Valuation Today
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... |
| https://www.youtube.com/watch?v=orhFVgzI_bw |
Prior to the Salary Cap
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.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.
Dealing with Complications
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.
To strip out goaltenders from our analysis (because valuing them is a different project altogether) we can simply determine how much of the average NHL team's salary cap is spent on goaltenders - turns out it's roughly 10% or you can consider that most teams use up 2 of their 23 roster spots on goaltenders (~8.7%). For our purposes we'll go with 8.7% because it's consistent with what we'll talk about below.
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 or 3 goaltenders on their roster (teams are allowed 23 players) I like to allocate 13.5 / 21 = 64% of the remaining salary cap to forwards (I use 21 because I already allocated 2 of the spots to goaltenders).
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 plays this season I would assign a value of:
If you do this for the rest of the minutes you come up with something like this:
- $204,233/min for Forwards at Even Strength
- $425,901/min for Forwards on the Power Play or Penalty Kill
- $173,578/min for Defencemen at Even Strength
- $340,389/min for Defencemen on the Power Play or Penalty Kill
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 in the advanced stats world will argue that Corsi (think of it as shots +/-) is a better predictor of success.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 Centerman of average skill he would normally produce ~1.8 points/60 minutes at even strength, 6.4 points/60 minutes on the Power Play and 0.6 points/60 minutes while on the Penalty Kill. So if this average Centerman 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 182 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 180 points was Mario Lemieux during his best ever season in 1988-89. Furthermore, if we compare this player to the average NHL Centerman who produces something closer to 60 points/season we would believe that this player is 3x better than average and so we should pay this player something like this:
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 - Alexander Ovechkin.
The data I have saved is a little old but from the 2011 - 12 season to the 2013 - 14 season (3 seasons) Ovechkin 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 to the right shows how Ovechkin compared to his peers.What this table shows is that Ovechkin is about 15% better than the average NHL winger at producing points at even strength but is almost twice as good as average on the power play (just watch this video to see why). There is almost no data for him on the penalty kill (because he almost never kills penalties) so we'll omit that comparison here.
So what this table is showing is that if Ovechkin performed at the same level as he did in 2011 through 2014 his team should be willing to allocate ~$5.7 million to him this season. This is obviously less than the ~$9.5 million his team actually allocates to him but that may ultimately come down to the metrics we chose. If we had chosen to compare Ovechkin against his peers based on Goals/60 minutes he would obviously have a more favourable number ($8.9 million). That's why the metrics we choose are important and may need more nuance than simply Points/60 minutes. At the end of the day though we can perform an analysis just like this no matter which metrics we choose.
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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