Avid watchers of prestige television know the penultimate episode is often the most exciting to watch.

A finale provides the denouement; wrapping up loose ends and closing out the story arc of the season or series. It’s the episode before the finale which provides the cliffhanger or plot twist, usually filled with the most suspense and action that can fit into 60 minutes.

The second to last end of a close curling game often provides greater tension and drama than the final frame. One down with last rock (“hammer”) in the last end is a straightforward path—do everything you can to score two points. No shot for two on your last throw? Try to take one and hope to steal in the extra end.

In the same situation just one end earlier, tactical choices can be complicated and taking the wrong turn could flip a team from heavy favourite to long-shot underdog.

Rachel Homan’s team was in this unenviable position against Silvana Tirinzoni’s Swiss side during the championship final of the Canadian Open. Down 3-2 in the seventh end, Team Homan talked through their choices on skip’s first stone.

They could hit the Tirinzoni stone mostly buried in the back eight-foot rings and roll away from the centre line. They could freeze to the stone, but it would be below the button and Tirinzoni could draw in and sit shot rock, making it probable they would be forced to a single point.

Ultimately, they decide to draw top four foot, attempting to score a deuce.

WAIT! Coach Don Bartlett calls a timeout and declares he wants hammer in the final end.

The squad went with his suggestion and switched their decision to a hack-weight hit. They removed the Tirinzoni stone but rolled out of the rings, leaving Swiss fourth thrower Alina Pätz the same shot they had originally planned.

Her outturn draw buried perfectly, sitting on the button. Rachel chose the runback in an attempt to blank the end, and missed.

Homan is now two down with hammer heading to the eighth and final end.

Where to begin?

Here’s the video:

Grand Slam of Curling on Sportsnet • Jan 21 2024

If Rachel hits and rolls to the open, it’s not certain Tirinzoni will choose to hit. The Homan squad know this and discuss the likelihood their opponent will instead draw around the centre guard. Sportsnet analysts Mike Harris and Joan McCusker mention it as well, referring to a similar situation in the fourth end of the men’s final.

One of my earliest Curl With Math blogposts examined this common scenario of being one up without hammer in the next to last end.

Essentially, the math indicates it is preferable for the non-hammer team to be aggressive, attempting a force or steal at the risk of giving up a deuce.

When watching this situation in recent years, extreme curl and lively rocks have usually forced the non-hammer team to hit the open stone rather than risk the draw. Most often the team with hammer can easily remove a perfectly buried stone and collect their deuce. The centre guard must be in a perfect position, and preferably a friendly colour. In the case for Tirinzoni (and Bruce Mouat in the men’s final) the centre line guard was ideal and the ice conditions, swingy but not excessive, allowed for a well-thrown draw to make things difficult for an opponent.

What should Team Homan do in this situation?

Beginning the end, scoring three or more is the preferred result, but that’s not a consideration now with three rocks remaining. Common thinking for the team one down in the penultimate end is “please just let me have an easy blank and let’s move on to the last end.” It’s not that teams want a blank, it’s simply the chance of being forced to a single point is too great and the reward for scoring two, and unlikelihood of three, is not substantial enough to encourage an aggressive strategy. Their opponent knows this, which is why they will counter with centre guards and attempt to force play to the middle, even at the risk of giving up two points.

Before Rachel’s first throw, statistics indicate the best result is to take two points and lead 4-3 heading to the eighth end without hammer. Consider some historic results …

For all women’s world ranking events from the last two years, five years and over a decade, win probability down one with hammer is about 39%. Looking at results over the past five years from games only between teams ranked in the top 25, it drops to 35%.

Looking at games between the top 10, it’s 36.6% … and between top five, 32%.

Now consider the five-year results of both skips. Homan has won 75% of the time when up one without and 59% when down one with hammer. Silvana is 68% and 56%, respectively. Both teams are—not surprisingly—really good and win more than they lose in either situation. The real puzzle to solve centres around what happens when these two specific teams play each other.

Digging into recent data between them, we find a very small sample size:

• 2022 Players’ Championship, with hammer and down one point, Homan scores a deuce to win 7-6.

• 2021 Players’ Championship, Homan is one up without hammer and wins 5-3.

• 2018 Olympics, Homan is up one without hammer and wins 10-8 (Team Tirinzoni in PyeongChang did not include Alina Pätz).

The debate over one up or one down will rage on for as long as this sport exists. Many will never agree but to me, with teams of equal calibre, being one up without hammer is better than one down. However, the scenario does not provide assurances to either side. It’s essentially an uneven coin flip.

