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Thursday, November 27, 2014

Aggression is the Better Part of Valor

What?  Aggression?  That's not right!  The correct phrase is "Discretion"...yadayada, "Valor" (or, if you're Canadian, "Valour").  Then again, at least one site tells me that Shakespeare was simply telling another one of his hilarious jokes.  Much of Elizabethan literature is lost in translation these days, but it's fair to say that William may have been the Stephen Colbert of his time.

There were several aggressive decisions made during the second Grand Slam of the season, The National, won by Mike "Money" McEwen.   Many of these choices were made by the winning squad, others by their finals opponent, Brad Jacobs.  Perhaps it's the 5 rock Free Guard Zone rule or maybe just evolution by the Next Generation, but there were some calls we may not have seen even 2 to 3 years ago.  Jacobs and McEwen are currently the top two teams in the world and given their level of play, it's difficult to argue with their on ice decisions.  That didn't stop Joan McCusker, Mike Harris and Kevin Martin in the Sportsnet booth from wondering aloud if several calls were correct and it certainly won't stop me from digging a little deeper to see if these squads are winning because of or in spite of their on ice strategy.

Round Robin: McEwen vs Jeff Stoughton

In the Second End, McEwen is down 1 and could play a tap for a single point to tie the game (blue line) but instead chooses to try a double for two or three (green line). 

McEwen is Yellow

The tap is not automatic but the double is very difficult.  The rock was almost fully buried and Mike needed the right combination of line and weight to make the shot.  The attempt was missed by a fraction and a steal of one was the result.  

Let's use a quick method of estimating this shot. Imagine you are the skip, standing on the ice in a nearly empty arena and watching the time clock tick away.   There is no excel spreadsheet available and you will need to do math in your head, just like in junior high.  With 6 ends remaining, the Win Expectancy (WE) for a team without hammer tied, 1 up and 2 up is 38%, 57% and 75%, respectively.  Let's round those to 40, 60 and 75.  If your opponent steals your WE becomes 1-.75 = 25%.

Let's assume you make the tap almost every time.  That leaves you with a WE of 38% (call it 40).  Start by guessing an equal chance for every outcome (steal 1, take 2 or take 3).  Multiply each WE by 1/3 (round quickly) and add them together.  13+20+25 = 58.  Presto!  That's the same as taking a single.  Even if you surrender a steal one in three attempts, it's the correct decision, if you can get the full 3 points one in three tries.

Astute readers will notice that there is some chance of a steal of 2.  If Mike hits the guard he'll drop to a 17% WE.  Granted, there is also a risk for a steal of 2 with the tap back.  In fact, given his previous rock appeared to grab, it's the second end and early in the event so ice conditions are still being evaluated, you might argue the hit is the safer shot.  Kevin Martin and Mike Harris discussed the call at the beginning of the next end and both felt it may have been the wrong decision, figuring Mike would make the tap 95% of the time.  Even if Mike does make the tap that often, given his abilities, I believe he chose the correct call.  However, changing the weight from firm board to normal hit (a decision made from the hack) may have been a mistake and decreased his chances of making the shot.

In the Fifth End McEwen now has a 3-2 lead without hammer.   Rather than hitting and possibly rolling to sit two (blue line), Mike choses to attempt a draw to sit one (green line).  

McEwen is Yellow

A very aggressive call.  With the amount of curl in this spot, he's able to bury past the guard but the length of the guard and large amount of curl also leaves Jeff a chance to follow him with a soft take-out or attempt a long runback to possibly score two points. Stoughton misses the hit attempt and McEwen steals to go up 4-2.

