Using Win Threshold to Aniticpate Next Season Part III

In Part I we explained what Win Threshold is, how it works, and which teams had the best Win Threshold (or which team’s offense is the best at scoring and defence is best at defending) last season. In Part II, we examined the Leafs offensive outputs based on shot percentages and shot totals, and factored in the new additions to the leafs in order to determine what kind of Goals For we can expect next season. Welcome to Part III, where we will discuss how our team is doing defensively, and specifically limiting shots.

First, I invite you to re-read Part I & Part II,  to re-familiarize yourself with this material, before we begin the analysis on the Leafs defensive system.

By the end of Part II, we calculated that the Leafs should be good for goal totals between 230-250, depending on potential injuries and the slight development of Nazem Kadri. That gave us the following table of output:

These projections, however, are based on the assumption that the Leafs will limit their opposition to exactly 2542 shots against again this year. This is chances of this are obviously extremely farfetched, and thus in this article we are going to try to determine what kind of shots to expect against our goalies this coming season.

Below is a distribution of the leaf’s shots against per game over the entire season. Obviously the shots fluctuate game to game based on the opposition, the offense generated, whether Lebda was dressed or not, etc. When averaging the Shots Against on a per game basis, however, a clear trend arises. Because the first few games the Leafs the year saw lower-than-average shots against, the Shots/GP is constantly going up. One would expect it to level off at about the half way mark of the season, however—this never occurred, the reason being, that our shot totals were increasing as the season wore on.

On Februrary 9th, 2011, Francois Beauchemin was traded from the Leafs back to Anaheim, in exchange for Joffery Lupul and Jake Gardiner. While this is an excellent haul from an asset aspect, Beauchemin was a defensive stalwart on the Leafs blueline that is extremely hard to replace.

In addition to the trading of Beauchemin, the Leafs also lost Kris Versteeg for draft picks, John Mitchell, and Tomas Kaberle. None of these trades, except for Lupul from Anaheim, gave the Leafs any sort of replacement into the lineup. Thus the defensive prowess of some of these players could not be replaced, evidenced by the fact that while the leafs finished the season with an average shots against of 31.0/gp, from October 9th – Februrary 8th they averaged 29.8 SA, whereas from Februrary 10 – April 9 they averaged 33.2SA.

Below is the breakdown in table format:

Looking at this breakdown, the increases in shots against after the trade deadline, and the knowledge that the Leafs were allowing 33 shots per game after the Beauchemin trade, one can expect that the leafs will continue to allow around 33 shots per game next season. This does not factor in any of the new additions, though, and is a pretty loose assumption. For this reason, we will look at some advanced statistics that will help us to determine the shots against we can expect.

In order to maintain consistency throughout or study, and based on the moves the Leafs have made, we can expect our opening roster to look like this:

CAPGEEK.COM CAP CALCULATOR

FORWARDS
Joffrey Lupul ($4.250m) / Tim Connolly ($4.750m) / Phil Kessel ($5.400m)
Clarke MacArthur ($3.250m) / Mikhail Grabovski ($2.900m) / Nikolai Kulemin ($2.350m)
Nazem Kadri ($1.720m) / Matthew Lombardi ($3.500m) / Colby Armstrong ($3.000m)
Mike Brown ($0.736m) / Tyler Bozak ($1.500m) / Colton Orr ($1.000m)
/ / Darryl Boyce ($0.650m)
/ / Joey Crabb ($0.650m)

DEFENSEMEN
Carl Gunnarsson ($1.325m) / Dion Phaneuf ($6.500m)
John-Michael Liles ($4.200m) / Luke Schenn ($3.500m)
Keith Aulie ($0.733m) / Cody Franson ($0.800m)
/ / Mike Komisarek ($4.500m)  


GOALTENDERS
James Reimer ($1.800m) / Jonas Gustavsson ($1.350m)

BUYOUTS: Darcy Tucker ($1.000m)

CAPGEEK.COM TOTALS (follow @capgeek on Twitter)
(these totals are compiled without the bonus cushion)
SALARY CAP: $64,300,000; CAP PAYROLL: $60,164,000; BONUSES: $1,000,000
CAP SPACE (23-man roster): $3,714,000

Based on this roster, we generate defensive stats for the following players:

EVEN STRENGTH:

PENALTY KILL:

POWER PLAY:

In Part II we also assumed each Skater would play only 74 games—to account for injuries—except for Connolly who will only play 60, Lombardi who will play 22, Colborne who will play 24, Crabb who will play 64, and Komisarek who will play 48. We will maintain these numbers for consistency and realism’s sake.

