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Sunday, April 3, 2016

Match Play Math

I know the Womens Worlds just finished and the men are getting underway to decide the global champion of 2016, but I want to talk about the Elite 10 and match play.

Let me begin by stating I really like match play. I enjoy competing in match play golf. In fact, given my propensity to spray a drive and balloon to a triple bogey on occasion, it's always nice to pick-up your ball and move to the next hole knowing you are still in contention. I enjoy watching the WGC World Match Play (with PVR) along with the Ryder and President Cups. Suggestion for those fathers out there, a great idea to plan your vasectomy around a Ryder Cup weekend so you can nestle into a couch with a bag of pees and watch it all without interruption.

When I heard of the idea to put a match play event in curling's Grand Slam I was intrigued to see how it would unfold. I wasn't sure if it would sell to the players and fans, but after two seasons I'm clearly buying. Others, however, may not be as interested. Some posters on CurlingZone found Gushue's winning draw to the button as a gimmicky end to a gimmicky event. To those naysayers, heed the advice given to me on my own displeasure with Skins and the Continental Cup. It's OK that something exists, even if you chose not to watch it. Mixing things up in what is becoming a crowded tournament schedule can't be bad for business, can it? As long as players will travel to participate and fans want to watch, we should be able to find one week on the schedule for curling match play.

With only two Elite 10 match play events completed, we have a very limited sample size to start a detailed analysis. However, since there were so much percentages thrown around on the Rogers broadcast and from other writers, as the curator of "Curl With Math" I felt it was important to share some numerical thoughts in order to protect my turf.

Everything that follows is based on an assumption the odds of any given end result in a halve (blank or take one), a steal, or a deuce (or more) each occurring 1/3 of the time. Early during this year's event, a graphic showed that steals were slightly more prevalent, and later in the week deuces seemed to make a comeback. Overall, if we use 1/3 for each outcome it gives us some indication of what we are looking for, and make my calculations fairly simple. After a decade or so, perhaps we'll have enough data to be more precise, though even 10 events is a small sample size.

From what I observed, the reason for more steals than "regular" curling appeared to be a result of teams often attempting a risky shot for two and missing, rather than playing for a halve and losing hammer the following end. This may not always be the correct strategy and I suspect over time we might see less steals and more halves. Oh, and sorry for those of you who call a halve a "carry over". It's not. Nothing is carried over to the next end, not even the hammer. Sorry to be the annoying kid who has to correct everyone, but I've been that way since I was 8. The mound is 60 feet and 6 inches (not 60 feet) from home plate. A "best ball" tournament is not where you pick up your ball and hit from the best spot, that's a scramble. In poker, you can't bet money (or a car) that isn't on the table or lose the hand because you are all in (something that occurred in nearly every movie poker scene up until Rounders in 1998). And an end or golf hole that is tied is "halved", not carried over. Carry overs happen in Skins.

Teams that are ahead will also likely adjust strategy, and the potential of a steal should reduce (and increase chance of a halve) as a team gets closer to a win. For example, a team 2 up playing the 6th end is less inclined to try a miracle shot for two if they have a simple shot for a halve and chance to be 2 up with 2 ends remaining. Again, we don't have enough data to verify the specifics and using a 1/3 for each possible outcome made my spreadsheet much easier. I was able to generate two charts that we will use for our analysis. The first chart shows the odds of winning (Win Expectancy or WE) given each situation. The second chart shows the probability of each situation occurring.
Chart 1: Match Play Win Expectancy
Chart 2: Match Play Probabilities of Situations
A few observations.
  • Unlike "regular" curling, a team starts the game with an equal chance at victory. A team winning the first end in match play moves to WE = 67% which is less than taking a deuce in "regular" curling (WE=74%) but more than blanking the first end (WE=61%).
  • A team that goes up two ends moves immediately into a dominant position at WE=83% or greater. Notice at the halfway mark (4 ends remaining) a team 2 up is at WE=88%. This is comparable to 2 up with hammer or up 3 points without in any other event. What appears close on the board (I'm only 2 ends behind with half the game to go) could in fact be a reason to change channels. Looking at Chart 2, you might notice the situation of up 2 or more ends at the break occurs 37% of the time. That means over 1/3 of games are very close to being decided just over an hour into the contest.
  • The 6th end will be played 95% of the time, so broadcasters can bank on 90+ minutes of coverage, but the 8th end is only played 50% of the time. With a draw of three games, that means 12.5% of the time, all games will wrap before the final end and 37.5% there will only be one game that reaches the final frame. By comparison, the 2016 Brier had around 25% of games failing to reach the last end.
  • After the 6th end, only 54% of games are tied or 1 up. That means 46% of games are either over (or virtually over) just 3 quarters of the way through the game.
  • Every game starts "tied" but odds of this close situation occurring drop quickly, from 1/3 of the time the very next end to just over 20% by the 5th end.
  • Being down 1 end with 3 ends to go (WE=26%) is close to being down 2 with hammer with 5 or 6 ends remaining. The 1 up situation doesn't go above 80% until the last end, and ultimately creates entertainment at any point in the game regardless of the outcome, assuming you don't mind draws to the button to determine the winner.
On the topic of draws to the button, I'm mixed. Depending where you fall on this debate, having the Elite 10 semifinals and finals all result in draws to the button was either the most dramatic and exciting finish of the season, or the hokeyest final weekend in curling history. I like the format that round robin games are worth more if won in regulation and a loss from a draw to the button still gains a team points in the standings (a la NHL Hockey). Unlike hockey, I don't think an overtime end with 3 (or 2) players would create more excitement. During the playoffs, however, I might prefer some type of extra play to determine a winner. The issue with a single extra end is the question of who gets hammer. If the odds of a steal, halve or deuce are actually 1/3, then the result becomes equal, except that it's likely not (a team tied with hammer in this situation can adjust strategy to their advantage) and 1/3 of the time the end is halved, and the game has to continue. Perhaps two extra ends, giving each team hammer once, and then only going to a draw to button if needed, could create a fairer contest, but we still end up with final draws to the button often and Sportsnet will be clamouring for an end to the broadcast by this point. The idea of no sweeping on the next attempt, should both draws cover the pin, really doesn't sit well with me as it fails to account for the team aspect of the game and adds too much uncontrolled risk to the proceedings.

No perfect answer here on final draws or assessing the level of entertainment value. On removing stopwatches (no), locking up brooms (maybe) and thwarting the tick shot (yes), but continuing to tweak the rules and format each iteration to test play for both this event and curling as a whole, a resounding yes.

The games might run short and often finish early, but the format puts rocks in play and scratches on skips foreheads. If match play is only one event in what is becoming a full 8 month curling season, ask yourself, why not?


  1. While we're annoyingly correcting.... A team that is up one playing 6 that plays a low risk shot to carry over (haha) will still only be up 1 with 2 ends to play.

  2. Thanks for the catch. I meant to say 2 up playing 6. I have now corrected.