9: A measure of game dominance


In most sports, the final score is an acceptable indicator of the difference in performance between two teams. There are games where garbage-time scoring affects the final score in a misleading way, but these cases are the exceptions. While some work has been done in other sports to better estimate the difference in performance between two teams, there isn’t much urgency to do so because the final score usually works well enough.

In curling, things are different. A 10-point win is always the result of one team’s domination of its opponent, and 5-point wins almost always are. But 3-point wins could be the result of one team’s dominance or require a difficult last shot to achieve victory. And one-point wins are definitely not decided by luck as often as they are in other sports.

In the semifinals of last week’s Baden Masters, Niklas Edin beat Peter de Cruz 7-3, and Jaap van Dorp beat Sixten Totzek 5-4. Which winning team was more dominant in its win? Well, we could look at the line score or better yet, watch the game. But in today’s society, people are busy and they can’t watch all the games. It would be helpful to have a measure of dominance so our busy friends could quickly know the true difference between teams in a random curling game from Grande Prairie.

One of the simplest ways to do this for a competition is to sum the win probability gained from positive events for the winner and divide by all of the win probability gained from positive events for both teams during the game. That’s some serious word soup there so let’s work through an example. We’ll use the Edin-de Cruz game.

          Score      WP-Edin    WP gained
End  de Cruz  Edin    60.1%   de Cruz  Edin
 1      2             24.7     35.4%
 2              2     39.2             14.5%
 3              0     39.1      0.1
 4              1     59.5             20.4
 5      1             62.8              3.4
 6      0             64.5              1.6
 7              1     60.4      4.1
 8              3    100.0             39.6
SUM     3       7              39.6    79.5 

Edin won, but not without some uncertain moments. De Cruz stole two in the first, adding 35.4% to his win probability. From there, Edin steadily took control. A botched runback on his second-to-last shot in the 7th allowed de Cruz to force Edin to one, sending Edin to the final end up one without hammer, with a 60.4% chance to win based on history.

Those win probabilities are based on men’s games over the last five seasons, so maybe Edin himself truly had a better chance in this case. But he was in that same situation in pool play against – to put it politely – “not top-100” Team Klossner and gave up two to lose. (That game would be a contender for surprise-of-the-year even with a full global schedule.)

In this one, Edin scored three in the final end, although he really only needed one for the purpose of winning. So the final score was a bit deceptive. In terms of our dominance measure, Edin scored 79.5/(79.5+39.6) = .668. I like a few numbers before the decimal point, so let’s multiply this by 100 and call it a dominance score of 67.

That number is meaningless without something to compare it to, co consider this: It was the least dominant win of all games in Baden decided by at least two points. For additional context, let’s compare it to that van Dorp one-point win in the semis.

          Score     WP-vanDorp   WP gained
End  Totzek  vanDorp   60.1   Totzek  vanDorp
 1      1              41.7    18.4
 2              3      75.8            34.2
 3              1      87.9            12.1
 4      1              90.1             2.2
 5      1              81.9     8.1
 6      1              64.5    17.5
 7      0              70.7             6.2
 8              1     100.0            29.3
SUM     4       5              43.9    83.8 

After scoring 3 in the second, van Dorp played from ahead the rest of the game. Yielding consecutive steals in 5 and 6 still allowed him to go into the final end tied with hammer after a blank in 7. That was a better situation than Team Edin faced going into 8. Van Dorp drew to the four-foot on his final shot for the win, producing a dominance score of 66, slightly lower than Edin. But all in all, the games were similarly close.

This measure has its weaknesses, mainly that a perfect score of 100 is attained if a team does not have any negative win probability events. This sounds good – and I like the idea of referring to such games as ‘perfect’ – but in fact it doesn’t distinguish between Yannick Schwaller’s win over Dean Hürlimann in the Schweizer Cup where he scored 3 in the first and then stole 5 and 4 in an epic bludgeoning and Edin’s win over De Cruz in pool play where he won 8-3 and De Cruz’s only points came when forced to single points with hammer.

