The idea goes as follows: the value of a goal can be considered to be the change in expected points earned by the team as a result of the goal. A last-second winner, for example, earns the team 2 points; whereas a second-half goal scored when the score is already 4-0 either way is virtually meaningless. I've done this before using a statistical sample of MLS games to derive expected point values, but this time I'm using a non-homogenous Poisson model (Dixon and Robinson, "A Birth Process Model for Association Football Matches") which is an improvement over a limited sample - especially given that Dixon and Robinson account for factors like stoppage time and find that fatigue linearly increases the scoring rate as the match progresses. Anyway... I've gone through the goals scored in MLS so far this season (through today's match), and weighted each goal by the change in point expectation that it caused. It turns out that certain players have scored or assisted at much more timely moments than others - for example, Juan Pablo Angel drops to clear 3rd as several of his goals have been either late insurance goals or late consolation goals, while Jose Burciaga's single 90th-minute winner rockets him all the way into the top 20 at this relatively early stage of the season. Arguably the most "flattering to deceive" player so far is Luciano Emilio, whose 6 goals are adjusted to a weighted 2.252 goals, and whose assist (weighted 0.531) is not particularly meaningful either. Top 20 Point Leaders (goal = 2 points) Code: Player Club Goals Asts Pts WG WA WP WP/Pts Johnson, Eddie KC 9 3 21 8.339 2.043 18.721 0.891 Twellman, Taylor NE 7 0 14 5.887 0 11.774 0.841 Angel, Juan Pablo NY 9 2 20 5.208 1.242 11.658 0.583 Galindo, Maykel CHV 6 2 14 3.533 0.986 8.052 0.575 Rolfe, Chris CHI 4 3 11 2.776 2.347 7.899 0.718 Gomez, Herculez COL 4 1 9 3.281 0.816 7.378 0.82 Altidore, Josmer NY 3 3 9 2.382 2.003 6.767 0.752 Cooper, Kenny DAL 4 2 10 2.897 0.919 6.713 0.671 Ralston, Steve NE 2 6 10 1.852 2.985 6.689 0.669 Gomez, Christian DC 3 3 9 2.396 1.384 6.176 0.686 Mathis, Clint NY 5 2 12 2.328 1.388 6.044 0.504 Moreno, Alejandro HOU/CLB 3 4 10 1.947 2.037 5.931 0.593 Ngwenya, Joseph CLB/HOU 3 2 8 2.594 0.649 5.837 0.73 Toja, Juan DAL 4 0 8 2.915 0 5.83 0.729 Cunningham, Jeff RSL/TOR 5 1 11 2.584 0.604 5.772 0.525 Thompson, Abe DAL 2 3 7 1.809 2.014 5.632 0.805 Dorman, Andy NE 5 2 12 2.116 1.289 5.521 0.46 Burciaga, Jose KC 1 2 4 1.899 1.716 5.514 1.379 Moreno, Jaime DC 3 1 7 2.723 0.01 5.456 0.779 Joseph, Shalrie NE 3 1 7 1.79 1.727 5.307 0.758 Top 10 Goal Leaders Code: Name Club Goals Weighted Johnson, Eddie KC 9 8.339 Twellman, Taylor NE 7 5.887 Angel, Juan Pablo NY 9 5.208 Galindo, Maykel CHV 6 3.533 Gomez, Herculez COL 4 3.281 Toja, Juan DAL 4 2.915 Cooper, Kenny DAL 4 2.897 Rolfe, Chris CHI 4 2.776 Moreno, Jaime DC 3 2.723 Ngwenya, Joseph CLB/HOU 3 2.594 Top 10 Assist Leaders Code: Name Club Asts Weighted Schelotto, Guillermo CLB 6 4.447 van den Bergh, Dave NY 4 3.953 Cooke, Terry COL 4 3.052 Ralston, Steve NE 6 2.985 Marinelli, Carlos KC 3 2.871 Victorine, Sasha KC 4 2.762 McCarty, Dax DAL 4 2.722 Davis, Brad HOU 3 2.69 Donovan, Landon LA 5 2.65 Arnaud, Davy KC 4 2.477 Questions or comments?
Very, very cool. As an actuary, I love this type of thing. Can goals be worth more than 1, or is the GWG in the 90th minute worth 1 and everything else is worth lesS?
Burciaga's GWG was worth 1.899 by itself. As it turns out, the average goal ends up being worth somewhere about 0.7, but obviously late GWGs are worth almost 2 (not entirely 2, because of the probability of the other team tying the game again) and late equalizers are worth around 1.
