Offensive Productivity Formula

[scaryice]

Hey, I was thinking. There should be a formula to take every offensive statistic, and put them all together to get one number to measure a player's offensive productivity.

We don't have access to really detailed stuff in MLS like passes completed, but we do have the basic statistics:

Goals
Assists
Penalty Goals
Penalties Earned
Fouls
Fouls Suffered
Yellow Cards
Red Cards

I don't know what the proper multpliers for each category should be, but here's a guess:

1.00 = Goals
0.60 = Assists

There have been 308 assists on 304 non-penalty goals this season. But an assist doesn't deserve to be equal to a goal. There are plenty of great balls that don't get finished, which makes this whole idea kind of hard to implement. I just arbitrarily chose 0.60 for now.

0.80 = Penalties Earned
0.20 = Penalty Goals
-0.20 = Penalty Miss

Penalties are made about 80% of the time. Pen goals should obviously be worth less than regular ones. Wasn't sure what exactly to use there, but I decided to make one penalty worth "one whole goal."


0.09 = Fouls Suffered
-0.09 = Fouls

Looking at MLSnet stats from this year, there are about 11 fouls per team per game this season.

-0.30 = Yellow Cards
-0.80 = Red Cards

Just picked numbers for these.


So, using these numbers, here's what I get for some of the league's top forwards. I divided it by minutes played, then multiplied it by 1,000 to make it look nicer.

2006 MLS Forwards

9.87-Ruiz
9.26-Eskandarian
8.94-Cunningham
8.60-Ching
8.49-Razov
6.54-Twellman
5.92-Moreno
5.89-Cooper
5.39-Donovan
4.75-Rolfe

Thoughts/ideas? Together, we should be able to come up with something good.

[scaryice]

I went back and did this for all the major attacking players in 2005. I only considered players who played 1,440 minutes or more (half the season exactly).

If a penalty was given away, that's -0.80 (opposite of earned). I also only counted "primary assists." These are the 18 players who scored a 5.00 or better:


1 Cunningham 9.26
2 Wolff 8.68
3 Twellman 8.67
4 H.Gomez 8.53
5 Donovan 8.28
6 Ruiz 7.62
7 C.Gomez 7.16
8 Rolfe 7.08
9 Sealy 6.78
10 Gaven 6.75
11 Noonan 6.75
12 Dempsey 6.45
13 A.Moreno 6.26
14 Buddle 5.89
15 De Rosario 5.80
16 Guevara 5.79
17 Cancela 5.53
18 Adu 5.29

[voros]

I tried to address this the same way you would do so in baseball. Ignoring goals and assists for the moment, I ran linear regressions on the rest of the stats and their relationship to goals scored per minute for the team. The problem is that after shots on goal, none of the others seem to be statistically significan. Total shots are sort of significant as there is a statistically significant relationship between it and shots on goal (obviously). But the rest don't seem to really correlate particularly well with goals scored by team one way or the other.

In other words the teams that draw more fouls don't really seem to score more goals. No less either, but no more. So I'm slightly uncomfortable giving any credit for the fouls suffered statistic.

Furthermore, because of the secondary assist, even the relationship between assists and goals at the team level is less than perfect (though strong for obvious reasons).

To me the best general statistics available out there to judge player quality remain things like percentage of games started, minutes per game, and then some sort of factor for the quality of team (IE, a starter for DC is better than a starter for Columbus). Obviously what you're really measuring there is what the coach and (more generally) the transfer market thinks of the various players. That has obvious relationships with player quality, but also has obvious problems (namely the appeal to authority problem).

I think goals is a pretty good statistic for forwards, but they're less than 20% of the players out on the field generally and it's hardly perfect for them either.

[scaryice]

In other words the teams that draw more fouls don't really seem to score more goals. No less either, but no more. So I'm slightly uncomfortable giving any credit for the fouls suffered statistic.

Furthermore, because of the secondary assist, even the relationship between assists and goals at the team level is less than perfect (though strong for obvious reasons).