Also, the lowest possible dominance score is around 57 in an 8-end game. That’s because in close games, there’s usually a lot of win probability at stake in the final end. Thus the dominance score can’t be less than about 60 unless teams trade monster ends – and thus large swings in win probability – throughout the game, an unrealistic scenario in high-level curling.

[Update: After thinking about this for the last 24 hours, this approach has a few more flaws I’m not comfortable with. I won’t be using this version of a dominance score on the site. But we do need a tool like this to improve our analysis of team performance.]

Still, this measure is good enough to tell a story that isn’t told by the final score. Edin’s semifinal win over de Cruz was about as stressful as van Dorp’s win over Totzek and we can now distill that concept into a single number. And the winning team always has a better score than the losing team, which is a reasonable requirement of such a metric.

Another way we can use the dominance score is to analyze which team was the most dominant throughout an event. For instance, here’s the average dominance score for each team at the Baden Masters in pool play:

      Team  Dom  Record
Edin 82.1 5-1
van Dorp 72.8 5-0
Schwaller 67.2 3-2
Retornaz 63.6 3-2
Totzek 56.5 4-2
Klossner 50.6 3-3
Schnider 50.4 3-2
de Cruz 47.6 3-3
Gempeler 43.7 2-4
Krause 35.3 2-4
Hoesli 34.2 2-4
Hess 32.1 1-4
Iseli 13.8 0-5

Because the dominance score is almost never below 60 for winners and at most 40 for the losers, winning percentage plays a role here. Still, Edin lost once more than van Dorp in pool play and still ended up being significantly more dominant. There were 41 games played in Baden, and including Edin’s perfect game against van Dorp in the final, Edin had five of the nine most dominant games in the event.

For the second consecutive week, Yannick Schwaller did not play up to his ranking of sixth in the WCT rankings entering the season. I’m tempted to use this time to point out he’s barely in the top 25 at DoubleTakeout.com, and I will do that, but I will also admit that Schwaller performed pretty well despite failing to make the playoff round.

Part of it is that his team has a knack for destroying teams ranked much lower than it. The other part is that they only had hammer in one of the five games and the dominance score will reward the non-hammer team more, all things being equal, since they need to overcome a 40% win probability at the start of the match. And that’s how it should be! The team starts without last rock can’t just barely outplay its opponent to win, they have to significantly outplay them. The dominance score naturally recognizes that.

Finally, despite taking Edin to the brink in the semi-finals, Team de Cruz wasn’t very sharp last week. By this measure, they performed worse than Team Klossner in pool play, whom they finished in a two-way tie for the final playoff spot. Based on dominance score they should have had an early exit. But we don’t decide ties by dominance score, we decide them by head-to-head results, and de Cruz’s win over Klossner allowed them to make the playoffs as the third seed from their pool.

Dominance score has to be used in context because it’s sensitive to the quality of opponent. Even in this event, the pools were a bit imbalanced. Schwaller, probably due to his inflated world rating, got to be in a pool separate from Edin and de Cruz, who were both in the DoubleTakeout top 10 before the event. If he had to play either of those teams, his rating may have suffered. And certainly over the course of a season, average dominance score isn’t a very useful measure without some adjustment for schedule.

But it seems pretty useful on a game level and even on a bonspiel level, where opponent strength is similar among teams. Soon, I’ll be adding a page with archived event forecasts like the ones I’ve produced the last two weeks, and after the event I plan to add the average dominance score for each player to this display.

By the way, dominance score could be applied to any competition where the win probability at any given time is known. In curling, we could get a more accurate score if we knew the win probability after each shot, and thus distinguish between ‘perfect’ games. Sports like football and basketball have an advantage where the win probability is known after each play. It’s impossible to have a perfect game in cases like that.

For now, we’ll have to accept our estimate based on scoring in each end. It’s at least an improvement on final score. And it could be a useful tool in evaluating a team’s performance from week to week. In the case of the Baden Masters, Team Edin won the trophy, and they clearly played the best, too. That’s not going to be case in every event. Maybe even most events. Now we have a way to know when that happens.