17: Even end theory


I do not know the history of desiring hammer in the even ends. Maybe it has been around for decades. Regardless, it seems to be conventional wisdom at this point that it’s really important to have hammer in the 6th end.

The reason I am writing about this is that I was watching Matt Dunstone and Kirk Muyres review their game in the 2019 Saskatachewan Tankard. This was an enlightening conversation and the topic of playing to get hammer in even ends came up. Matt basically admitted that he is a big believer in this approach. So much so that he thinks hammer in the second end is especially important. You can relive the conversation here.

Having thought about this for a few years, I have never been convinced as to why control in even ends should be so important.

It’s true that if you have hammer in an even end, you are guaranteed to have hammer at least as often as your opponent the rest of the game. But that’s true of having hammer in an odd end as well. The argument would be better if the hammer team always scored. Then having hammer in the even end would guarantee having hammer more often than your opponent. But how often does that situation unfold from the second end onward? Well, in the Slams since 2015, it’s happened in 8% of games. Alternating hammer from the fourth end onward has happened in 17% of games and alternating from the sixth end onward has happened 37% of the time.

But to continue my philosophical argument against the preference of having hammer in even ends, think of a two-end game. If you had the choice of hammer in the first end, you’d take it! Or at least you’d be crazy not to. If you get your deuce in the first end, you’re in great shape for the final end, even without hammer. If you blank, you’re in great shape. Even if you give up one, things are not bad for you.

I’m reluctant to disagree with Matt Dunstone. I mean, he sounds so confident. And Rachel Homan’s obsession for blanking the first end with hammer is at least partially rooted in a desire to own hammer in the second end. But this is the internet and it’s a place for disagreeing with experts. Now let’s move beyond my philosophical objections and into the numbers.

If the main benefit of having hammer in even ends is increasing your chance of hammer in the final end, then we should see that in the data. For starters, let’s answer the question: If you have hammer in end X, what are the chances you have the hammer in the 8th end? This, and all subsequent data used for this post, is from the Slams, both men’s and women’s, since 2015:

Hammer     %Hammer
in End...   in 8
   1        48.6
   2        50.0
   3        53.1
   4        51.2
   5        48.9
   6        55.1
   7        36.8

Well, lookie here, it turns out that the sixth end is the most likely end to set up hammer in the 8th. But…the advantage isn’t all that obvious with just a 55.1% chance of doing so. And the even-end theory really breaks down prior to that. The 2nd and 4th ends are right around the 50/50 mark for predicting hammer in the 8th. In fact, the 3rd end comes in second behind the 6th for predicting hammer in the 8th.

(A confounding issue here is that some games don’t make it to the 8th end. For the purpose of this analysis, I’ve only looked at games that either made it to 8th end or were conceded after the 7th, since we know who would have had hammer in the 8th in that case.)

Also interesting is that the team that has hammer in the first only gets hammer in the 8th 48.6% of the time. Of course, this is not going to convince anyone to chuck their draw shot challenge through the rings. Nor should it! Trying to set up hammer in the 8th is not something that really needs to be considered in the first end. Or in the 2nd, 3rd, or 4th. Maybe it matters in the second half of a close game.

How else might we find the hidden value of hammer in the even ends? Well, here’s a fun chart of winning percentage based on having hammer in each end.

       Win% w/ 
End     hammer
 1       59.8
 2       41.4
 3       44.6
 4       45.2
 5       44.0
 6       44.8
 7       42.7
 8       41.3

All this really tells us is that if team has hammer in any particular end (except the first), their opponent is the team that has scored most recently, and that team is more likely to be in the lead. Still, it’s a fact that if we know nothing else except that a team has the hammer in the 8th, they are probably not in a great position to win. This doesn’t really prove anything regarding the even-end theory, but I find it interesting that ending up with hammer in the final end is not in itself actually worth anything.

That focuses the issue a little better, though. It’s fair to say that teams don’t really want hammer in the 8th at all costs. In a game against an elite team, being tied with hammer in the 8th is a great position, and they feel the bridge to get there is to be tied with hammer in the 6th.

But if the justification for that approach is in the data, it’s hard to find. Teams tied with hammer in the 6th have won 62.0% of their matches in the Slams and teams tied with hammer in the 7th have won 62.9% of the time. Even if you want to say those numbers are effectively identical (which they are) you don’t hear any famous curlers saying they just want to be tied in the 7th with hammer.

Let’s redo the first table with more specific criteria. If you are tied with hammer in end X what are the chances of having hammer if the game is tied in the 8th?

Tied w/   %Tied w/
Hammer     Hammer
in End...   in 8
   1        58.7
   2        57.9
   3        65.6
   4        67.2
   5        71.2
   6        78.0
   7        100

There is no evidence here that having hammer in an even end with tied is more likely to set you up with hammer of a tied game in 8.

However, there is one unusual thing about being tied in the 6th with hammer. Here I’ll introduce a term called ‘force penalty’. It’s the difference in your win probability between blanking and getting forced.

 Before 6th end    After blank   After force    Force 
Margin   WinProb    Win Prob      Win Prob     Penalty
  -2      16.7        15.9          10.2        +5.7
  -1      46.7        35.9          37.1        -1.2
   0      62.0        62.8          64.1        -1.3
   1      83.5        89.7          84.1        +5.6            

It’s interesting that if you’re tied or down one with hammer in the 6th, the force penalty is really a force reward. Historically in the Slams, it’s actually been better for your chance of winning to take one than to blank in these situations. However, this is not a good enough reason to be obsessed about having hammer in the 6th. From a win probability perspective, it has still been marginally better to have hammer in the 7th when tied than in the 6th and that’s all that really matters. (That is, if those probabilities are truly representative of what will happen in future events.)

Still, this has interesting ramifications for strategic decisions in the 6th when tied. It is my understanding that teams are more willing to take a force in the 6th, but are any teams choosing a force over a blank on their final shot in the 6th? In the Slams, the force when tied in the 6th has actually improved a team’s chance of winning. If there were games going on, I would definitely be watching for this. Given the power of having hammer in the 8th at the elite level, this may even be defensible.

The fact that a force is not different than a blank means it’s possible that the team with hammer has some freedom to play more aggressively in the sixth. Maybe if such a strategy was used then being tied in 6 with hammer would be more advantageous than being tied in 7 with hammer. Unlike the analysis I’ve done for 8th end strategy in the past, getting a handle on this will require a Monte Carlo simulation as opposed to brute-force math. Once this situation comes up in a high-profile game, it will be worth revisiting.

User comments
  1. Curling Robots · 2021.01.18 · 12:04 pm

    The force penalty/reward is so interesting. Most would agree that it’s never a bad thing to be ahead, so it even makes sense that taking one in the 6th to go up 1 could be even better than blanking and staying tied. The whole “hammer in even ends” makes sense if you’re tied, but it’s interesting that you bring up that having hammer just means you’re more likely to be behind. (At any rate, if you never have hammer, you’re doing well: the 2018 BOOST National women’s tiebreaker and the 2017 Scotties 3v4 page playoff come to mind as extremes!) The whole 2nd end thing is definitely a bit much – perhaps a confused attempt by teams to extrapolate (i.e. hammer in 8 is good, so hammer in 6 should be good, so it must just be an even number thing…)

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