Because of this stupid box that I have to type everything in, I am unable to properly paste the table that I want to. Thus, I will have to split the following calculations by situation, and then amalgamate them all at the end. It may be confusing, but I will try my best to explain the calculations I will be performing.

The actual mathematical representation of our calculations are below the explanation, and above the table.

We will begin by looking at Nikolai Kulemin as an example. In Part II, we predicted that Kulemin should see similar ice time to last year, approximately 17:19/GP. We will begin by converting this number to seconds, to eliminate the colon. Thus Kulemin’s 17:19 is now expressed as 1039 seconds of Ice time per game.

In Part II we were able to predict the amount of shots he would take based on his career averages. Now we will be estimating how many shots he will personally allow while on the ice. One might say that this is subjective as there are 5 people on the ice at any point that a shot is taken, so they cannot specifically be counted against him—this will be accounted for.

To determine how many shots Kulemin will be responsible for, we must calculate his projected season ice time. We thus take the 74 games we predicted him to play, and multiply this by the 1039 seconds of ice time he will see per game. We then divide this number by 60 (60 seconds in a minute) to set us back to the total number of minutes we can expect (in 74 games). This number is 1281.43 for Kulemin.

Using the information in the tables above, we see that at even strength, Kulemin allows 27.1 Shots Against per 60 minutes of play. With a whole team of Kulemins, this would put us in the elite teams of the league. Unfortunately there are players like Joffery Lupul who allow 33.5 shots against per game. This shows us that not only did the loss of Beauchemin hurt us, but the addition of Lupul also hurt us in this department. Anyway, we will take total season ice time, and divide first by 60 to convert the minutes to a per 60 figure TOI/60, and then divide the total number by 60 so that it is consistent with our next calculation, giving us currently (TOI/60)/60. We will then take this whole number and multiply it by Kulemin’s SOGA/60, giving us ((TOI/60)/60)*SOGA/60

Or if we look at it another way, these are the measurements: ((Av Minutes/60)/60)*SA/60 or another way, (Av. Hours [decimal]/60)/60*SA/60. The two /60’s cancel each other out, and thus we are left with the ice time Kulemin is given over a game’s time, and the number of shots that are likely to be taken against, over the entire hour of the hockey game, while he is on the ice. For Kulemin, this number is 9.65. So we can expect about 9.65 shots against the Leafs over the entire game, while Kulemin is on the ice.

Now if we were to add up the total number of shots against for each player, we would probably end up with something around 200 shots against, which is complete false. For this reason, we have to factor in the number of players on the ice. Our next calculation will be to divide Kulemin’s 9.65 with the number of players on ice (per situation). So, at Even Strength we divide 9.65 by 5, at PP we also divide by 5, and at PK we will divide by 4. Running this equation, we have a value of 1.98 at even strength. This value indicates the number of shots we can directly attribute to Kulemin on a per game basis.

When we multiple Kulemin’s 1.98 shots against by his 74 Games, we determine that he allows 147 Shots against over the whole season.

Total TOI (m) = (TOI/GP (s)*(GP)/60 à Total Time On Ice Per Season in Minutes
SOGA/TOI/60 = [(Total TOI (m))/60/60]*(SOGA/60) à Number of Shots against per Game while the player is on the ice.
Average SA/GP = (SOGA/TOI/60)/(# Players on Ice) à This tells us how many shots are directly a result of our player’s ice time.
Total SA = (Average SA/GP)*(GP) à Number of Shots Against over a season that can be attributed to the player.

This gives us the following statistics at even strength:

Now looking at the totals, the 82 was simply an average calculation to ensure that we have the appropriate number of games played, which is true. The 60.613... is the average number of minutes played per game, and the 29.4 is the average shots against per 60. Finally, the 2911 shots against is reflective of the number of shots we can expect at even strength. This total is atrocious. The reason we don’t need to worry about it though is because it only looks at even strength, and while there are more shots allowed on the penalty kill, there are much less allowed on the powerplay. For this reason, we will have to perform the same calculations at 5v4 and 4v5.

