Levelling the Playing Field, Adjusting Goal Records in International Football

In recent years, we’ve witnessed a surge in international football records being shattered. Modern players are scoring at unprecedented rates, and while this is undoubtedly exciting for fans, it raises an important question: Are today’s goal-scoring feats truly comparable to those of past legends?

The landscape of international football has evolved significantly. The expansion of FIFA membership has introduced many new, smaller nations into the competitive arena. This influx has led to more matches where traditional football powerhouses face off against developing teams, often resulting in lopsided scorelines. Consequently, contemporary players have more opportunities to inflate their goal tallies against weaker opposition.

This shift poses a challenge when attempting to compare the goal-scoring records of current players with those from previous eras. The legends of the past often played fewer matches against a more consistent level of competition, making their goal tallies a reflection of performances against relatively equal opponents.

So, how can we level the playing field and make fair comparisons across different football eras?

Introducing a Weighted Goal System

To address this disparity, I embarked on a project to adjust goal records by accounting for the relative strength of the opposition. The idea is to assign a weighting to each goal based on the difficulty of scoring against a particular team at the time of the match. This method aims to provide a more nuanced evaluation of a player’s goal-scoring achievements.

Utilizing Elo Ratings

The foundation of this approach lies in the Elo rating system, a method originally devised for ranking chess players but now widely adopted across various sports, including football. Elo ratings provide a dynamic measure of a team’s strength, updating after each match based on the result and the quality of the opposition.

By leveraging historical Elo ratings, we can assess the relative strength of any two teams at the time they played. This allows us to calculate a weighting factor for each goal scored, reflecting the challenge posed by the opponent.

The Weighting Formula

The weighting for each goal is determined using the following formula:

\[\text{Weight} = 1 - k\times\frac{E-O}{E}\]

Where, \(E\) is the Elo rating of England before the match, \(O\) is the Elo rating of the opposition before the match and \(k\) a scaling constant that adjusts the sensitivity of the weighting to the difference in Elo ratings.

This formula adjusts the weight of a goal based on how much stronger or weaker the opposition is relative to England:

• If England faces a stronger team (\(O > E\)), the weighting increases above 1, acknowledging the greater difficulty.
• If England faces a weaker team (\(O < E\)), the weighting decreases below 1, reflecting the relatively easier challenge.
• The constant \(k\) controls how much the difference in ratings affects the weighting.

Interpreting the Weighting

Adjusting the \(k\) value alters the impact of the opposition’s strength:

• A higher \(k\) value (e.g., 2) amplifies the effect, giving more weight to goals against stronger teams and less to those against weaker ones.
• A lower \(k\) value (e.g., 1) minimizes the effect, resulting in a more uniform weighting across different opponents.

By experimenting with different \(k\) values, we can fine-tune the system to balance fairness and sensitivity, ensuring that exceptional performances against top-tier teams are appropriately recognized while maintaining a reasonable value for consistent scoring against all opponents.

For the rest of this post we use a value of \(k=2\).

Results

When I last wrote a post similar to this, Wayne Rooney had just broke the England National team goal record with 50 goals. Since then Kane has broke this record again (at the time of writing) with 69 goals. Using the above approach the updated top 10 of England goal scorers are (the “Ranking” is based on the weighted goals column):

Ranking	Name	Goals	Weighted Goals
1	Harry Kane	69	45
2	Gary Lineker	48	37
3	Bobby Charlton	49	36
4	Jimmy Greaves	44	35
5	Wayne Rooney	53	34
6	Michael Owen	40	30
7	Alan Shearer	30	23
8	Tom Finney	30	23
9	Nat Lofthouse	30	22
10	Frank Lampard	29	21

You can see that whilst Kane is still number 1 - his number of goals are significantly less. (Note that the adjusted number of goals here have been rounded to the nearest goal for ease of reading).

As may be expected Kane has the biggest change between actual goals scored (69) and the weighted number of goals (45) with a difference of 24, perphaps reaffirming the theory that modern day players are scoring a significant amount of their goals against weaker opposition than in the past. Gary Lineker moves from 4th in the all time list to 2nd.

At the other end of the table we end up with a number of people (41) who (because of the rounding as well) move from having scored at least 1 for England to being on 0 goals, but only four who go from more than 1 to zero:

Name	Goals	Weighted Goals
Tammy Abraham	3	0
Paul Ince	2	0
Tyrone Mings	2	0
James Ward-Prowse	2	0

Unfortuntaely Tammy Abraham’s 3 goals for England were scored against very much weaker opposition in the form of Montenegro (England won 7-0 on 14/11/19), Andorra (England won 0-5 on 09/10/21) and San Marino (England won 0-10 on 15/11/21).

If you want to have a look at the data you can access it all here) (which also includes the “Adjusted Total” which weights Friendlies as 0.5 and “finals” as 2x (as per the description here).

