Goalimpact is a rather complicated algorithm. Because we want to use it commercially, we don't publish its exact functions and to the readers it is more or less a black box. To shed some light on how it is working, we calculated the current month's update twice. In the second run, we added a single game, the 2:3 victory of Manchester City at Swansea. Comparing the first with the second run allows us to show the impact of this one game on all players in the database. Before the analysis starts, here the lineups.

Swansea City

Player	Goalimpact	Peak GI	Age	National Team	No. Games	No. Minutes
Gerhard Tremmel	64.4	64.4	35.2		290	26900
Chico	104.9	106.7	26.8	Spanien [U21]	154	12822
Ashley Williams	106.3	111.4	29.3	Wales	293	27142
Àngel Rangel	102.8	116.8	31.2		236	20807
Ben Davies	92.8	118.4	20.7	Wales	73	6426
Jonjo Shelvey	100.8	117.5	21.8	England [U21]	158	10158
Pablo Hernández	115.2	119.9	28.8	Spanien	242	16224
Wayne Routledge	100.6	105.4	29.0	England [U21]	356	25665
Jonathan de Guzmán	105.8	106.4	26.3	Niederlande	261	21103
Cañas	102.2	103.5	26.6		94	6600
Wilfried Bony	128.3	130.9	25.1	Elfenbeinküste	190	14894
Bench
Roland Lamah	100.3	100.3	26.0	Belgien	204	12903
Pozuelo	97.1	111.2	22.3		61	3326
Gregor Zabret	88.8	88.8	18.4	Slowenien [U19]	17	1581
Jordi Amat	100.8	117.9	21.8	Spanien [U21]	102	8618
Neil Taylor	111.4	114.5	24.9	Wales	97	8037
Dwight Tiendalli	102.6	107.0	28.2	Niederlande [U21]	228	18301
Álvaro	100.1	112.2	22.7	Spanien [U21]	131	6357

Manchester City

Player	Goalimpact	Peak GI	Age	National Team	No. Games	No. Minutes
Joe Hart	126.9	126.9	26.7	England	303	28260
Vincent Kompany	132.1	135.8	27.8	Belgien	340	29439
Aleksandar Kolarov	108.5	112.9	28.2	Serbien	237	18103
Matija Nastasic	101.8	126.8	20.8	Serbien [U21]	88	7755
Pablo Zabaleta	128.2	133.1	29.0	Argentinien	384	31986
Samir Nasri	127.1	128.2	26.5	Frankreich	404	28892
Jesús Navas	135.3	139.6	28.1	Spanien	414	33832
Fernandinho	141.6	146.2	28.7		242	20295
Yaya Touré	133.6	143.7	30.7	Elfenbeinküste	385	32359
Álvaro Negredo	114.4	118.9	28.3	Spanien	287	20549
Edin Džeko	130.9	134.8	27.8	Bosnien-Herzegowina	314	23402
Bench
James Milner	113.9	118.2	28.0	England	489	35240
Javi García	121.7	123.6	26.9	Spanien [U21]	218	16043
Jack Rodwell	94.9	106.3	22.8	England [U21]	137	8028
Costel Pantilimon	110.6	110.6	26.9	Rumänien	125	11524
Joleon Lescott	131.6	147.0	31.4	England	407	36586
Gaël Clichy	153.6	158.1	28.4	Frankreich	364	30709
Dedryk Boyata	95.2	105.3	23.1	Belgien [U21]	58	4012

The flow of action in that game was:

	Minute
Lamah for Hernandez	9
	14	0:1 Fernandinho
1:1 Bony	45
	58	1:2 Yaya Toure
	59	Garcia for Negredo
	66	1:3 Kolarov
	68	Milner for Nasri
Pozuelo for Shelvey	81
	90	Rodwell for Navas
2:3 Bony	91

Players that played the full game

Here is the change in Goalimpact of all players that played the full game. They had a goal difference of 2:3 or 3:2 depending on the team they played for. We expect players of Manchester City to improve and Swansea players to drop in Goalimpact.

Diff Goalimpact	Absolute Diff	Player	Team
0.21	0.21	Aleksandar Kolarov	Manchester City
0.19	0.19	Vincent Kompany	Manchester City
0.19	0.19	Matija Nastasic	Manchester City
0.19	0.19	Pablo Zabaleta	Manchester City
0.19	0.19	Yaya Touré	Manchester City
0.18	0.18	Fernandinho	Manchester City
0.17	0.17	Edin Džeko	Manchester City
0.16	0.16	Joe Hart	Manchester City
0.01	0.01	Gerhard Tremmel	Swansea City
-0.09	0.09	Wayne Routledge	Swansea City
-0.12	0.12	Jonathan de Guzmán	Swansea City
-0.15	0.15	Ashley Williams	Swansea City
-0.16	0.16	Àngel Rangel	Swansea City
-0.17	0.17	Chico	Swansea City
-0.20	0.20	Wilfried Bony	Swansea City
-0.20	0.20	Cañas	Swansea City
-0.22	0.22	Ben Davies	Swansea City

At first glance, the change is how it was expected Manchester's players increased their score, while Swansea's players didn't fare that good. Interestingly, the City players didn't all change by the same amount. There is more than one reason why this is the case.

