Bet and William Hill). These data simply represent the pre-match chances that either team will win the match, or a draw would be the outcome of the match.

These odds start to shift during the match. Naturally both team’s chances of winning slowly decline as the match goes on (assuming that no goals are scored), while the chance of the match finishing in a draw slowly increase. As the match comes closer to the 90^{th} minute, the shift in chances will accelerate, until the match comes to a close. It’s easier represented graphically than it is in words, so please look at the graph below to see the shift in odds during a match where no goals are scored.

In the event of a goal, a shift occurs in these odds. Obviously, the chances of outcome that the team that scored the goal will win the match immediately shift upwards, while the chances of both other outcomes shift downwards. Also, the chances of the outcome that the leading team will win the match will start to increase towards 1 as the match goes on, with the chances of the other outcomes decreasing towards 0.

At any given moment during the match, an expected value can be computed for the amount of points any team wins from the match. Simply multiply the chance of a win by 3 and the chance of a draw by 1. Should a team at any point during the match have a 30% (or 0.3) chance of winning and a 35% (or 0.35) chance of drawing the match, the expected value for the amount of points won from that match would be 3 * 0.3 + 1 * 0.35 = 1.25.

The value of scoring a goal at that point in the match can simply be computed by taking the difference between the expected value for the amount of points won from the match just before the goal and immediately after the goal.

In order to compute the effect that a goal has on the chances of the three possible outcomes of the match, data from the whatifodds.com website are used. Unfortunately the site is no longer online at the moment, but it projected the shift in odds that would occur in the event of a goal. It allowed the user to enter a goal for either team at any moment in the match.

**Summary**

The value of each goal scored is estimated by taking the difference in the value for expected points taken from that match. This is estimated using a curve that takes into account the quality of the opponents, whether the match is played at home or away, the minute in which the goal is scored and the goal differential before the goal is scored.

Using this estimate, the minimal value for a goal scored is zero, like for any goal not changing the odds of which team will win the match. Think of a 94^{th} minute 6-0 goal for that. The maximum value added is close to two, which would apply to any dying second winning goal, as it would shift an almost certain draw to an almost certain win.

**Top scorers of the Eredivisie 2010/11**

During the 2010/11 Eredivisie season, a total of 987 goals were scored, of which 28 own goals were not included in this analysis. With any goal increasing the goal differential above 4 considered to have no value, the average value of each goal was 0.54. The tables below list the top-20 goal scorers in terms of the absolute amount of goals scored and in terms of the total amount of value added using the present weighted goal scoring metric.

Conventional Top-10 Goal scorers

Player |
Team |
Goals |
Value added |

Vleminckx | N.E.C. | 23 | 10.37 |

Bulykin | ADO | 21 | 13.44 |

Junker | Roda | 20 | 7.09 |

Matavz | Groningen | 16 | 4.11 |

Dzsudzsak | PSV | 16 | 7.11 |

Toivonen | PSV | 15 | 7.50 |

Castaignos | Feyenoord | 15 | 9.32 |

Sigthorsson | AZ | 15 | 7.38 |

Everton | Heracles | 15 | 7.68 |

Van Wolfswinkel | Utrecht | 15 | 7.69 |

Weighted Top-10 Goal scorers

Player |
Team |
Goals |
Value added |

Bulykin | ADO | 21 | 13.44 |

Vleminckx | N.E.C. | 23 | 10.37 |

Castaignos | Feyenoord | 15 | 9.32 |

Amoah | NAC | 11 | 7.91 |

Granqvist | Groningen | 11 | 7.90 |

Boymans | VVV | 11 | 7.78 |

Poepon | De Graafschap | 12 | 7.71 |

Van Wolfswinkel | Utrecht | 15 | 7.69 |

Everton | Heracles | 15 | 7.68 |

Toivonen | PSV | 15 | 7.50 |

Only five players feature on both lists, as the third to seventh ranked players on the weighted goal scorers lists all wouldn’t make the conventional top-10. Another striker result is the disappointing 4.11value that Tim Matavz created with his 16 goals. The average amount of points that Groningen won with each of his goals was 0.26, while the overall average amount of points won per goal was 0.54.