With all these calculations in place, we can use a final calculation to determine the approximate shot totals we can expect against next year:

Shots Against = ((ES Shots/Predicted TOI)*(Predicted TOI-PP TOI-PK TOI))+PP SA+PK SA

This equation takes our total shots at even strength and establishes a Shots/Minute ratio. We must multiply this ration by the total predicted ice time less the powerplay ice time and the penalty kill ice time. After this, we add the powerplay shots against and the penalty kill shots against, to determine our total shots against. When we include the numbers:

Shots Against =((2817/60.614)*(60.614-7.2664-4.76169))+99+310
Shots against = 2667

There is just one problem with this statistic:

Because of the new additions of players like Franson, Liles, Connolly,etc. Who have powerplay ice time based on their past teams, and because of the prediction-nature of these time on ice totals, our total time on ice values are a little bit off.

The above data stats that the leafs will play an average of 60.614 minutes per game, including 4.76169 Penalty Kill time and 7.2664 Power play time.

I am unable to find exact data on the average minutes played by the leafs last season, but this is what we can conclude: last season the leafs went to overtime 18 times, and to the shootout 11 of these times. Thus, our total number of minutes is (64*60)+(11*65)+the ice time of the last 7 games. Below are those games:

 
Using these numbers, our average ice time becomes:
= ((64*60)+(11*65)+63.13+63.43+61.25+64.6+62.52+60.7+64.03)/82
= 4994.66/82
= 60.91

The Powerplay and Penalty Kill data is available on NHL.com, however, and was on average 6.67/GP and 5.48/GP, respectively. We can now use our accurate totals to determine the true values expected. When we factor in the true total ice time, the increase in penalty kill time, and the decrease in powerplay time, we should actually expect 2714 Shots Against.

And just to verify these stats, we have one more metric we can use to estimate our special teams time. The far left columns express the average penalties drawn and taken by each player per 60 minutes.

 In our ‘Total Penalties Taken’ column, we divide the TOI/GP in seconds by 60, to give us the number of minutes each player plays each game. We then multiply this number of the percentage of the season they play (GP/82), and multiply it again by their PTAKE/60. The same process is done for PDRAW.

I will have to come back to this section, as I believe there is something extremely wrong with this data. If you look, Colton Orr only has a 15.54 penalties. Perhaps these 15.54 fighting majors, but that still seems low. As I said, I will have to return here. Regardless, the important part is the totals at the bottom. If we look at the first set of totals, it is the sum of all the total columns. They seem low, but the data is normalized so if the penalties taken are low, the penalties drawn are also low. The second set of totals takes the first, divides by 82 games, and multiplies by an average of 2 minutes per penalty, giving us 4.63PK minutes and 5.82PP minutes per game. These numbers are eerily similar to the numbers we actually had this season.

The real strength behind this analysis can be seen through the ratio. If we look at last season’s 6.67PP and 5.48PK, and divide one by the other, we have a ratio of 1.217 PP minutes for each PK minute. If we look at our projected totals, it comes out to 1.2 PP minutes. In addition, if we divide our projected PP by PK, we come out with 1.257 PP minutes—again, pretty similar. What this tells me is not that we should change the totals, but that we can be confident with our projection.

Regardless, I have run the same final calculation, factoring in the average number of shots allowed by each player per game, in every situation, and the time they play in each situation. If we use the new totals of 4.65PK minutes and 5.82PP minutes, our total shots against over the whole season is 2703—slightly less than last season.

Projections of any number between 2667-2713 can be made with confidence, and a slight deviation from these numbers should also be expected just because of chance. I will run five different calculations to determine an expected ranking, and we will be able to make a judgment on our final Win Threshold.

Just to explain this, 2690 is an average of 32.80 shots per game over the whole season. This would rank the Leafs 29th in the league, 0.3 shots per game better than the 30th team, and 0.2 worse than 28th. What I’m saying is that while the stats paint this picture, it is unlikely that this will actually occur. Perhaps the new assistant coaches, Aulie’s improvement, an improvement on Lombardi’s stats, etc. will help improve this number.

This is the problem with posts like these: they are completely hypothetical. Regardless, I am enjoying putting these together, and I hope it was informative. As you can see, with the goal output we anticipated in Part II, and the shots against we expect here, we will rank 8th in the conference for Win Threshold, and 17th in the league.

Part IV, the final part, will look at our goaltending situation and whether or not we can reach our Win Threshold.