I'm making lists of only primary assists for each MLS season. Looking back, I almost wonder if there were different "official scorers" for each home team like in baseball?

As for fouls, that's the team though. Surely if you suffer more fouls than you commit, that's the sign of a good player? Or a creative one at least? It's one of the few stats we have that we can try to do something with.

I mean, Kyle Martino draws a lot of fouls; even though he sucks, he should get some credit for doing that right?

Unfortunately we don't have detailed stats like passes completed. Here's what the Actim Index does for the Premiership:

Complex mathematical formulae were devised to calculate the value of each player's contribution, match by match. In simple terms, the Actim Index comprises four calculations:

Calculation 1 - Assesses a player's contribution to a winning team, based on points won by the team when he appeared.

Calculation 2 - Assesses a player's performance in each game, by allocating points for actions that positively contribute to a winning performance such as shots, tackles, clearances and saves. It also takes points away from players for negative actions such as yellow/red cards and shots off target.

Calculation 3 - Allocates points based on time of the pitch.

Calculation 4 - Allocates points for goal scorers.

[voros]

I'm making lists of only primary assists for each MLS season. Looking back, I almost wonder if there were different "official scorers" for each home team like in baseball?

As for fouls, that's the team though. Surely if you suffer more fouls than you commit, that's the sign of a good player? Or a creative one at least?
Well it depends on what you mean by 'creative.' If drawing fouls really were a signature of having creative players, then it only makes sense that the more creative players you had, the more fouls your team would draw. So teams that draw more fouls should show at least some signal-to-noise when it comes to creating goals. I haven't found it.

Ultimately the goal of any player is to help his team win games, and I think if we're going to look at the statistical evaluation of individual players, we have to do so in that context. If teams who draw more fouls don't do noticeably better than teams who don't, can't we really question how important doing so really is, both directly (the value of the resulting free kicks) and indirectly (the 'third-variable' eveidence with regards to skill).

[scaryice]

Looking back at MLSnet's numbers for last year, they have 170 more fouls committed than suffered. Hmm...

[tachyon1]

Looked at these stats for a couple of epl seasons but never got around to doing much else with them.

I correlated various individual stats with team goals scored.

Shots on target vs goals scored;statistically significant and positive correlation.
Shots off target vs goals;sig and +ve.
Shot attempts vs goals;sig and +ve.
Goal assists vs goals;sig and +ve.
Long passes per game vs goals;sig and +ve
Short passes per game vs gls;sig and +ve.
Percentage of completed passes in own half vs gls;sig & +ve.
Percentage of completed passes in opponents half vs gls;sig & +ve.
Total crosses vs gls;not quite significant & +ve.
Cross completion vs gls;not sig & +ve just.
Dribbles per game vs gls;sig & +ve.
Dribbles completed vs gls;sig & +ve..
Tackles made vs gls;not sig
Tackles won vs gls;not sig +ve.
Interceptions made vs gls;not sig & +ve.
Offsides by forwards vs gls;not sig & slight neg correlation.
Fouls conceded by team vs gls;not sig & neg correlation.
Yellow cards vs gls;not sig & -ve.
Blocks made vs gls;sig & -ve.
Clearances vs gls;sig & -ve.

Correlation of course doesn't prove causation.

T.

[tachyon1]

Adding fouls drew vs gls scored;not sig,totally random scatter plot.

Fouls drew correlate to fouls conceded.Significant and +ve.

Basically "You kick us,we'll kick you."

T

[tachyon1]

Adding red cards.

A red card worsens a team's expected goal supremacy by around 1.45 goals over a whole game.

So more generally a red card costs a team
1.45(X^0.83),where X is the proportion of the game remaining to be played.

You could use that but it'd be time dependent for every dismissal.

A catch all figure would be about 0.58 of a goal because the average time of a sending off(in he EPL anyway) is about 60 minutes.

About a quarter of dismissals however come in the last ten minutes.

Red cards are statistically significant to team performance and even a simple logistic regression on red cards verses wins/non wins picks it up fairly quickly.

