Using Weighted Shots To Predict Goal Difference in Subsequent Games.

As a follow up to the previous post, here is the changing relationship between a side's weighted shot differential compared to their opponents, for goals, shots that went wide and shots that were saved after a certain number of matches and the goal difference in the remainder, as suggested in the comments by Tango.

The EPL has 38 games,

So, for example, the projection for the goal difference in games 3 to 38 inclusive is found by multiplying the oerall GD in games 1 and 2 by 2.9, adding the differential of shots that went wide after two games multiplied by 0.43 and adding the save differential after two games multiplied by 1.24. The constant is universally close to zero.

r for each regression after each number of games is in the final column and peaks at mid season.

Correlation Between Shot Type Differential in Previous Games & Goal Difference in Remaining Games.

After x Games	Goal Difference  Coefficient	Shots Wide Differential Coefficient	Shots Saved Differential  Coefficient	Relative Weight for GD	Relative Weight for Wide Shots	Relative Weight for Saved Shots	r
2	2.9	0.43	1.24	1	0.1	0.4	0.57
3	2.5	0.59	0.92	1	0.2	0.4	0.67
4	2.3	0.40	0.71	1	0.2	0.3	0.72
5	1.9	0.38	0.57	1	0.2	0.3	0.76
6	1.8	0.33	0.45	1	0.2	0.3	0.77
7	1.6	0.25	0.37	1	0.2	0.2	0.79
8	1.4	0.24	0.30	1	0.2	0.2	0.79
9	1.2	0.22	0.27	1	0.2	0.2	0.76
10	1.1	0.17	0.24	1	0.2	0.2	0.76
11	1.05	0.15	0.19	1	0.1	0.2	0.77
12	.99	0.15	0.16	1	0.1	0.2	0.78
13	.91	0.13	0.14	1	0.1	0.2	0.81
14	.82	0.11	0.14	1	0.1	0.2	0.81
15	.75	0.09	0.14	1	0.1	0.2	0.80
16	.72	0.09	0.12	1	0.1	0.2	0.81
17	.6	0.06	0.14	1	0.1	0.2	0.81
18	.55	0.02	0.15	1	0	0.3	0.80
19	.46	0.02	0.14	1	0	0.3	0.78
20	.43	0.01	0.13	1	0	0.3	0.79
21	.39	0.01	0.12	1	0	0.3	0.78
22	.36	0.01	0.10	1	0	0.3	0.79
23	.31	0	0.09	1	0	0.3	0.76
24	.28	0	0.09	1	0	0.3	0.77
25	.25	0.01	0.08	1	0	0.3	0.75
26	.20	0.01	0.08	1	0	0.4	0.74
27	.17	0.01	0.07	1	0	0.4	0.72
28	.15	0	0.07	1	0	0.4	0.70
29	.13	0.01	0.05	1	0.1	0.4	0.69
30	.13	0.01	0.04	1	0.1	0.3	0.69
31	.11	0.01	0.03	1	0.1	0.3	0.66
32	.08	0.01	0.03	1	0.1	0.3	0.64
33	.06	0.01	0.02	1	0.2	0.4	0.60
34	.05	0.01	0.02	1	0.1	0.5	0.56
35	.04	0	0.02	1	0	0.5	0.48
36	.02	0	0.02	1	0	0.7	0.40
37	.02	0	0	1	0	0.2	0.32

The Weighting Game.

Shot counts verses goal counts as a predictor of future performance is a debate that that is being fought out not only in football, but also in hockey. Sample size is at the heart of the issue. Goals are obviously more important in terms of who wins the match, but they are relatively rare events. Whereas shots accumulate at a faster rate, building up sample size, but play only an intermediate role in deciding the outcome.

It is perhaps unfortunate that a distinction has arisen between shots and goals because they are merely classifications of a single larger group. Namely, they are all goal attempts, but with different actual outcomes.

