# The Loser Point & Skewed Incentives in the NHL

Humans are risk averse. We see it in every aspect of life. We hate losing. We hate failure. When failure happens we attach added meaning to it, we invent extremely detailed and complicated explanations for it... often just as a coping mechanism for how badly we feel when we encounter it.

NHL coaches are human. They too hate failure. They too are risk averse. They feel the sting of losing more than the average fan because their livelihood - their entire career - is being assessed through every lost point, every lost opportunity for a win.

Unfortunately for NHL coaches, and hockey fans everywhere, the NHL point system is structured such that our inherent risk aversion - manifested in the fear of losing available points - drives uninteresting, defensive, boring hockey to the top of the heap.

There has been much discussion of the flaws of the loser-point in professional hockey. The angst that goes along with rewarding teams that failed to win - in some effort to console them for making it to the extra frames of overtime or the shootout - is vast. In one of the most effective illustrations of an NHL coach’s mindset, Ken Hitchcock had the following to say in an interview with Kevin Paul DuPont of the Boston Globe a few years ago:

"I like when you are playing all out, all the way, but I’ve got to tell you as a coach, if there’s five minutes left in the game, and it’s tied, I’m not necessarily thinking about winning it. I want at least a point. A lot of coaches think like that. We have to think like that. Because to get zero points in a tie game with 10 minutes left is devastating.”

"If you can put more value in it, I am all for it. But to me, right now when there’s 10 minutes left in a hockey game I want that one point, at least. I’ve got to have it. That’s how you get in the playoffs."

- Ken Hitchcock, Jan 14 2017

In the 1999-2000 season the NHL decided that both teams making overtime deserved a point - including the loser. Coming out of the 2004-05 lockout, the NHL implemented the shootout in an effort to entice new fans with a skills competition and remove the negative perception that went along with tied games. The winning team would be awarded a full 2 points, while the loser would still obtain 1 point for getting to extra time.

The addition of the shootout following the 2004-05 lockout altered the math slightly - and helped the league go along with the sentiment that ties are bad for business. Unfortunately, guaranteeing that at least ONE of the two teams making the extra frame was picking up yet another point pushed things even further in the negative direction that is strangling the sport.

Just how far we’ve gone in that direction is the part that I’m not sure the league - or most of its fans - have explored in particular depth. Since the addition of the shootout, the proportion of NHL games that goes to OT has seen an approximately 50% increase as shown in the above graph.

Back in 2015, the Journal of Sports Economics published an article by Michael J. Lopez on the Inefficiency of the NHL Point System. Lopez is an associate professor of statistics at Skidmore College with a Ph.D. from Brown University who has also published work on the impartiality of NHL referees. In the article on the inefficiency of the point system, Lopez argues that incentives are increased for teams to shoot for Overtime when playing non-conference opponent and that late season games are far more likely to head for extra time than those near the start of the year. His analysis shows that there is now approximately a 5% observed increase in the probability of non-conference games going to overtime in comparison to the prior point system. Additionally he showed that late season games in April now head to OT almost **TWICE** as often as they did under the old point system.

Tyler Dellow (Now of the NJ Devils but at the time of the Athletic) delved into how teams perform late in tied games, and quantified what most observers have likely gathered just by watching their favourite team creep towards overtime with regularity late in the 3rd period. Essentially NHL teams play far more conservatively late in games, with shot attempts, goals and shooting percentages all declining somewhere between 8% to 25%.

Putting numbers to the final results of the incentives of the NHL point system, and identifying the cause itself doesn’t necessarily highlight just how strong they are for outside observers. Despite the fact we know that teams play in such a conservative fashion (yes EVEN the good ones), and despite the fact NHL coaches publicly share their fear of sacrificing points late in tied games it remains challenging to wrap one’s head around.

Where this seems most obvious is the angst and anguish percolating in Leaf land these days (perpetually?) about the team trying to improve defensively at the expense of their offense.

Mike Babcock had these wonderful thoroughbreds and he wouldn’t let them run. He kept trying to rein things in, and it was just this massive mistake. He shouldn’t have been so worried about defense because, with all of their high flying offense, the Leafs could just pound the opposition into submission with the gift of goals.

We’d all like to see unfettered offense. Unfortunately - that isn’t what the incentive system pushes - and it isn’t the ideal way to increase a team’s point share in the standings. The Leafs are now over a full calendar year into the tenure of new bench boss Sheldon Keefe, and the preaching around team defense has reared its ugly head again.

In his book Soccermatics: Mathematical Adventures in the Beautiful Game, David Sumpter explores the incentives around point reward systems in professional football. Sumpter is a professor of applied mathematics at Uppsala University in Sweden who specializes in modeling social dynamics and complex biological systems. His analysis explored the effects of playing attacking or defending soccer on a team’s point expectation, and was focused on the shift in the Premiership from a 2-1-0 point system to the 3-1-0 system that was implemented way back in 1981.

Essentially, Sumpter’s analysis shows that teams should be playing attacking soccer up until their opponent is twice as likely as they are to win in a wide open attacking game. This is largely a result of defending making draws more likely than wins or losses. Because a win is three times as valuable as a draw, there is very little reason to make such a tactical shift.

We can walk through a similar undertaking to analyze the current NHL point system if we make a few assumptions:

First off, lets assume that once teams get to overtime they are roughly equally likely to win or lose. While it may be comfortable to assume that stronger teams are more likely to win in extra time, most analyses indicate that the short time frames and chaotic nature of 3-on-3 OT, along with the essentially random distribution of when goals will be scored, make it amazingly challenging to predict which team will score first. In practice a team may not win 50% of their over time or shootout games, but we can’t do much better prediction wise.