There remains the question of course as to where red cards cause poor performances and where poor performances cause red cards.

T

[tachyon1]

Re red cards,
just picked a EPL season at random.

Teams that had a red card(and the other team didn't) won 26% of those games.A team with that record would have a seasonal goal difference of about -0.45 goals per game.

Teams that didn't have a red card(and neither did the other side) won 37.5% of their games.A team with that record would have a seasonal goal difference of about +0.1 goals per game.

The difference in goal difference is about 0.55 goals per game,which ties in with the thought that a red card on average costs a team 0.58 of a goal.

T

[tachyon1]

Adding,the effect of the absence or presence of a team's main striker.

It's easier to deduce the worth to a team of it's best player because the size of the effect should be larger than for lesser run of the mill players.

Since the player's absence should be essentially random(due to injury),taking a team's results with and without it's main striker and pooling all teams from the same division should give you a ball park figure.

If you do this for several seasons in the EPL you find that if a team is without it's main striker then they score around 0.3 less goals per game.

That equates to around 2.5 less wins per EPL season.

You can do the same for keepers and their absence loses a team about 0.2 gls per game or 1.4 wins over a full season.

You could also introduce an interaction term to your regression and see if there's an extra combined effect of losing both your main striker and your main keeper for the same match.

Sample size'd be an issue but it'd make for an interesting exercise.

T

[Sagy]

tachyon1,

Do you have the data (and inclination) to check what is the correlation (for a team not individual) between Defensive (caught the other team) Offside and Goal Scored as well as Offside (number of time caught) and Goals.

Thanks in advance,

Sagy

[tachyon1]

Hi Sagy,
I've looked again at the scatterplot for offsides verses goals and it's a mess.So I've chucked alot more individual games data at it and some trends are starting to appear.

You seem to get the results you'd expect.Namely the team that scores more goals and presumably does more attacking gets caught offside slightly more often.Although team styles do play a part and alot of offside flags get 'played on' on a fairly random basis.

Most of the stats are pre the 'active or non active' instruction to refs.

Here's the general equations for the correlations that you're interested in.

Number of times Team A catches Team B offside=3.7-(0.093*(average gls per game scored by Team A)).

Number of times Team A is caught offside=3.4+(0.16*(average gls per game scored by Team A)).

So if Team A is expected to score 1.8 gls against Team B,who are expected to score 0.9 gls.You'd expect Team A to get caught offside around 3.7 times and Team B around 3.54 on average.

Not a huge difference.

T

[Elninho]

Re red cards,
just picked a EPL season at random.

Teams that had a red card(and the other team didn't) won 26% of those games.A team with that record would have a seasonal goal difference of about -0.45 goals per game.

Teams that didn't have a red card(and neither did the other side) won 37.5% of their games.A team with that record would have a seasonal goal difference of about +0.1 goals per game.

The difference in goal difference is about 0.55 goals per game,which ties in with the thought that a red card on average costs a team 0.58 of a goal.

T

But how about playing down a man, per 90 minutes? The distribution of red cards over the course of a match should be increasing toward the end - while straight red cards can happen at any time, second yellows tend to be later in the match for the simple reason that the first yellow has to be given first.

[tachyon1]

That's just a quick and dirty 'does the theory roughly fit the data'.

If you want more specific you have to use the 1.45(X^0.83),combined with the current score and the relative team strengths before the dismissal.

That fits individual occurances of dismissals very well.

A 90th min dismissal at 0-5 costs your team vitually nothing.It might cost you more in the game the player then has to miss....or it might actually improve you longterm if his replacement turns out to be a much better player.

Adding.It depends what the player was doing to get dismissed.Verbally abusing a ref in midfield's probably not going to add much to the cause.Tripping an opponent as the last man to preserve a lead late in the game is probably a cost effective move.

Losing a player for the last ten minutes costs you 0.23 of a goal so if a player's better than 3/1 to score (including from the subsequent free kick),you probably bring him down.

Maybe you should be crediting players for some types of red cards.