Recently I wrote a piece on the relationship between shot distance and scoring. The main takeaway from that article is seen in the following chart:
There’s a distinct non-linear relationship between how far a shot is taken from the net and how likely it is to go in. This would suggest that teams and players that get closer to the net to take shots (or have a defence which keeps shots to the outside) will be more successful. I stated in the previous article that I think incorporating shot distances into shot differentials is a natural and obvious enhancement to ratios like Corsi and Fenwick. But how best is this accomplished? I’ll propose a new methodology in this article.
First, a thought experiment. Imagine a player has the following game in terms of even strength shots while on-ice:
- Shots for: goal
- Shots against: miss, save, save
How did he do? The newspaper writer might look at this and say, “hell, he was +1, that’s all that matters”. The stats blogger might look at this game and say, “hold on there, his unblocked shot attempt ratio was +1/-3, which is a Fenwick percentage of 25%. He got lucky, and over the long run, if he sustains a similar percentage he’s in big trouble”. Both positions have a kernel of truth in them, but is there a way to extend this conversation?
What if I told you the distances of the previous shots were:
- Shots for: 11 feet
- Shots against: 66 feet, 35 feet, 51 feet
Well, it seems that the one shot he was on the ice for was a gold-plated chance, while the three shots against were from further out. Are the three further away shots still better than the one close one? One way to settle this would be to look up the probability of each of those shots going in the split second they leave the stick, based on how far away they were shot from. Regardless of whatever chaos theory needs to occur for that shot to result in a goal or not, what would we expect the probability to be if you freeze-framed your TV right as the puck leaves the blade of the stick?
The previous exercise I’d done resulted in a table of observed probabilities of unblocked shots of certain distances going in. I could create a logarithmic function to model this relationship, but for now I’ll just use the pure observed probabilities seen through almost 3 years of shots data, or 219,881 even strength non-empty net unblocked shots. Let’s translate the shot distances of our above player into expected goal probabilities:
- Shots for: 15.2%
- Shots against: 1.2%, 3.9%, 1.8%
Now, let’s add up these expected goal probabilities to come up with his overall expected goals for and against:
- Expected goals for: 0.152 = 0.152
- Expected goals against: 0.012 + 0.039 + 0.018 = 0.069
Based on what happened in that game, we’d expect the player to be on the ice for about 0.15 goals for and 0.07 goals against — this means his one dangerous shot was more than twice as likely to result in a goal as all three of the shots taken against him combined.
We can express this as a percentage, just like Corsi or Fenwick: Expected goals for/(Expected goals for + Expected goals against) = 0.152/(0.152 + 0.069) = 68.8%
This player’s team would have scored about 69% of the expected goals that night while he was on the ice, even though his Fenwick% was only 25%. Now, you can probably picture this same calculation being applied against all of this players’ shots for and against while on the ice to come up with his expected goal differential for a season. I’ve gone ahead and done this for the current Oilers’ season so far, up to and including Oct 29’s game versus the Leafs:
Some of these players have tiny samples so far, but remember that these small numbers involve the exact same number of events as their traditional Fenwick numbers, which are already in the hundreds for many of them. The numbers shown here are the expected number of goals you’d expect them to be on the ice for based on their shot differentials and those shots’ locations. You can already see some patterns emerge when you compare the expected goal % to traditional fenwick%:
- Players like Ryan Smyth, Ryan Jones, and Jesse Joensuu are “known” as players who take the puck to the net, and these numbers bear that out. Players of this type have value in terms of steering the play towards the net, through whatever means necessary (driving the net with the puck, getting rebounds, or creating enough space to receive a pass). They are involved in higher percentage plays, resulting in EG% that are higher than their Fenwick% would usually show.
- The only guys whose EG% is below their Fenwick% are Gazdic and Ben Eager. I’d expect goons to do especially bad in this metric, as they get outshot and their shot distances for are probably quite far.
- A highly skilled player like Ales Hemsky can have a much higher EG% than his Fenwick%, as he may be really fulfilling the stereotype of choosing to take a less number of shots in favour of getting quality looks at the net.
Now, you can also express these as rates per 20 minutes to get a sense of who are high and low-event players:
Ryan Smyth is still the Golden God here, showing off his quality-shot creating prowess, but we also see that he gives up the highest amount of expected goals against per 20 minutes, so we’ll call that the cost of goods sold in this case. The rare finds on this list are guys who have both high rates of creation and lower rates of allowance — players like Arcobello, Belov, and Hemsky have shown this ability with decent sample sizes.
You also see who tend to give up a high amount of quality chances — 2nd on this list for expected goals against per 20 mins is Nail Yakupov, who by reputation and by eye seems to be having issues on the defensive side of the puck. Other players like Eberle on forward, and Nick Schultz, Smid, and Ference (!) also seem to be struggling here. Also notice the chasm between Belov’s low expected goals against and the next highest defenceman. Love that Russian.
And this all isn’t just for evaluating players. You can use the exact same concepts to rate teams as well. Now, I’m not technically inclined enough to replicate this for the entire league, but I can tell you what’s going on with the Oilers. Their Fenwick% as a team in all even strength situations this year is 46.9%. Their total expected number of goals for is 26.4 vs 27.1 expected goals against, for an EG% of 49.3%. They’ve actually scored 28 and given up 35 so far. This should tell you that their problems are related to their goaltending not reaching the league average levels the expected probabilities are based on (ie, their goaltending has sucked so far).
Remember, this is accounting for “quality” as seen in shot distance. If the Oilers were giving up a ton of 10-bell chances and hanging their goalies out to dry, they’d have a higher number of expected goals against, and they just don’t.
There are other aspects of shot quality, such as if a shot was a rebound, a one-timer, shot after a lateral pass, a breakaway, etc which are not accounted for here. But this is a simple way of accounting for the quality of all kinds of shots in a transparent way. I’d imagine you could rig up your own expected probabilities to try to account for some of these things. There’s a lot of ways this analysis could grow further.