When allocating credit for goals to individual players in the past, I've used a fairly simple rule: each goal is 50% shooting and 50% playmaking. Playmaking was initially determined by assists, but I later changed this to assist attempts to lower the impact of a teammate's poor finishing on the playmaker.
What about things like winning penalties, corners, and fouls? Or even intercepting a pass in a dangerous area? Those should count for something, but they don't show up as assists. To determine the effect of these, I looked at every goal scored this season, and counted up the last two events leading up to the goal. Here's the final tally:
|Standing tackle won||61||4.59%|
|Shot on target||42||3.16%|
|Shot off target||22||1.66%|
|Ground tackle won||19||1.43%|
|Aerial duel won||13||0.98%|
|Shot hit post||7||0.53%|
|Player subbed on||6||0.45%|
|Opponent tackle lost||6||0.45%|
|Goalkeeper pick up||2||0.15%|
I think that the 50% playmaking element can be divided amongst these to give a more accurate picture of attacking contribution. We might take a few of these out - turnovers obviously don't help you score goals, and I think its safe to assume that the off-target shots are not related to the goals (instead, these are probably mistakes on the ensuing goal kick). As for the rest, I'm sure we can all picture goals in our head that had these events leading up. Aside from open-play passes, we can see that quite a few goals are scored directly or indirectly from free-kicks, recovering loose balls, tackles, and rebounding shots.
The thing that got me started on this was brainstorming how to incorporate possession into my defensive metrics. Passing the ball to a teammate isn't generally thought of as defending, but if the other team doesn't have possession, they can't score. Similarly, tackles and interceptions aren't directly related to scoring goals, but they can lead to counter-attacks, which in turn lead to goals. Once again, credit where credit is due.