A detailed look at his goal scoring tally explains this disappointing figure. Twelve of his sixteen goals were scored at home and only four of his goals were equalizers or goals giving his team the lead. The relatively low value of his goals seems well represented in the present weighted goal scoring metric.

In conclusion, a weighted goal scoring metric uses an estimate of the value of each goal scored, which allows for a more realistic top scorer evaluation.

**Post script**

Several readers have suggested that this proposed weighted goal scoring metric tends to punish players for playing in teams with superior defenses. This post script has been added in order to find out if this is true, and if so, to what extent.

Teams with superior defenses are indeed less often confronted with goal differences of -1 and 0, and may therefore be expected to have a lower average value per goal scored. On the other hand, we’ve learned from the recent offensive and defensive performance analyses that superior defenses are often paired with superior offenses. So the below-average value per goal scored might just be compensated by the fact that strikers playing on teams with superior defenses are also exposed to more goal scoring opportunities. Lets find out…

League position | Scored | Conceded | Value added | Value per goal | |

Ajax | 1 | 72 | 30 | 26.5 | 0.382 |

Twente | 2 | 65 | 34 | 38.5 | 0.610 |

PSV Eindhoven | 3 | 79 | 34 | 31.5 | 0.448 |

AZ Alkmaar | 4 | 55 | 44 | 32.4 | 0.640 |

Groningen | 5 | 65 | 52 | 29.1 | 0.469 |

Roda | 6 | 65 | 50 | 29.9 | 0.471 |

ADO | 7 | 63 | 55 | 39.4 | 0.644 |

Heracles | 8 | 65 | 56 | 29.3 | 0.476 |

Utrecht | 9 | 55 | 51 | 28.9 | 0.570 |

Feyenoord | 10 | 53 | 54 | 30.1 | 0.627 |

N.E.C. | 11 | 57 | 56 | 30.4 | 0.564 |

Heerenveen | 12 | 60 | 54 | 33.1 | 0.577 |

NAC Breda | 13 | 44 | 60 | 29.5 | 0.658 |

Graafschap | 14 | 31 | 56 | 21.1 | 0.700 |

Vitesse | 15 | 42 | 61 | 22.4 | 0.538 |

Excelsior | 16 | 45 | 66 | 31.6 | 0.721 |

VVV Venlo | 17 | 34 | 76 | 18.5 | 0.547 |

Willem II | 18 | 37 | 98 | 25.7 | 0.694 |

Average | 29.3 | 0.574 |

As we can see from this table, the average total value added per team was 29.3. Ajax was the only from the top half of the table to scored more that 0.5 below this number, indicating that the total amount of goals scored did in fact compensate for the reduced value per goal in teams with superior defenses. Even though, some interesting differences can be noted among the teams. Most notably, ADO (39.4) and Twente (38.5) outscore their rivals, which merely indicates a higher number of comebacks after conceding first.

*Eredivisie*

Sander

13 June 2011

Interesting read. The metric is still a little flawed – it punishes players for being on a team with a good defense, for instance – but it’s miles better than a simple goalscoring measure. I’d love to see this combined with assists to get a clearer picture of the offensive value of a player.

I’m a little surprised to see Dzsudzsak fall off the list, really. Intuitively I would have guessed that most of his goals came in high-leverage situations, but it seems I’m wrong in that regard.

11tegen11

13 June 2011

It’s certainly true that players are punished for playing on teams with superior defenses. That will be one of the issues to work on in the future…

Dzsudzsak did indeed score 9 of his 16 goals to either equalize or put PSV a goal up (leverage -1 or 0 goals), but still didn’t make the cut for the weighted top-10. His 7.11 puts him in 15th place. This is certainly partly due to PSV’s defensive record and overall higher odds of winning matches. But then again, this would allow him more goal scoring opportunities too…

Lesley

4 January 2012

I really like this post and I’d be curious if there’s another way of calculating the expected outcome of each match at any certain minute without the whatifodds.com website.

I’m trying to do something similar (as a start) for my favorite Spanish team (and then maybe extend it to the whole Spanish league).

Where do you get your data from, in an easy downloadable format, preferably?