Updated, as of today. I meant to post this earlier in the week... but while posting right after a Thursday game means it falls right in the middle of a MLS "week", in this case the leaderboard is unchanged as no player anywhere near the leaders figured in the scoring in KC-LA. In the top 20 point leaders, the top scorers seem to have stratified themselves into a few tiers with big gaps between them. In the first tier are Eddie Johnson, Taylor Twellman, and Juan Pablo Angel, who have consistently not only scored, but scored important goals for their teams. The second tier consists of Ante Razov, Maykel Galindo, and Luciano Emilio. Luciano Emilio may be the goal leader, but most of his goals have been scored when DC United was already either leading or trailing by 2 or more goals, and so have had less impact on the result. The third tier consists of Landon Donovan, Pat Noonan, and Christian Gomez; and the fourth tier consists of Josmer Altidore, Guillermo Barros Schelotto, Jaime Moreno, Steve Ralston, Brian Ching, and Fred. As it turns out, this probably reflects this season's performances a bit better than the actual (raw) leaderboard. What seems to separate players like Ching and Noonan from the pack is not so much how many goals they score, but when they score them. I find it interesting that Luciano Emilio's reputation for poaching tap-ins is reflected by this method of goal-weighting, seeing as degree of difficulty is NOT a factor. Perhaps it is indicative that teams are more likely to have big defensive breakdowns and allow tap-ins when the winner is largely already determined - either because the intensity of play has dropped, or because substitutes who normally would not be used are getting garbage minutes. Top 20 Weighted Point Leaders Code: Player Club Goals Asts Pts WG WA WP Johnson, Eddie KC 15 5 35 12.885 4.189 29.959 Twellman, Taylor NE 14 3 31 12.668 2.658 27.994 Angel, Juan Pablo NY 16 4 36 12.356 2.196 26.908 Razov, Ante CHV 11 8 30 7.697 6.037 21.431 Galindo, Maykel CHV 12 5 29 7.287 4.109 18.683 Luciano Emilio DC 19 1 39 8.958 0.531 18.447 Donovan, Landon LA 7 9 23 4.064 6.674 14.802 Noonan, Pat NE 7 4 18 5.654 3.158 14.466 Gomez, Christian DC 7 8 22 5.128 4.022 14.278 Altidore, Josmer NY 8 4 20 5.146 2.688 12.98 Schelotto, Guillermo CLB 4 9 17 3.052 6.742 12.846 Moreno, Jaime DC 6 6 18 4.726 3.072 12.524 Ralston, Steve NE 3 12 18 2.25 7.604 12.104 Ching, Brian HOU 7 0 14 5.799 0 11.598 Fred DC 6 6 18 3.359 4.835 11.553 Ngwenya, Joseph CLB/HOU 7 3 17 4.602 1.433 10.637 Sealy, Scott KC 4 2 10 4.495 1.549 10.539 Movsisyan, Yura KC/RSL 5 0 10 5.269 0 10.538 Ruiz, Carlos DAL 7 2 16 4.743 0.97 10.456 DeRosario, Dwayne HOU 5 5 15 3.647 2.921 10.215 Top 10 Weighted Goal Leaders Code: Player Club Goals WG Johnson, Eddie KC 15 12.885 Twellman, Taylor NE 14 12.668 Angel, Juan Pablo NY 16 12.356 Luciano Emilio DC 19 8.958 Razov, Ante CHV 11 7.697 Galindo, Maykel CHV 12 7.287 Ching, Brian HOU 7 5.799 Noonan, Pat NE 7 5.654 Movsisyan, Yura KC/RSL 5 5.269 Altidore, Josmer NY 8 5.146 Noteworthy stats: Scott Sealy (4 goals, 4.495 weighted) is 16th, ahead of 7-goal scorers Landon Donovan (4.064 weighted, 19th), Andy Dorman (3.946 weighted, 21st), and Ben Olsen (3.423 weighted, 26th). Top 10 Weighted Assist Leaders Code: Player Club Asts WA Ralston, Steve NE 12 7.604 Kljestan, Sacha CHV 10 6.757 Schelotto, Guillermo CLB 9 6.742 Donovan, Landon LA 9 6.674 McCarty, Dax DAL 7 6.081 Razov, Ante CHV 8 6.037 Cooke, Terry COL 7 5.62 van den Bergh, Dave NY 6 5.395 Smith, Khano NE 6 4.925 Fred DC 6 4.835 Noteworthy stats: Christian Gomez (8 assists, 4.022 weighted) is 15th; Sasha Victorine (7 assists, 4.594 weighted) is 11th. Shalrie Joseph (just 3 assists, but 3.993 weighted) is 17th. Also worth noting: this season, the average (mean) goal has been worth about 0.688 weighted, which is to say that it has changed the team's expected points from the match by 0.688. In previous seasons, I used a cruder method based on MLS statistics rather than a Poisson model, but empirically the mean has been near 0.7, which makes this season fairly consistent with previous ones.
This is brilliant and similar to a 'clutch' goal statistic I have used in the past. Like you I used an empirical distribution from five years worth of Premier League data. The Dixon and Robinson stuff looks great. Thanks for the post. Please check out my site www.thefootballreview.co.uk if you are into all things football sabermetric.