Secondly, for the ease of analysis, we can assume the effect of defending impacts evenly upon both teams. That is to say, the defending team reduces their opponents probability of winning by the same factor as their own. If their chances of winning are cut in half, so is their opponent’s. This assumption is less reliable, but it simplifies the math considerably for this mental exercise.

Consider an imaginary team that has a 60% chance of winning in regulation, a 30% chance of losing in regulation, and a 10% chance of going to over time assuming both they and their opponent play all out offensively with no apparent regard to defending (like in a Leafs-Oilers game!). Logically this team is twice as good as it’s opponent.

In a full out attacking situation for both teams, the point expectation for this one game would thus be given by:

E = 0.6*(2 pts RegW)+0.05*(2 pts OT/SOW)+0.05*(1 pt OT/SOL)

E = 1.35 pts

A team with this expected point total in every game should theoretically obtain around 1.35*82 = 110 points in a season.

Now let’s pretend the 60% team we are discussing is abysmal defensively, doing very little to defuse their opponent’s attack despite their best efforts. They can reduce their opponent’s chances for a regulation win only marginally, while simultaneously damaging their own efforts on the attacking end thus lowering their own chances of winning in regulation.

Let us say they are 10% effective on D (i.e. they reduce their opponent’s chances of winning in regulation to 27% from 30% while simultaneously reducing their chances from 60% to 54%). We now obtain the following point expectation when the team tries to defend:

E = 0.54*(2 pts RegW) + 0.095*(2 pts OT/SOW) + 0.095*(1 pt OT/SOL)

E = 1.365 pts

When this team defends (even ineffectively), they theoretically improve from a 110 pt team to a 112 point team.

The expected point total increases. Despite the only marginal ability to deflect their opponents offense - the reality is that increasing the likelihood of Over Time is beneficial. This is true for a team that is TWO TIMES better than their opponent in an all out offensive game, even if they are WELL below average defensively.

Where this becomes harder to process is if you think - BUT my team isn’t surrendering 10% of their offense to defend marginally. The reality is they see the effectiveness of their attack decline by 50%, just to reduce their opponents offense by only 10%... That WOULD be a considerable problem… or so you might think.

Except even THAT level of disparity in defensive and offensive impacts doesn’t make the point expectation worse. It actually rises even further. If your team’s 60% probability of winning in regulation drops all the way down to 30% while their probability of their opponent winning in regulation drops from 30% to 27%, we obtain the following point expectation:

E = 0.3*(2 pts RegW) + 0.285*(2 pts OT/SOW) + 0.285*(1 pt OT/SOL)

E = 1.455 pts

It rose their point expectation even further. They have now risen from a theoretical 110 point team to 119 points. Virtually anything that increases the chances of Over Time actually raises the point expectation. Consider the absurdity of an NHL team that makes NO effort to attack. A team that purely seeks out 0-0 draws that head into Over Time. Let’s say their opponents still squeak through the occasional goal in 10% of their games, thus giving us the following:

E = 0.45*(2 pts OT/SOW) + 0.45*(1 pt OT/SOL)

E = 1.35 pts

That number may look familiar. It is the exact same point expectation as the team we began with - the one that has a 60% chance of winning in regulation and 30% chance of losing in regulation when they and their opponent play full out offensive hockey. You get the same expected point outcome with a team that has a 0% chance of winning in regulation and a 10% chance of losing in regulation... the ultimate "defensive" team.

In order to visualize these changes quickly, I created the table below. Through examining it we can see what combination of regulation win and loss probabilities produce similar expected point outcomes for individual games.

What becomes obvious is that defense is three times as important as offense during the NHL regular season. Decreasing a team’s probability of winning in regulation matters significantly less than decreasing their probability of losing in regulation. Any decline in the probability of losing in regulation requires a commensurate three fold decline in the probability of winning to get to the point of hurting a team’s point expectations. This highlights why NHL coaches place such a massive emphasis on defensive performance.

An interesting point for consideration arises with the NHL playoffs though. There is no point reward system in the post season and all games are played until a winner is determined. In such a system, every increase to the probability of winning in regulation is directly equivalent to a reduction in the probability of losing.

Offense suddenly reverts to being equally important to defense, and ineffective defending by a good offensive team is no longer worth the effort if it is costing them goals. If NHL teams with high powered offenses and marginal defending are thinking the key to winning in the playoffs is defensive hockey, they are likely mistaken. It probably makes more sense for teams in this mold to try and win 7–4 than it does to grind out 2-1 wins.

Last year Tampa Bay ranked 4th in the NHL post season with 3.08 goals per game, but largely operated as a one line team that tried to tamp down their opponents en route to their Cup victory. They also only registered 10 of their 16 playoff victories in regulation (62.5%).

Pittsburgh won their two most recent Stanley Cups despite icing a comparably marginal defensive group by NHL standards. Their goal scoring skill outpaced the ability of other teams to restrict their offense, and nobody was handing out points for OT or moral victories. They averaged 3.06 goals for per game across their 2015–16 and 2016–17 Cup runs, and won 26 games in regulation out of 32 (81.25%).

The Penguins only played 4 games that went to OT in the playoffs in 2016–17, and they won only 2 of them. That is the lowest number of OT wins for a Stanley Cup Champion since the 2007-08 Detroit Red Wings side won, playing only 2 OT games en route. Interesting side note? That team was coached by Mike Babcock.