Goals are shots (or headers) that result in a goal, saves are on target shots that are saved and misses are shots that go high or wide of the target.

The most recent rumblings from hockey arises from renowned sabermetrician, Tom Tango's use of different types of shots (he includes blocked efforts also), from the first half of a season to predict goals or specifically goal differential from the second half.

He uses the different types of shot differential, with appropriate weightings in the first half of a season to predict goal differential in the second. The post can be found here and the application to football is obvious.

I have therefore updated a similar approach using data from Joe B's football data site (So no blocked shot data as a separate category). The aim was slightly different. I set out to determine the final goal difference for EPL teams, based on their goal difference and shooting differential at various times during the season.

Final goal difference is strongly correlated to finishing position and with the odd exception finishing position is also related to team strength. And knowing where a side is likely to finish well before they actually arrive at that position is an obvious advantage if we wish to know how they are likely to perform during that 38 game journey.

I therefore split goal attempts into shots that went into the net (or goals), attempts that were saved and off target attempts and totaled the cumulative differential between each Premiership team and their opponents from the second match of the season until the penultimate game.

For example, after 14 games, Arsenal currently have a +7 goal difference, a +91 differential in shots that went wide and +34 differential in shots that were saved.

I then regressed these differentials against the final goal difference after the 38th game to get the changing relationship between the three variables and the side's ultimate goal difference after two games all the way up to 37 games played.

All three types of shots are important in predicting the final goal difference of teams. But the relative importance in predicting future goal difference from shots that are saved or go wide, declines in relation to the importance of shots that result in a goal (or goals for short), as the number of games increases.

In addition, the values of the coefficients is also dependent upon how many matches are in the sample. The respective goals, wide shots/headers and saved shots/headers coefficients are 3.91, 0.43 and 1.24 when calculated after just two matches and, as you would probably expect 1.02, 0, and 0 after 37.

So far this season each team has played 14 matches and the coefficients for current goals, wide shots and save differentials when used to predict future final goal difference are respectively 1.91, 0.13 and 0.14. If we use these figures for each team, the final projected league goal difference for each side is as shown below.

Projected Final Goal Difference Using Shot Differentials After 14 Games.

Position	Team	Projected GD.
1	Chelsea	46
2	Man City	40
3	Southampton	31
4	Arsenal	28
5	Man Utd	20
6	West Ham	10
7	Everton	6
8	Liverpool	4
9	Swansea	2
10	Newcastle	0
11	Tottenham	-3
12	Stoke	-4
13	West Brom	-12
14	C Palace	-13
15	Hull	-22
16	Sunderland	-23
17	QPR	-26
18	Leicester	-26
19	Aston Villa	-26
20	Burnley	-29

At the moment these figures are merely another rating system, albeit one that appears to reasonably predict the likely quality of the current side. Villa, for example appear to have been fortunate in the way in which they have won numerous single goal victories. And a wider appraisal incorporating extra shot information reduces their rating compared to their current league position.

To illustrate how the projections have fluctuated for a single team, here's how the projected final goal difference has varied for Arsenal using the updated coefficients after each game week of the 2014/15 campaign to date.

Projected Final Goal Difference For Arsenal from Shot Differentials Updated Weekly.

Games Played by Arsenal.	Final GD Projection.
After 2 Games.	+13
3	23
4	16
5	24
6	25
7	17
8	22
9	24
10	31
11	27
12	26
13	27
14	28

We can demonstrate the use of such ratings and perhaps their predictive potential by converting these weighted shot derived ratings into match odds and comparing them with a reliable benchmark, such as the current bookmaking odds.

Stoke entertain Arsenal on Saturday. Arsenal's projected final goal difference is a rounded up +28, Stoke's is an also rounded up -4. Or +0.74 and -0.1 per game, conveniently in the currency of goals.

Home field is running at 0.38 of a goal. So Arsenal are 0.84-0.38 of a goal superior away to Stoke.

