How to Calculate GAON/60 and Similar Behind the Net Statistics

I'm sure you all read and cogitated JP's recent statistical breakdown of the Capitals' blueline. The post contained an impressive amount of Behind the Net statistics, which help qualify a player's contributions on a more significant level than many traditional hockey statistics. This FanPost is meant to be a tutorial of sorts regarding how these statistics are calculated. For more information about these advanced statistics, check out the excellent FAQ on the Behind the Net SBN blog. There is another FAQ on the main BtN website as well. They are definitely worth a read for your personal edification.

If you are like me, you were at one point confused by what these metrics meant, how they were derived, or what the units of measure were. When I first discovered Japers' Rink, I had no idea what stats like GAON/60 or TOI/60 meant. The FAQs linked above do a good job explaining what these stats mean, but I never managed to find any resources out there that clearly and concisely showed how to calculate these metrics. Rather than put others through the same painful learning curve, I decided to demonstrate and annotate the process here.

I imagine there are different levels of familiarity with this subject. Many of you already know what this stuff, and that is fine. Just humor me. On that note, allow me to play the role of Professor Bradley for a moment and explain the "forces of hockey [stats]."

The first thing I want to clarify is what "over sixty" or "/ 60" means. The loose definition is that this stands for "per sixty minutes." In fact, this is what the key on BtN's stat page says; however, this can be misleading. It is important to remember context here. "Over 60" actually means sixty minutes of a specific context. This context could mean even strength, power play, or penalty kill. Broken down further, it can mean 5-on-5, 5-on-4, 4-on-5, 4-on-4, etc. Always keep context in mind when looking at advanced hockey statistics.

Allow me to demonstrate calculating a BtN statistic, namely, GAON/60. This stands for "goals scored against while a player is on the ice over sixty minutes of a given context." Much easier to say GAON/60, eh?

Let's use Jeff Schultz as an example. The following calculation is for Schultz's GAON/60 during 5-on-5 play for the 2008 - 2009 season. The necessary data can be found here. It may seem redundant calculating this metric using data from this page when the metric itself is listed there as well. I agree, but this is just an example to demonstrate the process.

For the sake of clarity, I will use the "T-chart" method taught to me in chemistry class during high school. This helps show how units of measure cancel out. It also helps determine whether we should multiply or divide by a given number. Using the BtN data, we know that Schultz was on the ice during 5-on-5 play for a total of 41 goals against last season. This is shown below.

Step 1:

The above statistic shows goals against per season for Schultz; season meaning the 82 games in '08 - '09. Schultz did not play the full 82 games last season though. He played 64 games. To make this adjustment, we divide by 64.

Step 2:

Note that the "Season" unit will cancel out. This leaves us with GAON per games played by Schultz. We are trying to break this down by 60 minutes, so we need to convert from games to minutes. There are 60 minutes per game, so we will divide here.

Step 3:

Note that the "Games" unit will cancel. This leaves us with GAON over 60 minutes. So we are done, right? Do not forget context here. We want GAON per 60 minutes of 5-on-5 play. Schultz did not play a full 60 minutes of 5-on-5 hockey every game, so we need to make an adjustment. From the BtN page, we know that Schultz had a TOI/60 at 5-on-5 of 15.42 minutes. This means that for every sixty minutes of hockey played, Schultz was on the ice for an average of 15.42 minutes at even strength, five-on-five. In order to make the units cancel appropriately, we divide by TOI/60 here.

Step 4:

Note that the "60 Minutes" unit will cancel. This leaves us with GAON per Minute of 5-on-5. We still are not done though. In the current state, the metric is GAON per one minute of 5-on-5. This is not a very helpful statistic. We want "per sixty minutes of 5-on-5."

To get this metric, we do a little mathematical trickery. The identity property of multiplication states that any element multiplied by one is itself. We are going to do this here. In this case, "one" means "60 minutes divided by 60 minutes." This is shown below.

Step 5:

(Note: If the images are getting too small to read, I apologize. SBN's FanPost editor sets a maximum size for pictures. Just click on the image to see it at full size.)

The "60 Minutes" numerator is going to be multiplied into the current value of the expression. However, the "60 Minutes" denominator is going to remain in the units of measure for the final value. Note that the "Minutes" values cancel one another. This leaves our units of measure for this statistic as GAON per 60 minutes of 5-on-5 hockey, which is our target metric. If we multiply/divide through, we see that Jeff Schultz was on the ice for 2.49 goals against per sixty minutes of 5-on-5 hockey.

Final Result:

This image shows which units cancel and which numbers are multiplied and divided into the equation. The unit cancellations are color coded.

The above example demonstrates the entire, unequivocated process, unit cancellations and all. For a quick and easy approach, this is a simpler method for these calculations:

1. Find the statistic across the entire season for a given context
   
2. Divide by games played by the player
3. Divide by TOI/60 for the given context
4. Multiply by 60

This method applies to all BtN aggregate, or "over 60," statistics. Here is an example for GFON/60 - which stands for goals for on the ice over sixty - using Alex Ovechkin. Alex was on the ice for 78 goals for last season during 5-on-5 play. He played in 79 games and was on the ice for 15.94 minutes at even strength, 5-on-5 per 60 minutes (per game).

And there you have it. During last season, Ovechkin was on the ice for 3.72 goals for per sixty minutes of 5-on-5 hockey. This formula can be applied to any BtN "over 60" metric. Goals/60, Assists/60, GAOFF/60, etc.

I hope this helps some folks out there. Even if you knew what these statistics meant already, hopefully seeing how they are calculated reveals a little more about their significance. Fortunately, Behind the Net does all the dirty work for us, but I for one always like to know where statistics come from. If I made any egregious errors here, please let me know and I will fix them right away. Questions? Comments?