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*How We Value NHL Players*

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**Fan Valuation**

Like most things associated with professional sports there are lots of opinions on how much athletes get paid. Unfortunately, there are very few people who have ever been trained in valuing anything so these opinions don’t tend to be very good. Just look at this article where the author barely even bothers to produce comps (comparable player contracts) to justify his assertions – mostly he just talks about how bad the players are. Other opinions at least tend to be based on comparables, like this one, but often the players chosen don’t work very well because they were signed at different times, have different free agent statuses, or they simply omit players that don’t conform with the view they are trying to prove. My favourite comments on this subject though come from people who aren’t fans and just want to moralize on why athletes are paid so much…

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**Prior to the Salary Cap**

In fairness to fans though, before the NHL instituted a salary cap in 2005 fundamentally valuing players was very difficult because every NHL team had different financial resources and they don’t share that information with the public. So without a fundamental way to determine what players should be worth the only way fans could determine their value was through a comparable analysis (i.e. Colorado paid Sakic $X/year so Federov is worth $Y/year). This is of course the kind of analysis I was criticizing above but it was actually all you could do during this period. Unfortunately, this approach has continued to today even though the salary cap provides us with a better way of determining a player’s value.

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**Post-Cap Valuations**

Now that the NHL has a salary cap there is a better way of determining a player’s value than comparables. The reason this is true is that you now have two constraints to work with instead of one – the salary cap and the total ice time available.

The easiest way to think about this is that NHL teams have a certain amount of money they can spend on players (let’s call it $50 million/year for the sake of argument) and they will need their players to play for ~60 minutes/game x 82 games/year x 5 players = 24,600 minutes/year (games occasionally go to overtime and teams are shorthanded for a part of most games so 60 minutes/game isn’t perfect and we can adjust for this later but for now let’s just go with 24,600 minutes/year). So if you thought all your players were equally talented you would simply pay them $50,000,000 / 24,600 minutes or $2,033/minute they played. What that would mean is that a player who plays 20 minutes/night for all 82 games would be worth:

**20 minutes/game x 82 games x $2,033/minute = $3,333,333/year**

Life is never quite this simple of course because players don’t all perform equally with their ice time, teams need to pay goaltenders, players get injured, etc. The point to keep in mind though is that fundamentally having two constraints allows you to perform this kind of analysis. We obviously need a way to account for these complications but if you can do that then you can actually value a player without resorting to cherry-picked comps or baseless opinions.

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**Dealing with Complications**

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**The Easy Ones**

The easiest complications to deal with are things like ice time. The NHL provides a lot of data on their games so it’s relatively easy to find out that over the last 3 seasons:

• NHL Forwards played 153.9 minutes/game at Even Strength and 24.6 minutes/game on the Power Play and Penalty Kill.

• NHL Defensemen played 100.6 minutes/game at Even Strength and 17.1 minutes/game on the Power Play and Penalty Kill.

What you can also find out is that 25% of all goals in the NHL are scored while one team is short-handed. Not only is that an interesting fact but because there are more goals scored per minute during these minutes we can choose to allocate more of our salary dollars to these minutes if we choose (and I do). To me it seems reasonable that if 25% of the goals are scored during this period of time we should allocated 25% of the dollars to it as well (of course this assumes that teams want to win and to win they need to score more goals than the other team but I don’t think this is a stretch…).

To strip out goaltenders from our analysis (because valuing them is a different project altogether) we can either determine how much of the average NHL team’s salary cap is spent on goaltenders – turns out it’s roughly 10% every year or assume because 2 out of 23 roster spots are taken by goaltenders they should receive 2 / 23 = 8.7% of the salary cap (either way it’s in that ball park).

Then you then need to decide how to allocate dollars between forwards and defencemen. Given that teams typically carry 13 or 14 forwards, 7 or 8 defencemen and 2 goaltenders on their roster (teams are allowed 23 players) I like to allocate 13.5 / 21 = 64.3% of the remaining salary cap to forwards (basically assuming a team carries 13 forwards half the time and 8 defencemen the other half).

Hopefully, you’re with me this far because with just these assumptions we can start calculating how much each minute of ice time is worth to an NHL franchise. For example, for every power play minute an NHL defencemen played last season I would assign a value of:

If you do this for the rest of the minutes you come up with something like this:

• $208,810/min for Forwards at Even Strength

• $435,445/min for Forwards on the Power Play or Penalty Kill

• $177,468/min for Defencemen at Even Strength

• $348,017/min for Defencemen on the Power Play or Penalty Kill

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**The Tricky Part**

The most challenging part of deciding a player’s value is deciding how his performance compares with his peers. Today with the growth of the advanced stats movement there are even more ways of looking at performance and there isn’t much agreement anymore on the right approach. Even the once loved +/- stat is now widely criticized. Personally, I still like points as a measure of performance although many will argue that Corsi (think of it as shots +/-) is a better predictor of success.