Arsenal should be, based on our projections, 0.46 of a goal superior, on average at the Britannia. If we run this figure through a Poisson, we might get a 47% chance of an Arsenal win, 26% for Stoke and 27% the draw. Best odds, as of Thursday night are 50%, 23% and 27%.

So the projections broadly agree with a robust business model, at least for the Potters and below I've applied the method to the remaining games this weekend.

Odds Derived from Shot Differentials and Final Goal Difference Projections for Week 15.

Game (Home Team First!)	Home Win % (Predicted/Best Price)	Away Win%.	Draw%.
Man City v Everton	67/63	14/16	19/21
Liverpool v Sunderland	62/64	15/14	23/22
Newcastle v Chelsea	19/13	57/63	24/24
Spurs v C Palace	53/63	21/14	26/23
Stoke v Arsenal	26/23	47/50	27/27
QPR v Burnley	47/47	26/25	27/28
WHU v Swansea	49/41	24/30	27/29
A Villa v Leicester	45/43	28/28	27/29
Southampton v Man U	48/36	25/37	27/27
Hull v WBA	39/40	33/31	28/29

The majority of the odds fall within touching distance of those available to bet on and those few that don't do so for rational reasons, such as Manchester United's chaotic "getting to know you" phase, combined with Southampton's recent injuries.

By weighting shot types and applying coefficients appropriate to the number of matches played, it appears possible to project team strength with sufficient accuracy to mimic the bookmakers appraisal of Premiership teams.

Dixie Dean. Head and Shoulders Above the Rest.

In this post I looked at the goal scoring record of Wayne Rooney compared to other England international strikers and particularly the difficulty of comparing scoring feats spread across very different eras when scoring environments varied.

The game has undergone many fundamental changes since its inception in the late 19th century, either tactical or through tinkering with the laws of the game, most notably the offside rule. And the effects of these changes can be seen in the average number of goals that were scored in total in league matches contested in the top flight of English football.

The early matches were particularly goal laden, briefly averaging just over 4.5 goals per match, but with noticeable post war peaks occasionally arresting the decline, the average has settled at a level just above 2.5 goals per match.

Therefore, the number of goals a top striker might expect to claim in a season was largely dependent upon the goal environment when he played and the maximum number of games he could and did actually play.

Of course, the holder of the most league goals scored in a division one season lies with Everton legend, Dixie Dean, who scored 60 goals in the 1927-28 season. However, not only was that season played in the midst of a post Great War scoring peak following the relaxation of the offside rule,(an average of 3.82 league goals were scored per match), but the season consisted of a maximum of 42 games.

Uneven numbers of games can be partly accounted for by taking individual goals per game. Dean, as far as I can find appeared to play in only 39 of the possible 42, although his scoring record was bolstered by penalty kicks, a luxury not available to the very earliest players.

Even with the occasional spot kick, Dean's record of 1.54 goals per game is astonishing. But to attempt to level the playing field further we can use the general relationship between the goals per game rate of scoring of the division's top scorers and the goal environment that prevailed at the time, denoted by the average goals scored per game.

For simplicity, the regression indicates that the top goal scorers across the eras have scored their goals per game at a quarter the rate of the average total goals per match during that season.

So Dean, playing when a match might average nearly four goals in total, would have been expected to score a goal a game, were he to follow the habit of the league's leading scorers across the ages.

Leading Scorers Relative to the Goal Environment at the Time

From the table above, even though Dean was playing when goals were more common and the top tier was an expanded version of its current form, his record is unsurpassed. No player gets close to his over performance compared to the expected rate based on the goal environment in 1927.

If Dean had performed to the typical level of a league leading scorer, he would have been expected to claim 39 goals in 1927-28, rather than his actual total of 60.

Virtually every decade of the last two centuries are represented in the list and there is a mixture of the familiar and the not so familiar names in the list of the top division's most formidable scorers.