# Comparing real-time stats with Fenwick

Matt Martin hits a lot of people every year. He led the league in Hits for the last three full seasons and also leads the league in hits so far this year. How is he able to rack up all of those hits over the course of a season? Well first he has to simply play some part of the season (duh). Secondly he has to play in a lot of games. Thirdly he has to get a good amount of ice time. But there’s a 4th dimension that we haven’t considered: he needs on-ice opportunities to hit someone.

We can adjust each factor pretty easily starting from the top and working our way down. Hits per season. Hits per game. Hits per 60 min. In order to approximate how many opportunities Martin has to hit someone on the ice we need to know how often he’s on the ice when his team doesn’t have the puck. For this we can approximate puck possession by Fenwick.

Martin’s current Fenwick is 54.5%. What would happen if his Fenwick was 50%? Well, we would then presume that he would be on the ice with more opportunities to hit someone and should scale his Hit statistics accordingly. In Martin’s case we see that he has 218 hits this season. He played in 46 games and thus has 4.7 Hits/GP. He has played 505 minutes and thus has 25.9 Hits/60 min. But then we’d also make another adjustment based on his Fenwick. We’d take his 25.9 Hits/60 and divide by (50/Fenwick). So 25.9/(50/54.5)=28.2 Fenwick-adjusted Hits/60. We’d expect him to have 28.2 Hits/60 if he were on a team where his Fenwick was 50%. We can do the same algebra for other defensive metrics such as Takeaways and Blocked Shots.

I looked at these defensive player stats until the all-star break (min 20 GP), taking into account Games Played, TOI, and Fenwick.

We see that Martin still leads the pack in totals, in rate stats, and even possession-based stats. Players like Zac Rinaldo and Ryan Reaves see a drop in their Fenwick-adjusted Hits/60 since they are already on the ice for a considerable amount of time without the puck.

Since Takeaways occur less frequently than Hits, we see less of a change per 60 minutes. One thing to point out from this list is that Hossa’s great possession numbers on the Blackhawks offers less opportunities for Takeaways which hinders his Takeaway season totals. But based on on-ice opportunity, he’s Top 6 in the league.

Blocked Shots is another stat that occurs in low frequency and requires a lot of events to tease out the signal from the noise. Kris Russell leads the league in Blocked Shots, but has had ample opportunities to do so since his team is playing without the puck a lot when he’s on the ice.

The point of all of this is to convince you that possession-adjusted stats are more explanatory than not. To show this, I looked at player season stats from 2013 and 2012 to see how well they correlated with each other. Here’s what I found:

Hits/60 2013 v Hits/60 2012 -> R2 = 68.7%

F-Adj Hits/60 2013 v F-Adj Hits/60 2012 -> R2 = 80.9%

TkA/60 2013 v TkA/60 2012 -> R2 = 23.6%

F-Adj TkA/60 2013 v F-Adj TkA/60 2012 -> R2 = 42.5%

BkS/60 2013 v BkS/60 2012 -> R2 = 58.0%

F-Adj BkS/60 2013 v F-Adj BkS/60 2012 -> R2 = 72.7%

In all instances, we see that possession adjusted stats correlate better from 2012 to 2013.

There are some pitfalls to this logic, or perhaps questions that might need answering.

• Fenwick is only an approximation for possession and may not be a true indicator of time on/off the puck
• Not all time a team doesn’t have the puck presents an opportunity for a hit, takeaway, or blocked shot.
• Perhaps we should only consider away games to account for scorer bias when it comes to these running stat totals
• The last thing I want to do is piss off Bill James. He once said something along the lines of “Don’t multiply or divide A by B unless there’s a gosh-darn good reason to do so”. So we have to look at why we’re dividing hits by Fenwick. Does the fact that a player hits so many people specifically cause his Fenwick to go up or down? If so, then the two or not independent and we shouldn’t make this adjustment.