Pulling the Goalie (Some Math Would Have Sent the Preds to the Playoffs Last Year)

April 16, 2024

To the disappointment of our clients who are avid Preds fans, neither Rory nor I follow hockey very closely. I know shockingly little about the sport – I still haven’t quite figured out what “icing” is. But I do know the bare minimum; that is, I know every NHL team shares the same goal – winning the Stanley Cup.

For the uninitiated (*ahem myself* - I had to look this up), qualifying for the Stanley Cup playoffs is based on points acquired throughout the season. The point scoring system is simple – two points for a win, one point for a loss in overtime or shootout, zero points for a loss in regulation. Understanding the point system has critical implications for strategy, as we’ll soon see.

The most exciting part of a hockey game is typically in the waning minutes of the third period or overtime (for all the football fans, 3rd period = 4th quarter) when one team is down a goal and they pull the goalie. That is, they send their goalie to the bench and replace him with another attacker. This gives the trailing team six attackers against the leading team’s five defenders + goalie. This makes it easier for the trailing team to score a goal (more attackers than defenders) but also easier for the leading team to score if they manage to clear the puck to the other side of the ice (the net is empty). It is the ultimate high risk move in sports. Though high risk, it is sensible. The trailing team has little time left to score a goal to force overtime/tie and thus earn a point in the standings.

As it is a desperation ploy, you typically see teams pull the goalie with very little time left in the game. Cliff Asness, a hedge fund manager possessing the rare combination of mathematical brilliance and considerable writing prowess, conducted a fascinating study in 2018 to determine the optimal time during a hockey game to pull the goalie. The results are surprising. If you’d like to see the math, you can find his paper here. To summarize, when both teams have their goalies safely ensconcing the net, either team has a 0.65% chance of scoring during any given 10-second interval. When one team pulls the goalie, their chances of scoring increase to 1.97% per 10-second interval, while the team who retains their goalie’s odds of scoring increase to 4.30%.

Pulling the goalie has a negative expected value, as it increases the odds of the leading team scoring more than it does the odds of the trailing team with the goalie on the bench (the team retaining their goalie can get a shot on an empty net!). But margin of loss is meaningless in hockey, what matters is standings points. At a certain point in the game, the trailing team optimizes its ability to increase standing points by employing any strategy that increases their odds of scoring a goal regardless of the impact on their opponent’s odds of scoring a goal. Losing by two goals rather than one has the same result on the quest to the Stanley Cup – zero standings points. But forcing overtime or a shootout will result in one or two points in the standings. Most striking is how early in the game a standings-points maximizing team ought to pull the goalie. Asness and his team found a team trailing by one goal should pull the goalie with 6:10 remaining in the third period. When trailing by two goals, the optimal time to pull the goal occurs at the 13:00 mark (not even halfway through the third period)!

The compound effect of optimized goalie-pulling over a season is striking. A team practicing optimal goalie-pulling gains an average of 0.05 standings points per game, which equates to 4.18 points over a full 82 game season.[i] 4.18 points may sound trivial, but last season the 8th best team in the Eastern conference (the top eight teams in each conference make the playoffs), the Florida Panthers, scored 92 points. The Pittsburgh Penguins and Buffalo Sabres came in 9th and 10th with 91 points. Practicing optimal goalie-pulling would have earned the Penguins or the Sabres a chance at the Stanley Cup. The same is true of the Calgary Flames, the 9th best team in the Western conference and the 10th place Nashville Predators, who’s respective 93 and 92 points were less than 4.18 points behind the Stanley Cup playoff-qualifying Winnipeg Jets’ 95. A little algebra could have sent the Preds to the playoffs last year.  

But you never see teams pull the goalie with six minutes to play. You certainly never see the goalie on the bench with thirteen minutes remaining. Trailing teams typically wait until about 1:30 remaining in the final period. Pulling the goalie earlier feels reckless, and it risks the other team running up the score. Coaches lose sight of the purpose of the game – it is to accumulate standings points, not to minimize the margin of defeat. Losing a game by one goal in regulation has the same outcome on the season as losing by five goals. But losing by five goals makes the coach look worse than losing by one, and coaches are more motivated by optics than most care to admit. They end up focused on the risk of increasing the margin of defeat rather than the risk of failing to earn a point in the standings. Their decision-making framework focuses on the wrong risk.