I'm not entirely certain why Mike would attempt this shot.  It appeared he could get his final rock in the same spot by making a hit and roll, removing any chance for a deuce.  Perhaps he was concerned a failed roll would leave Jeff a possible double for two.  McEwen could have stuck on the nose and a double would not have been possible but a single for Jeff would have been nearly automatic. Mike may have been more comfortable with ice and conditions for the draw vs the hit and roll.  One last, not very likely explanation, Mike had a brain fart and thought he was sitting shot stone.  A surprising decision that worked out in the end. The WE moved from 65% to 81% by stealing rather than forcing Jeff to 1.  If Stoughton had scored 2, McEwen's WE would have dropped to 37%.  Using our head math from before, if Mike is able to steal 50% of the time and Jeff gets two the other half, it's approximately equal to the hit (1/2 of 80 + 1/2 of 40 = 60).  Given that Jeff will sometimes still only get 1 point, The steal chance could be less than half in order to be the correct call.  I appreciate aggressive play but suspect the decision here may have introduced more risk than was necessary.  

With hammer in the Extra End, rather than peel a centre guard, McEwen chose to draw around and sit two in the four foot.  He slipped a foot heavy and actually left Stoughton some hope.  

McEwen is Yellow

Jeff's final rock lost its handle, perhaps because of a pick, and McEwen took the win without having to throw his last shot.  The draw around vs peel tied with 3 rocks to go, attempting to get position before your opponent, is a play more often seen in the women's game.  I was surprised at the call, as were the commentators, but Mike may have felt his second shot, sitting top four foot in the open, would provide an angle raise if needed.

Championship Final: Mike McEwen vs Brad Jacobs

This was a facinating game that was filled with aggressive calls right form the beginning.  In the very First End, rather than draw for a single (blue line), McEwen chooses to try an angle raise for 2 points (green line). Our panel of experts in the booth are surprised by the call.  The result is a missed shot, a steal of one and an early lead for Jacobs.  

McEwen is Red

Let's evaluate the risk in this decision and decide if it is the correct call.  Naturally, if Mike expects to make a 30 degree angle raise of 12 feet 100% of the time, it is clearly the right decision.  I expect team McEwen recognizes this is a difficult shot and they are taking some risk at an attempt to gain early control.  

How difficult is this shot?  Every curling shot has a margin of error.  For big weight hits, where a rock is moving nearly straight, you can start to examine the margin as a physics problem of angles.  I could not find any studies on the impact of curling rocks (please let me know of any), but I did find this study on pool.  Essentially, the further you move from a nose hit the less margin for error.  Also, the angle of approach (based on the target stone being a centre or corner guard) will also reduce the margin for error.  The final chart (copied below) shows how the margin of error will decrease based on the angle of impact.  

From the results they describe two examples:

a straight-in shot is 1.15X (15%) easier than a 30 degree cut angle shot.

a straight-in shot is 1.97X (97%) easier than a 60 degree cut angle shot. 

A straight back raise is generally 80-85% successful at this level.  If we assume Mike is on the higher end, and we estimate an angle of 30 degree, then his success rate will be approximately 74%.   Keep in mind, I have over simplified this for the purpose of discussion and I'm using a pool study to apply to curling, but it does appear to make sense.

If McEwen draws for the single their WE is 61%.  With the raise attempt, three likely outcomes will occur:

Mike misses and Jacobs steals 1 (WE = 43%).  

Mike is able to contact the Jacobs stone and remove it, but also rolls out and scores 1 (WE = 61%).  

Mike makes the shot and scores 2 (WE = 74%).

Like above, let's start by guessing there is an equal chance for each outcome.

WE = (.43+.61+.74)/3 = .59

That's 59% or nearly the same as the WE of a draw for 1.  That's not even taking into account the odds of making the draw to the full four foot in the first end (Kevin mentions it's likely 85 or 90%).  A high percentage shot, but certainly not automatic.

Mike is betting on his odds of hitting and removing the stone in the rings greater than 2/3 the time he attempts the shot, and sticking around half the time he's successful.  Based on a pulled-out-of-my-rear pool analogy, appears to be a reasonable call.

Perhaps team McEwen has been practicing these types of shots, and this is simply an indicator of the future of the game.