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**Assuming We Can Agree…**

Now I don’t want to bog this piece down arguing about the proper metrics to use in evaluating players…so assuming we could agree on a metric what would we do with it? For the sake of argument let’s say we agreed that points are the best way to value a player’s performance our next step would be to convert the raw numbers into rates (i.e. Points/Minute or Points/60 Minutes).

The reason we need to turn these values into rates is because ice time is our main constraint (i.e. we already turned the salary cap into $/min) and it’s also more appropriate as a measure. The reason I say it’s more appropriate can be summed up in a thought experiment about a player who played the entire game without ever taking a shift off:

*If we assume that this theoretical player is a Winger of average skill he would normally produce ~1.6 points/60 minutes at even strength, 4.4 points/60 minutes on the Power Play and 0.3 points/60 minutes while on the Penalty Kill. So if this average Winger played every minute of the game and we assume his team played an average of 47 minutes/game at even strength and 7 minutes/game on the Power Play and 7 minutes/game on the Penalty Kill this player would produce approximately 148 points!*

*With those kinds of point totals you would think that this player (who we already defined as absolutely average) is the next coming of Gretzky! I mean the last player to break 140 points was Mario Lemieux and that was 20 years ago! Furthermore, if we compare this player to the average NHL Winger who produces something closer to 50 points/season we would believe that this player is 3x better than average and so we should pay this player something like this:*

Clearly something is wrong in this example because there is no way we should ever play one player $47.7 million per season (in fact you’re not even allowed to) and what is wrong is that we didn’t convert this player’s performance into rates. Had we done that we would have of course seen that he is the epitome of average and not multiplied his value by 3 which would mean that he’s worth $15.9 million/season. If this still feels high think of it as one player doing 4 jobs (most teams play 4 Wingers of each side/game) and doing them all in a perfectly average way. Another way of thinking about it is that instead of paying this Winger $15.9 million you could divide the minutes evenly between 4 (Left or Right) Wingers and if they also performed in an average way you would get exactly the same number of points and they would be worth ~$4.0 million each.

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**What If the Player Isn’t Average?**

No two players actually have the same performance and some are far better (or worse) than average so if we are going to be able to value NHL players our rate metrics had better work better than raw numbers did in valuing players…to see if rates work any better let’s examine a player most can agree is better than average – Sidney Crosby.

So what we can see from this table is that Sidney Crosby performed at levels consistently above his peers. The metrics I prefer to use are Points/60 minutes at even strength and on the power play and Goals Scored Against/60 minutes on the penalty kill (a higher number is obviously bad in this case…). So using those metrics the table shows Crosby’s relative success.

Looking closer at the ‘Multiplier’ column shows that Crosby is about twice as good as the average NHL center at producing points at even strength and is almost 50% better on the power play. He also doesn’t kill a ton of penalties but when he does he’s about 30% more effective than the average center.

Now that we know how Crosby compares to his peers let’s figure out what that level of performance would be worth this year with a $73.0 million salary cap. The table below shows the calculations.

So what this table is showing is that if Crosby performed at the same level as he did over the last 3 years his team should be willing to allocate ~$9.3 million to him this season. Fortunately, for the Penguins, however, Sidney is only slated to eat up $8.7 million in cap space next year making his contract a slight bargain.

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**Now What**

After reading this I hope you agree with me in that there is only so much ice time and only so many dollars so we should be able to value an NHL player’s contributions to their team. The two remaining challenges in valuing players are determining what performance really is (discussed at length above) and forecasting future performance.

We haven’t spent much time talking about future performance in this piece but using this approach it should be clear that to determine future value we would need to know both the future performance and the future salary cap. Both of these things are inherently unknown and some observers might suggest they are too unknown to even try but ultimately that is the only way to really evaluate what a player will be worth in the future (so we’ll need to do this if we want to sign players or criticize player signings!). I will also point out that this is very similar to how a Research Analyst values publicly traded companies (I used to work in this area).

In the case of publicly traded companies a Research Analyst will create a financial model based on the company’s unique situation and will then have to make a number of assumptions about what will happen in the future (I used to value Oil & Gas companies and therefore we made assumptions about the price of oil and natural gas for example). To get a sense of how many assumptions go into the valuation of publicly traded companies check out this introduction to Discounted Cash Flow valuation. Suffice it to say that there are a lot more assumptions in coming up with a value for Exxon Mobil than there would be in valuing NHL players…

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**Final Thoughts**

There is a fundamental way to value NHL players based on their performance and ice time. There are some challenges in determining what performance teams should be paying for and to do a proper job we would also need to forecast future performance and changes in the cap. That said, I don’t believe these challenges are insurmountable and in future posts I will make some assumptions on these items and publish the resulting player valuations.