Data

If you want to have a look at the data in a little more detail (but without downloading the whole datefile above) the below is a sortable table for England players with at least 40 caps):

Name	Caps	Total Goals	Goals per Cap	Weighted Goals	Weighted Goals per Cap
Peter Shilton	125	0	0.00	0	0.00
Wayne Rooney	120	53	0.44	34	0.28
David Beckham	115	17	0.15	12	0.10
Steven Gerrard	114	21	0.18	13	0.11
Bobby Moore	108	2	0.02	1	0.01
Ashley Cole	107	0	0.00	0	0.00
Bobby Charlton	106	49	0.46	36	0.34
Frank Lampard	106	29	0.27	21	0.20
Billy Wright	105	3	0.03	2	0.02
Harry Kane	103	69	0.67	45	0.44
Kyle Walker	93	1	0.01	1	0.01
Bryan Robson	90	26	0.29	18	0.20
Michael Owen	89	40	0.45	30	0.34
Kenny Sansom	86	1	0.01	1	0.01
Gary Neville	85	0	0.00	0	0.00
Ray Wilkins	84	3	0.04	3	0.04
John Stones	83	3	0.04	2	0.02
Raheem Sterling	82	20	0.24	14	0.17
Rio Ferdinand	81	3	0.04	2	0.02
Jordan Henderson	81	3	0.04	2	0.02
Gary Lineker	80	48	0.60	37	0.46
John Barnes	79	11	0.14	8	0.10
John Terry	78	6	0.08	5	0.06
Stuart Pearce	78	5	0.06	4	0.05
Terry Butcher	77	3	0.04	2	0.03
Tom Finney	76	30	0.39	23	0.30
David Seaman	75	0	0.00	0	0.00
Joe Hart	75	0	0.00	0	0.00
Sol Campbell	73	1	0.01	1	0.01
Jordan Pickford	73	0	0.00	0	0.00
Gordon Banks	73	0	0.00	0	0.00
Alan Ball	72	8	0.11	6	0.08
Martin Peters	67	20	0.30	14	0.21
Paul Scholes	66	14	0.21	11	0.17
Tony Adams	66	5	0.08	4	0.06
Dave Watson	65	4	0.06	3	0.05
Harry Maguire	64	7	0.11	4	0.06
Alan Shearer	63	30	0.48	23	0.37
Kevin Keegan	63	21	0.33	15	0.24
Ray Wilson	63	0	0.00	0	0.00
David Platt	62	27	0.44	20	0.32
Emile Heskey	62	7	0.11	5	0.08
Chris Waddle	62	6	0.10	5	0.08
Declan Rice	62	5	0.08	4	0.06
Emlyn Hughes	62	1	0.02	1	0.02
Gary Cahill	61	5	0.08	4	0.07
James Milner	61	1	0.02	0	0.00
Ray Clemence	61	0	0.00	0	0.00
Marcus Rashford	60	17	0.28	14	0.23
Peter Beardsley	59	9	0.15	7	0.12
Des Walker	59	0	0.00	0	0.00
Phil Neville	59	0	0.00	0	0.00
Jimmy Greaves	57	44	0.77	35	0.61
Jermain Defoe	57	20	0.35	10	0.18
Paul Gascoigne	57	10	0.18	7	0.12
Gareth Southgate	57	2	0.04	1	0.02
Johnny Haynes	56	18	0.32	14	0.25
Joe Cole	56	10	0.18	6	0.11
Stanley Matthews	54	11	0.20	9	0.17
Kieran Trippier	54	1	0.02	1	0.02
Glen Johnson	54	1	0.02	1	0.02
Glenn Hoddle	53	8	0.15	6	0.11
Gareth Barry	53	3	0.06	2	0.04
Paul Ince	53	2	0.04	0	0.00
David James	53	0	0.00	0	0.00
Trevor Francis	52	12	0.23	9	0.17
Teddy Sheringham	51	11	0.22	9	0.18
Phil Neal	50	5	0.10	3	0.06
Geoff Hurst	49	24	0.49	18	0.37
Ron Flowers	49	10	0.20	8	0.16
Eric Dier	49	3	0.06	3	0.06
Colin Bell	48	9	0.19	8	0.17
Jimmy Dickinson	48	0	0.00	0	0.00
Theo Walcott	47	8	0.17	5	0.11
Trevor Brooking	47	5	0.11	5	0.11
Mick Channon	46	21	0.46	17	0.37
Gary Stevens	46	0	0.00	0	0.00
Mark Wright	45	1	0.02	1	0.02
Bukayo Saka	43	12	0.28	6	0.14
Phil Foden	43	4	0.09	3	0.07
Martin Keown	43	2	0.05	1	0.02
Chris Woods	43	0	0.00	0	0.00
Jimmy Armfield	43	0	0.00	0	0.00
Peter Crouch	42	22	0.52	14	0.33
Danny Welbeck	42	16	0.38	9	0.21
Tony Woodcock	42	16	0.38	11	0.26
Steve Coppell	42	7	0.17	5	0.12
Phil Thompson	42	1	0.02	1	0.02
David Batty	42	0	0.00	0	0.00
Owen Hargreaves	42	0	0.00	0	0.00
Mick Mills	42	0	0.00	0	0.00
Paul Robinson	41	0	0.00	0	0.00
Bob Crompton	41	0	0.00	0	0.00
Jude Bellingham	40	6	0.15	5	0.13
Phil Jagielka	40	3	0.07	2	0.05