In the Second End, McEwen is now one down with hammer.  On his final shot there appears to be a simple draw for two points (blue line).  Instead, Mike chooses a hit attempt on a partially open stone for three (or the same deuce if he rolls too far).  

McEwen is Red

The result is a shade light and/or a fraction wide.  McEwen hits the yellow Jacob stone but spins away and sits 3rd and 4th shot by an inch.

At first glance, I liked the call.  There was still a high probability of two and even if you miss (which he did) you're tied without hammer and 3/4 of the game still to come. So what do the numbers say?

Three possible outcomes, McEwen will score 1, 2 or 3.  Each results in a WE for McEwen of 43%, 62% or 75%, respectively.

Let's use thirds again to start the analysis.

WE = (.43+.62+.75)/3 = .6

Low and behold, this is nearly the same as if they draw for two to go one up.  It is McEwen's analysis of the ice (Mike Harris mentions it's a fresh spot) and confidence in weight that will determine his assessment of his chances.  I tend to think he's getting two or three more than 66% of the time and was just unfortunate with the result (missed it by a fraction of an inch).  If we assume that will occur 80% of the time, he only needs to make a trey 20% of the time for the call to be correct.

Announcers Kevin Martin, Mike Harris and Joan MCusker were not as forgiving of this call and all suggested during the start of the next end that McEwen should have drawn for two.  Words like "boost" and "momentum" were used, interestingly just as Jacob's second E.J. Harndon flashed a hit.  

Momentum is one of the most overused word in sports yet has the least amount of measurable impact on a result at a highly competitive level.  I share the same thoughts of Grantland NFL writer Bill Barnwell, who has written often about momentum and discussed it at length following the Raven's Super Bowl win in 2013.  In a non-contact sport like curling, it doesn't fundamentally exist, except related to the movement of the rock down the sheet or transferred during a take-out.  The idea is, given the bad situation that occurred (held to 1 point instead of scoring 2), one team will now rise to the occasion and play better than they had and the other team will be distraught and lose their focus.  You could sell me on the idea of the latter under the right circumstance (Olympic Gold Medal game) or era (before curlers became althletes), but to consider that a team suddenly improves from their expected abilities is simply folly.  

Sorry, my son's new favorite show is Top Gear and words like "folly", "brilliant" and "rubish" have now taken hold of my internal lexicon.

On the final shot of the Fifth End, McEwen, now tied 2-2 with hammer, chooses to run back his own centre guard onto a Jacobs rock sitting on the pin.  Given the amount of curl, a draw tap for one point would not have been difficult.  Mike Harris and Kevin Martin comment that this is not a common choice and McEwen is keeping a potential blank in play (in fact, his preferred outcome).  Given his abilities to make runbacks (as stated earlier, likely 85% or even higher) it's not a very dangerous call, but it may not be the best choice.  Assuming he'd make the draw for one 90-95% of the time, he's not giving away very much and is adding a chance to blank, which nets him an extra 4% WE (65% to 61%).  He might be anxious to hold hammer in the 6th to have "Two-Hammer-To-One". I've spoken previously about this approach (most notably in my book End Game, click on the link above to get yourself a copy) and I'd suggest most teams at this level against similar competition should not introduce additional risk in order to be in this position.  Harris and Martin are, reasonably, estimating the average skip of this calibre will make the draw tap more often than the raise, so it's usually going to be the incorrect call (though not by much).  If Mike McEwen believes his odds are equal to make either shot, he should play the raise.

McEwen scores one and goes up 3-2 heading to the sixth end.

In the Seventh End it's Brad Jacob's turn to try the "risky" shot for two rather than draw for one point (blue line) to tie.  Down 3-2, rather than be forced to a single and face an unlikely steal in the final end (20% WE), they choose the runback attempt (green line).

Jacobs is Yellow  

Brad chooses to play control weight and the result is a soft glance on the shot stone but they fail to move it far enough and McEwen  steals 1 point.  This appeared to be a difficult shot. Jacob's rock sitting top eight appeared to almost and reduce chance of hitting the red stone on the inside.

