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# How much does a standings point cost in the NHL?

Estimating the amount of money NHL teams need to pay for each point of improvement in the standings.

It's been a whirlwind summer for the hockey analytics community so let me start by congratulating all the recent hires around the league. It's unfortunate for all of us that a lot of talent has been swept away, their ideas no longer available for public consumption, but what we're left with is no doubt satisfying. A tremendous amount of work was put into the past five to ten years worth of statistical analysis in the sport and we're now seeing the real effects of that work. People are paying money for that insight and, for those that do, the price right now is in the thousands while the gains are in the millions.

I could have entered the fray, but declined. It was a mix of a lot of things. Mostly, I'm very happy with my career and despite the amazing adventure it would have been, I choose to stay with you, writing for free for Fear The Fin, in the comfort of my home. But if I had, what would I be doing now? What are Sunny Mehta, Eric Tulsky, Tyler Dellow, Brian Macdonald and Kyle Dubas, among others, all doing now?

The very first task, and I have no doubt about this, is to compute the cost of an NHL standings point. There are a few ways to skin that cat but, ultimately, it must be done. That's the whole bag. Accumulate as many points as possible, while spending efficiently. Any player evaluation system must rest at some currency, and no doubt the final currency is dollars per point.

The traditional sabermetric method is through the use of a theoretical "replacement level" team. No such team has or ever will exist. But we construct this theoretical team so that we have a baseline value for our salary, and a baseline value for our point system. Basically, we're asking the question, if you took a team full of players that are paid the minimum NHL salary, how many points would they accrue? It turns out there is no right answer. We obtain an answer through statistical modeling, but really we're just drawing an arbitrary line in the sand. Which, historically for the NHL, has been 52 points.

 Season Total Spending Replacement Level Salary League Average Salary Above Replacement Level Points Above Replacement level \$/Point Above Replacement level 2013-14 \$1,866.01 \$12.65 \$49.55 40 \$1.24 2011-12 \$1,782.86 \$12.08 \$47.35 40 \$1.18 2010-11 \$1,699.55 \$11.50 \$44.58 40 \$1.11 2009-10 \$1,647.79 \$11.50 \$42.85 40 \$1.07 2008-09 \$1,615.07 \$10.93 \$41.76 40 \$1.04 2007-08 \$1,404.75 \$10.93 \$34.75 40 \$0.87

Dollars are in millions. If the table above looks familiar it's because I basically stole it from Gabe. I adjusted a few things like corrected actual minimum salary on a yearly basis, and converted everything to points (because wins is a nebulous concept in the NHL).

Before we get into the dollars and sense (ha!), we should first talk about replacement level value. If you're a fan of The Hitchhiker's Guide, and all you want to know is the number 52, feel free to skip to the ***.

Why do we need to know how well a bunch of scrubs play? It's because we want to know the value of minimum salary in the NHL. It's our talent floor. Its the theoretical value that doesn't cost a team anything to acquire. Freely available talent at the NHL level is better than you or me. It's what the minimum salary buys you, which for most teams is somewhere between a bottom-line player and a career AHLer. In our example above, if we fielded a completely replacement-level team and a player on that team was injured, we would be forced to replace him with a freely available (and thus minimum salary) player. That player would theoretically completely replace his cost and his value, thus not costing the team any more salary, nor providing any more (or less) talent.

The number 52 is the amount of points a team of replacement-level players would earn at the season's end. It's derived from Tom Awad's GVT system, which in very basic terms attempts to quantify a set of players' value relative to a "threshold." I won't go into the details which you can find here. Also, I ran some of the numbers myself to make sure it still fit. Replacement level players are good for somewhere between a 38 and 42% Goals For percentage clip on average. Over the course of a season that works out to about 52 points if we assume Alan Ryder's win probabilities were correct. It's nice when things like that align.

***

The table above is the layout for the calculation of the cost of a point in the NHL by year. We start by taking the whole amount spent by the league (Column 2) and divide that by 30 to get the league average salary. Next we calculate how much it would cost a front office to field a completely replacement-level team: 23 players times the league minimum (Column 3). If you subtract that value (replacement team cost) from the average salary spent by the league, you get the average cost above replacement by the league (Column 4). The number 40 (Column 5)  is derived from the difference between the amount of points accrued by a completely league average team (92), and the replacement level team (92-52 = 40). This allows us to calculate our final cost of a point, which is the points above replacement divided by the salary above replacement (Column 4 / Column 5 = Column 6).

The cost of a point has climbed as salaries have increased, mirroring the increase in total revenue of the NHL. It's important to know that using this method includes every type of contract. We know that entry-level, RFA and UFA contracts are all different, with the competition (increase in demand) for UFAs driving up the cost of a point derived from a UFA contract.  I'll save that calculation for a different day, likely when we have a better system of evaluating the contribution of a player to his team's accrual of standings points. Suffice to say, UFAs are more expensive than the \$/point listed in the table.

This does give us a taste of value though. For example, if we take P.K. Subban's recent \$72 million contract we can say that the Habs believe he's worth 58 points above replacement level over 8 years, or 7.25 points above replacement level per year. As it turns out, that may not be a crazy estimate (the reality is likely less than 58 points above replacement given that it's a UFA contract, and so the \$/point is more likely in the \$1.25-\$1.35M range).