Karlsson and the problem with counting stats

To follow up on yesterday's musings, questions should be asked, but let's first accept that counting stats are just that: a count.  Wins and Points are counted in the standings; counting goals can help you evaluate how player production relates to wins but even then it doesn't completely evaluate the player.  Evaluating the amount of goals a team needs to win a game and then looking at a player's goals per game can help you evaluate the player's contribution to wins via goals but it does not evaluate the entire ice surface.

To yesterday's post; I simply took giveaways, takeaways and the sum of these, then divided those numbers by the TOI, multiplying by 60 for the amount of time in a regulation game.  To be fair, some of this is already done by sporting charts.  My first issue with my basic math is that the average game is longer than 60 minutes...but I digress.  Here are the findings for the Senators after the Calgary game:

Player	Pos	SUM/TOI* 60	GvA/TOI *60	TkA/TOI *60
Mark Stone	R	2.13	1.71	3.84
Zack Smith	C	1.54	0.86	2.40
Erik Condra	R	1.48	0.87	2.36
Bobby Ryan	R	0.83	1.23	2.06
Curtis Lazar	C	0.78	0.87	1.65
Alex Chiasson	R	0.71	0.36	1.07
Jean-Gabriel Pageau	C	0.70	1.12	1.82
Mike Hoffman	L	0.62	2.13	2.75
Milan Michalek	L	0.50	0.56	1.06
Mika Zibanejad	C	0.35	1.24	1.60
Chris Neil	R	0.32	0.32	0.65
Colin Greening	L	0.27	1.60	1.87
Kyle Turris	C	0.20	1.67	1.87
David Legwand	C	0.14	1.43	1.57
Clarke MacArthur	L	0.00	1.86	1.86
Marc Methot	D	-0.61	0.91	0.30
Cody Ceci	D	-0.89	1.44	0.55
Mark Borowiecki	D	-0.91	1.24	0.33
Jared Cowen	D	-1.00	1.80	0.80
Erik Karlsson	D	-1.11	2.63	1.52
Chris Phillips	D	-1.52	2.07	0.56
Eric Gryba	D	-1.61	2.17	0.56
Patrick Wiercioch	D	-2.15	2.51	0.36

First things first, defencemen finish last in the sum of giveaways - takeaways / Time on Ice * 60.  The reasons for this should be obvious, defencemen are trusted with the puck in the defensive zone and usually in higher risk situations attempting to move the puck to the offensive zone.  Forwards get to forecheck and attempt to create giveaways.  Karlsson is the defencemen's exception, his aggresive style of play creates more takeaways than his compatriots.

The second thing you notice is that although Karlsson has the most takeaways, his ability to create takeaways and his time on ice places his sum of giveaways/takeaways divided by time on ice 4th on the team amongst regular defencemen.  Corsi darling Patrick Wiercioch is last on the team in this statistic however does this make them less valuable than the defencemen ahead of them?  What this basic stat doesn't identify is the amount of passes a player attempts or the amount of time they have the puck on their stick.  Offensive defencemen like Karlsson tend to have the puck on their stick more than their defensive counterparts, leading to a higher possibility of turning the puck over (and also of scoring a goal, registering an assist, etc.)

This is basic, and led to more questions to me:
How do you evaluate the value of the stat?  How many giveaways/takeaways lead to a goal?  How many goals lead to wins?  The NBA actually tracks the amount of points stemming from turnovers.

Also, what was the location of the giveaway?  A giveaway in the defensive zone should lead to a higher percentage of goals against...but maybe not?

The timing of the giveaway should be important as well.  A giveaway during a powerplay leads to less time with the man advantage therefore does it affect the odds of scoring a goal more than a giveaway during 5 on 5 play?  And a giveaway in the last minute when leading by one goal is much more stressful than a giveaway during the first period but are their values the same?

How important is puck possession time and why aren't we tracking this?

Also...how do you calculate clutch?!?

Did this bring any questions to your mind?