• The score of each player is based on all observed minutes. The number of minutes prior to this games wasn't the same for all players and hence the weight of the additional information of the Swansea game is different for every player. We expect players with few past observations to move, on average, more. That said, the bulk of the players changed about the same amount just in opposing directions for the two teams.
• Additionally, the rating of each player changed and, in turn, the results of the past games are re-assessed based on the new information. Therefore, we find second order changes in the scores. In case of Tremmel the second order changes apparently even out-weighted the first order change as his score slightly increased despite the defeat.
• Although Bony scored two goals, that didn't help him a bit in Goalimpact terms. Scoring and conceding are attributed to all players of the team equally. Playing selfish (not implying that Bony did) doesn't pay off. You can't game the score to improve your personal assessment at the expense of the team easily.

Players that played only a part of the game

The influence of the game on the players' Goalimpact can be larger than for those players that played the whole match. Some observations

• Navas and Nasri won the match 3:1 during their field time and hence saw the largest increases. The same in reverse happened to Shelvey who, as only player, lost 1:3.
• City's Rodwell and Milner actually saw dropping Goalimpact as they the goal difference was negative while they were on the pitch. Conversely, Swansea's Pozuelo gained despite his team losing because he achieved a positive goal difference.

Players of the teams that did not play

As the Goalimpact of all players that played changed, their new assessment of strength is used to value the other team members. Remember that a players performance is adjusted by both the skill of the team mates and the opposition. Here are the teams' players that did not play.

Diff Goalimpact	Player	Team
0.03	Leon Britton	Swansea City
0.03	Nathan Dyer	Swansea City
0.02	Garry Monk	Swansea City
0.02	Michel Vorm	Swansea City
0.02	Michu	Swansea City
0.01	Jordi Amat	Swansea City
0.01	Neil Taylor	Swansea City
-0.01	Martín Demichelis	Manchester City
-0.01	Costel Pantilimon	Manchester City
-0.01	Dedryk Boyata	Manchester City
-0.03	Kun Agüero	Manchester City
-0.03	Micah Richards	Manchester City
-0.04	Gaël Clichy	Manchester City
-0.04	Joleon Lescott	Manchester City
-0.05	David Silva	Manchester City

The table looks a bit like the first table in reverse. Every Swansea player that did not take part in the defeat saw his score increase, while all players of City that didn't win lost points. But the size of these changes is small compared to the size of the change of involved players.

Players from other teams

With the change of the Goalimpact of the players, the Goalimpacts of all their opponents change, too, because their performance is corrected for the rating of the opposition. Some players of other clubs may have been former City or Swansea players and hence change like the team members that did not play. In total 2985 players changed their rating by more than 0.01. But only few 0.02 or more. Here is the list of them.

Diff Goalimpact	Player	Team
0.03	Edgar Davids	Barnet FC
0.03	Javier Zanetti	Inter
0.03	Kevin Phillips	Crystal Palace
0.03	Ryan Giggs	Manchester United
0.02	Mark Gower	Charlton Athletic
0.02	Bart Goor	KFC Dessel Sport
0.02	Óli Johannesen	TB Tvöroyri
0.02	Dutra	Yokohama F. Marinos
0.02	Carlos Galván	Universidad Cesar Vallejo
0.02	Rolando Schiavi	Shanghai Shenhua
0.02	Lars Kleiven	Elverum Fotball
0.02	Ian Goodison	Tranmere Rovers
0.02	Kristian Bergström	Atvidabergs FF
0.02	Tero Taipale	Kuopion PS
0.02	Hernando Patiño	Deportes Quindio
0.02	Tibor Dombi	Debreceni VSC
-0.02	Julien Escudé	Besiktas
-0.02	Frederic Kanouté	Beijing Guoan FC
-0.02	Ivan Rakitic	Sevilla FC
-0.02	Mario Balotelli	AC Milan
-0.02	Luis Fabiano	Sao Paulo FC
-0.02	Nigel de Jong	AC Milan
-0.02	Kolo Touré	Liverpool FC
-0.02	Adriano	FC Barcelona
-0.02	Diego Perotti	Sevilla FC
-0.03	Carlos Tévez	Juventus
-0.03	Federico Fazio	Sevilla FC
-0.03	Fernando Navarro	Sevilla FC
-0.04	Gareth Barry	Everton FC

Some of the players are what you'd expect intuitively. Former opponents or team mates from the Premier League or the Champions League. But some of the names that changed are less obvious. The interaction of all the scores is so complex that a specific movement is not only a black box to the reader but also to us. We would need to research the link between those players and the players of Swansea vs. Manchester City. They must have met. Somewhere, somehow. Directly or indirectly.

Even though these changes are minor, they are not neglectable. A single came has little influence on the players that did not play, but there are many more games that a player did not play in then that he played in, so the entire effect is substantial. That is the prime reason why we try to collect as many data as we can. More sometimes is more.