The problem with considering “we want hammer in the last end” is that regardless of the decision on Rachel’s first stone, Alina still has a final shot to influence what happens. The analysis for Homan should emphasize “what do we think Tirinzoni will call and what do we want Pätz to throw?”

If the Canadians believe Tirinzoni will always hit an open Homan stone, they likely should play Coach Bartlett’s call, a hack-weight hit. Most often they will be left with a simple blank, and occasionally Pätz will make a perfect hit and roll and Homan will have a runback or board-weight blank attempt.

If Homan believes—as Mike, Joan and I suspect—that Tirinzoni will draw around the centre guard, her decision is less clear.

A fascinating tactical choice that was not considered: If you know Tirinzoni will draw and you want to blank, the preferred call might be to hit and roll out, which is what actually happened.

Homan likely makes the runback over 80% of the time and in the instances where Pätz is unable to perfectly bury the stone, it’s an easy blank.

If Rachel’s first shot sticks around in the rings and Alina draws behind centre, the option to blank won’t be available.

Despite this, Team Homan does not appear to be pleased with the outcome of skip’s first stone.

Let’s move from the numbers to analyze body language. Watching on television, Team Homan appeared out of sorts and not in a position to execute to their optimum ability. Throughout the process—and particularly following the timeout—the squad seems uncertain of their direction, less assured with what they are trying to accomplish, and the result is two missed shots and a steal of one for Tirinzoni.

Using analytics can identify the correct mathematical decision but there are always other variables, and the choice is not always clear. More important than making the “right” call, effective communication can help a team align on common objectives and perform at their best.

Following Team Hasselborg’s gold medal at PyeongChang 2018, second Agnes Knochenhauer commented on their use of analytics.

“Firstly, it always comes down to how well we perform out there on the ice,” she said. “But what we could see when we started to work with the numbers was that our own performance in combination with the statistics gave us confidence in certain scenarios and patience in others. We’re using the statistics to put the four of us on the same path, so that we all know how to take on each opponent. It gives us strength and courage as a team.”

Agnes Knochenhauer • Stephen Fisher-World Curling Federation

The appearance of uncertainty and lack of unified confidence in team strategy is what came across my TV screen at home. In hindsight, calling the timeout earlier, something they did consider, may have improved their focus on the task and helped with execution, regardless of which shot was called. To be clear, the analysis from my couch could be completely wrong. It’s entirely possible the Homan squad were comfortable and at ease with the situation as it unfolded.

Back to the math.

We considered the desired outcome; one up without hammer is a small preference over one down with hammer. Next to evaluate are the undesirable outcomes; being forced to a single point or surrender a steal. What are their chances of winning?

When tied without hammer and with one end to go, Homan wins 30% of the time, in line with numbers for all ranked games between the top 25 teams. However, Tirinzoni has an 88% winning percentage when tied with last stone, one of the best of any team on the World Curling Tour.

What about two up without hammer? Tirinzoni has won 92% of the time, well above the tour average of 84%.

The numbers indicate if Rachel cannot blank or take two points, she is choosing between two bad options. Considering these outcomes, I would lean towards being tied without hammer because of the sample size from all teams … but given Team Tirinzoni’s capabilities, it’s not an automatic decision and frankly, both outcomes stink.

Assuming Tirinzoni will ignore an open Homan stone and draw around the centre guard, if Homan is confident in the ice and her weight and can beat Pätz there, I prefer their original call to draw top four foot.

If Rachel is most or fully buried and shot stone, above the tee-line, Tirinzoni will be forced to a decision. She could have Alina attempt a runback attempt, pick out the Homan stone or follow the draw and hope to make Rachel’s final draw for two points as difficult as possible. A runback is unlikely to lead to a steal and more often a deuce or blank appears to be the result.

The risk for Homan is leaving the stone open enough that Pätz plays quiet hit weight and sits two, but in some instances this still might leave a possible double and roll out for the blank.

In the early days of the Curl With Math blog, this is the point where a graph, table and equation might show up to explain my analysis. No need to grab your abacus and you can keep the calculator in the drawer for now; I’ll summarize the results.

Given ice conditions, colour and location of the guard, Tirinzoni should, if Homan hits and sticks, ignore the open stone and draw behind the centre guard if Pätz can make the draw at least half of the time. It’s reasonable to assume that everyone, including Silvana and Rachel, expect her chances are higher. Based on that belief, Homan needs to make the come around draw as little as 40% of the time for it to be the correct call.

Ultimately, Team Homan pulled off the comeback from two down in the eighth end and stole the victory in the extra-end (!) against the four-time and reigning world champions.

Like most television episodes of your average sitcom, despite many hijinks and shenanigans over the first 20 minutes, everything worked out in the end.

That Curling Coach Timeout