Throwing in on the first shot of the game might be cowardly, but later in the game, throwing in on your first shot is a matter of tactics. And looking at how teams handle this decision provides some insight into how modern curlers think about the game.
If the difference in score is two or more, most teams act the same. The leading team throws in and the trailing team puts up guards. But it’s when the margin is within one that we can see some interesting trends in the sport as a whole and also among teams.
Take the case of being up one without hammer. Based on shot statistics from recent seasons, here is how often teams throw a guard on their first shot depending on the ends remaining:
The sawtooth pattern is the signature of even-end theory. In the even ends (an odd number of ends left), teams without hammer are more willing to throw in on their first, making it more difficult for the opponent to earn a multiple score which would presumably increase the opponents chance of having hammer in the final end.
Whether this is rational was a topic here last year, and it remains an open question. But the shot data can help us in our search for answers. The development of true win probability allows us to understand what’s at stake in this decision. In elite curling if you are up one without hammer in the 7th end of an eight-end game, a blank lowers your win probability by 5.0% (4.5% for women). But a blank in the 6th end actually raises your win probability by 4.3% (2.3% for women).
So maybe if you are the non-hammer team, you are cool throwing in on your first, increasing the chance of a 6th-end blank, and in turn, increasing your chance of getting hammer in the final end.
Which is fine, but the thing is a steal is enormously valuable at this point, too. For the men, it increases your chance of winning by 30.0% and for the women it’s 25.9%. Just (mostly) forfeiting this possibility on your first shot simply because the end number is divisible by two seems…well, at least worth questioning.
Anyway, it’s not like everyone does this. About a third of the time, teams are throwing guards in these situations in the fourth or sixth end of an eight-end game. The issue of which strategy is right (and it’s not like there is going to be a singular right strategy, anyway) is complicated. For now, I’d just like to identify which teams are even-end adherents.
For that I will compare a team’s guard percentage in these spots (up one, without hammer) with 1, 3 or 5 ends left to their guard percentage with 6 or 4 ends left. With 2 ends left, almost everyone guards, so we need to ignore those cases. Unfortunately, there are only 24 teams that have at least ten cases in both odd and even ends, but let’s look at the extremes.
First, here are the five teams whose strategy depends the most on whether the end is an even number:
Even ends Odd ends Diff
Ulsrud 1/16 6.2% 23/25 92.0% 85.8%
Gushue 7/28 25.0 21/21 100.0 75.0
Cotter 3/17 17.6 13/15 86.7 69.1
Epping 6/18 33.3 11/11 100.0 66.7
Bottcher 0/28 0.0 13/20 65.0 65.0
Thomas Ulsrud is basically retired and Jim Cotter, while having been to like 40 Briers, is not really on the elite level. The most interesting thing on here is that Team Bottcher will not throw an opening guard in an even end when leading.
And if I include cases with seven ends remaining, they’re 0-for-37 in throwing guards in an even end and up one. Among elite teams, they are unique in their refusal to guard in these spots. Impress your friends the next time you see Bottcher play. If they’re leading in an even end without hammer, they’re going to start by throwing a draw and it’s going to be an in-turn.
Here are the five teams that care the least about even ends:
Even ends Odd ends Diff Carey 11/19 57.9% 7/14 50.0% -7.9% Einarson 11/18 61.1 7/12 58.3 -2.8 J Koe 4/11 36.4 4/10 40.0 3.4 Dupont 5/20 25.0 9/21 42.9 17.9 Jones 16/30 53.3 21/29 72.4 19.1
I didn’t mention that I have not separated the men from the women in my trove of shot data, but that’s a future project. Anyway, you see that four of the five teams here are women’s teams. And in fact, there is less of an even-end signature among elite women’s teams compared to elite men’s teams.
In the limited data we have, Chelsea Carey and Kerri Einarson actually have a negative split. They don’t care whether an end is divisible by two, divisible by three, a prime number, or a part of the Fibonacci sequence. They are usually going to guard but sometimes not, based on factors that are far beyond my infantile understanding of curling strategy.
But what about a team’s behavior when they have hammer? Well, that data is equally interesting, but we’ll stop here for now and dig into that next week.
Last Week in Curling: There was lots going on last week. In Switzerland, #7 Peter de Cruz and his team punched their ticket to the Olympics with a four-game sweep of #13 Yannick Schwaller. If there is such a thing, it was a close sweep, as Schwaller led in two of the four games going into the tenth end and another game went to an 11th. If the Olympics started today, Team Schwaller would be the eighth-best team not in the Olympics. There should be a separate Olympics for those teams! The IOC tells me I have used up my quota of the word Olympics.
Rachel Homan and Silvana Tirinzoni continue their game of hot potato for the top spot in the women’s ratings. Tirinzoni went 3-2 in Basel, losing to #36 Irene Schori and then in the semifinals to eventual champ Eve Muirhead and three randomly-selected Scottish players assigned to her team.
The Canadian trials direct event resulted in #6 Matt Dunstone and #11 Mike McEwen earning berths to the actual Olympic trials in December while #11 Casey Scheidegger, #13 Laura Walker, and #26 Kelsey Rocque made it through on the women’s side.
There was other stuff going on, too. Like Kevin Koe and Brendan Bottcher making their season debuts in Okotoks. Team Koe won the event by beating Bottcher in the semifinals and red hot #9 Ross Whyte in the finals. Koe and Bottcher swap spots in the ratings with Koe moving to #4 and Bottcher dropping to #5. This leaves #2 Brad Gushue as the lone top 20 men’s team yet to play.
Speaking yet again of Bottcher, we haven’t commented on the test rules changed to be used in the worlds this season, but we’ll probably get around to it when the worlds happen in April. In the meantime, I’m backing Brendan Bottcher’s refreshingly open-minded view on the matter for now.
Finally, Chelsea Carey’s new team has made its debut in the ratings at #37 after winning the Craven Sport Services Curling Classic in suburban Saskatoon. It wasn’t a very strong field and Carey hasn’t yet beaten a top 25 team this season, but her team is the highest ranked in Saskatchewan for now.
“They don’t care whether an end is divisible by two, divisible by three, a prime number, or a part of the Fibonacci sequence.” Not sure why I found this so funny, but I laughed.
Interesting how you brought up that throwing in means basically forfeiting the chance to steal. Especially looking at the teams that care least about even ends, I wonder if this might be a good metric for determining how offensive/defensive a team plays, and whether it aligns with their tendencies towards offense/defense in other scenarios.
Next week I’ll have the data for teams that guard when they have hammer (and the game is close) and there are some similarities among teams but some differences, too.
Also, “forfeiting” was a pretty strong word. Obviously you can draw and still steal if your opponent ignores your shot, but there’s certainly a signal there that you aren’t playing as hard for a steal if you throw in with your first.
Great work here, Ken! It would be interesting to see how these two strategies impact the outcome distributions for the end. Do multi-point ends decrease in likelihood with an increase in blank rates? Is there a difference in the probability of stealing (you say forfeiting this potential, but is that true? by how much)?
Definitely not forfeiting, but more like “willing to forfeit”. Obviously, if your opponent is playing hard for a deuce you’ll still get some steals. It will be interesting to see how the two distributions differ and it’s easy enough to check. I hope to write up something on that soon.