Two down playing the last end, WE is 11%.  Tied without hammer is 20%.  One up without hammer is 58%.  I'll spare you the formulas, but if Brad can get a deuce even 1 in 5 tries and only gets a single 2 in 5 (a steal happens 40% of the time), then it's clearly the correct call (WE=24%).

It's important to mention that these Win Expectancy numbers are based on over a decade of 4 Rock Free Guard Zone.  The 5 Rock Rule that is now being played during Grand Slams does not have enough data to be meaningful, but we can expect some adjustment in favour of the team that is down with hammer in all situations above.  This should give even more support for some of what appears to be "riskier" decisions.  

One more great aspect of the 5 Rock Rule. Just as I was about to turn the channel after the 7th end, I couldn't.  Jacob's odds to win aren't much better than 11% (even if they take two they are in the same position as the 4 Rock Rule in the extra end).  However, 5 Rock FGZ final ends play out dramtically and there always seems to be something to watch.  In this case, Brad had an angle raise double to tie the game and barely missed it.  Entertaining.


All this discussion of aggression and risk got me to thinking about some new statistics.  If the data was captured, it would be fairly simple to track the risk factor of skips.  In ends where a decision on the final shot will determine 1,2 or even 3 outcomes, vs a simpler shot that will likely be a single outcome (usually a force to one), a measurement of the difference in WE could be calculated to see how much "risk" a particluar skip is willing to take on.  I'll ponder this one a little more, talk with Gerry at CurlingZone and come up with something for another day.  For now I'm tired and need to get a good nights rest to prepare for a full slate of NFL Football during U.S. Thanksgiving (minus the Turduckin).

Until Next Time...


  1. Is there any way that your WE stats can be incorporated into the broadcast as the skip is deliberating on crucial calls? Maybe team up with Gerry? I love K Mart's gut feel analysis because as a great skip you get a sense of the flow and momentum of the game, but if the stats agree or disagree with a decision I would love to know.

    1. I created Win Expectancy back in 2006 with the help of Gerry and Dallas from CurlingZone. It's been used a few times on TV, usually when discussing the 60/40 odds in the final end of a 1 point game. In the National finals, Kevin Martin mentioned "3%", in relatiuon to the difference in odds between blanking and taking 1 point. Like OPS and WARP in baseball, I doubt WE will become a common stat that's used on a graphic, but you never know.

  2. There were a lot of interesting and aggressive calls in that final, and you could argue that both skips went over the top on several occasions. Still, I think the double takeout attempt vs Stoughton in the round robin was the right call. The tap is not so easy as it seems, it is a shot that you do not play that often, as simple as that. I also quite like McEwen's call in the second end vs Jacobs to try and get three. It wasn't so difficult but he definitely underthrew it. After the shot, you could feel that he knew it was a great chance to stamp his authority on that game early on. All other calls in this article arwe questionble, to say the least.

  3. I don't know of any studies of angles precision for curling raises and runbacks, but it's pretty easy to calculate based on the collision of two circular objects. I've constructed a spreadsheet that calculates the delta-overlap required to make a shot for any particular angle and distance. The precision required of course depends on the length of the runback. For a 10 foot runback (straight-back) the tolerance to catch the target rock is about plus/minus 5% or about 1/2 inch either away. To runback and stick, you probably need to reduce that figure by half. The precision required falls off slowly as overlap decreases, and increases rapidly beyond a half-rock to a quarter rock. At 30 degrees, precision required is 80% of nose. It doesn't drop below 50% of nose until you get to about 1/8 rock. I'd be happy to share the spreadsheet with you.

    Your article inspired an instruction article for our club newsletter on the topic of angles (with math). I always enjoy your analysis of probabilities. Good stuff.

    1. Would be great to get a copy of the spreadsheet. You can connect with me at

  4. Great article Kevin!! Always enjoy your analytical perspective. I am also be interested in Rogers spreadsheet. Looking forward to your next offering. Gerry