### In my first post here at MLHS, I wrote an introduction to advanced statistics which generated some good discussion in the comments. A number of the comments were with respect to WOWY analysis and some more specifically with respect to Kessel and Bozak.  I will delve into that more here in my second post.

As explained in my introduction to advanced statistics post, WOWY is short for “With Or Without You” and looks at how the team performs when two players are on the ice together and when they are each playing apart from each other. So, for Phil Kessel and Tyler Bozak, we would look at how the team performs in three situations:

1. Both Kessel and Bozak are on the ice together
2. Only Kessel is on the ice
3. Only Bozak is on the ice

This table shows how the Leafs have performed in these three situations according to CF% (corsi for percentage, or percentage of shot attempts for and against that the Leafs took), GF% (goals for percentage, or percentage of goals for and against that the Leafs scored) and GF20 (goals for per 20 minutes of play). I included GF20 individually because I wanted to show how Bozak impacts the teams offensive production more specifically when Bozak is on the ice.

## Kessel + Bozak WOWY

A WOWY comparison of Kessel and Bozak
Stat2010-112011-122012-132013-144-year
Kessel with BozakCF%46.5%48.8%46.9%44.6%46.7%
Kessel without BozakCF%47.1%50.7%43.0%43.6%46.3%
Bozak without KesselCF%48.2%39.2%25.5%28.5%40.2%
Kessel with BozakGF%42.5%47.7%51.7%56.2%49.7%
Kessel without BozakGF%56.3%48.9%64.3%46.2%49.2%
Bozak without KesselGF%22.7%38.9%75.0%25.0%32.1%
Kessel with BozakGF200.730.930.971.190.95
Kessel without BozakGF200.901.151.400.720.98
Bozak without KesselGF200.370.881.000.670.62

Tables are good, but charts are often easier to quickly draw conclusions from. Here are WOWY charts for CF% and GF%:

Let’s start with the first chart looking at CF%, which can act as a proxy for puck possession but specifically measures which team is getting the most shot attempts. Anything over 50% means your team is getting more shot attempts than they are giving up; that is generally a good thing. As you can see, the lines for Kessel with Bozak and Kessel without Bozak are almost identical, indicating that Bozak had very little impact on Kessel’s overall statistics. Conversely, when Bozak is apart from Kessel, Bozak’s CF% stats tank, meaning Kessel (along with Lupul/JVR) has a significant positive impact on Bozak’s statistics. This would indicate that Kessel is not dependent on Bozak whereas Bozak is definitely more dependent on Kessel.

When looking at GF%, though, we see that until last season Kessel had a better GF% apart from Bozak than with Bozak. This reversed last season, when Kessel was better with Bozak than without. Over the past 4 years combined, Kessel’s GF% with Bozak and without Bozak is almost identical, which is consistent with what we saw with CF%.

Remember that sample sizes are significantly smaller when dealing with goals than shot attempts. There is much more fluctuation and randomness in these statistics, so we are more looking for trends than absolute numbers. This small sample size is a big reason for Bozak’s good GF% away from Kessel in 2012-13. In that season, Bozak only played just under 60 minutes of ice time apart from Kessel and in that ice time he was on the ice for 3 goals for and 1 goal against for a GF% of 75%. That isn’t anywhere close to a large enough sample size to draw any conclusions from. The overall trend we see in both the CF% and GF% charts are that Bozak has little or no effect on Kessel’s overall on-ice stats.

I wanted to look at GF20 specifically to see if Bozak is having an effect offensively or defensively on Kessel’s statistics. Here is how Bozak and Kessel’s GF20 WOWY chart looks.

For three straight seasons (2010-11, 2011-12 and 2012-13), Kessel had a higher goals for rate without Bozak than with Bozak but that reversed last season when Kessel’s had a better GF20 with Bozak than without. One season does not make a trend, though, and until last season the offensive production of the Leafs was significantly worse when Kessel was with Bozak than when Kessel was not with Bozak. Did something change last season? Has Bozak figured something out that has reversed the trend? We’ll have to see what next season brings. I suspect it was just an anomaly, but I’ll leave it up to Bozak to prove otherwise.

Now, we have to keep some perspective on these “without you” statistics for both Kessel and Bozak. When Kessel isn’t playing with Bozak he has mostly been playing with Grabovski or Kadri, both pretty solid centers so it makes it easier to maintain his “without Bozak” numbers. That said, Kessel has generally been as good or better with those other two than with Bozak over the past 4 seasons, so it makes for a difficult argument that Bozak is actually a better player than either of those guys or more deserving of #1 center role.

For Bozak, when he is not playing with Kessel (particularly the past couple seasons) he has generally been playing with 3rd line players like McClement, Kulemin, Raymond, Komarov, etc. in very defensive roles. This could have a significant negative impact on his without Kessel statistics. That said, over the past 2 seasons, Bozak’s CF% without Kessel is 27.5% and his GF% without Kessel is 37.5%. These are horrifically bad numbers and pretty difficult to justify, but could in part be due to Bozak being used to win defensive zone face offs when without Kessel. If he loses a defensive zone face off, he gets stuck on the ice for a bunch of shots against. If he wins the face off and Leafs clear the zone he heads to the bench getting no benefit of any subsequent offensive chances. This certainly would be a factor but I have serious doubts it is enough to justify a 27.5 Corsi percentage. Playing with Jay McClement a fair bit certainly doesn’t help, either, as McClement consistently put up poor possession statistics every year (that article is another example of how one can use WOWY’s in player evaluation).

I hope this provides a little more detail as to how one might conduct a WOWY analysis of a pair of players as a method of determining which players are more critical to the on-ice success of the team. In the example of Kessel and Bozak, there is little or no evidence that Bozak is integral to Kessel’s production where as there is a lot of evidence that Kessel is integral to Bozak’s production. As always, if you have any questions feel free to ask in the comments.

ICYMI: An Introduction to Advanced Statistics

To better understand this analysis, please see David Johnson’s post: A Guide to WOWYs