The same concept holds true when constructing portfolios. It is paramount to think of the right risks when making allocation decisions. Investors often make the mistake of fixating on the increased volatility of a change to their portfolio rather than evaluating whether the change will increase the portfolio’s odds of achieving its stated purpose. Increasing a soon-to-be-retired couples’ equity allocation from 60% to 70% will increase the volatility of their portfolio, but (in some cases) it may also increase the odds of the portfolio fulfilling its purpose - funding a 30-year two-person retirement in an inflationary environment. In this case, worrying about the increased volatility is akin to worrying about the opposing team running up the score. The risk that matters isn’t temporary volatility, it’s running out of money. Portfolio decisions should be guided by a focus on the right risks. Yet time and again, we see investors and their advisors building portfolios to address the wrong risk.

“My portfolio lagged the S&P 500” has been a nearly ubiquitous sentiment among the investing public since around 2010, as large cap U.S. equities (the S&P 500) have been the dominant asset class over the last ~15 years. This complaint’s implied corollary is “the goal of my portfolio is to beat the S&P 500 this year.” I will leave our opinion that beating an index over an arbitrary period of time is not a prudent goal for another discussion. If that is indeed one’s goal, its achievement will be realized through concentration, not diversification (yet most investors echoing this complaint are the owners of diversified, sometimes beautifully so, portfolios).  If you put a gun to my head and demand I beat the S&P 500 this year, I would construct a portfolio that looks quite different from the portfolios we presently manage! It would look less like a diversified portfolio and more like a concentrated bet on a handful of assets or sectors. It might have some Bitcoin or call options on Nvidia or semiconductor ETFs or something like that. Lots of risk! A much higher possibility of catastrophic loss than the diversified portfolios we manage. But if you are demanding I beat the S&P 500 while holding a gun to my head, I am not really worried about catastrophic loss. If the S&P 500 does 10%, the result of both a +9% return or a -90% return is a bullet to the brain.

I mentioned previously I suspect one reason teams eschew optimal goalie-pulling is the coach’s fear of poor optics. The strategy increases the probability of the opposing team running up the score, the pain of which is compounded by watching the puck sail effortlessly into an empty net. This phenomenon is well documented in sports and displayed by a reluctance among basketball coaches to embrace the three-point shot, reticence among football coaches to go for it on fourth down, and chronic undervaluation of walks and outs among baseball coaches/GMs (Billy Beane of Moneyball fame discovered this). Every coach’s goal is winning a championship, but his incentives are to keep the fanbase happy week to week. Keynes was ahead of his time when he said it is better to fail conventionally than to succeed unconventionally.

Many wealth advisors experience similar misalignment of goals and incentives as hockey and football coaches. The client family’s goal is the long-term stewardship of their wealth to maximize the probability of successfully fulfilling their hopes and dreams. The advisor’s incentives are to keep the family happy amongst daily market fluctuations, a bear market roughly every four years, and an unrelenting news cycle. The advisor is paid for as long as the family continues working with him, so his incentives prioritize short-term appeasement of emotions over long-term fulfillment of goals. This, I suspect, is why we meet prospective clients with portfolios with new tech stock positions added after a massive runup in tech stock prices (Ah your advisor bought Nvidia recently, what do you know…), or who stuffed a massive portion of their net worth into short-term debt instruments yielding 5% in 2023 just before the equity markets did +25%, or tell us stories like – and I’m not kidding – “our advisor got us out of the market in March of 2020 and got us back in the following year.” *

These decisions fall somewhere on the continuum between suboptimal and wealth incinerating. Frankly, they drive Rory and I nuts.

We prefer to succeed unconventionally than to fail conventionally.

If the mathematics instruct us to do so we’re pulling the goalie, optics be damned. 

Sean Cawley, CFP®

 *That is, out after a 30% decline and back in after a 70+% advancement. This lands on the wealth incinerating side of the aforementioned continuum.  


Neither asset allocation nor diversification guarantee against investment loss. All investments and investment strategies involve risk, including loss of principal.

Content here is for illustrative and educational purposes only. It is not legal, tax, or individualized financial advice; nor is it a recommendation to buy, sell, or hold any specific security, or engage in any specific trading strategy. Results will vary. Past performance is no indication of future results or success. Market conditions change continuously.

This commentary reflects the personal opinions, viewpoints, and analyses of Resolute Wealth Management. It does not necessarily represent those of RFG Advisory, clients, or employees. This commentary should be regarded as a description of advisory services provided by Resolute Wealth Management or RFG Advisory, or performance returns of any client. The views reflected in the commentary are subject to change at any time without notice.

[i] Clifford S. Asness & Aaron Brown, Pulling the Goalie: Hockey and Investment Implications. March 1, 2018. Page 5.