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Thursday, December 18, 2014

Giving Points Away: Part II

I never intended a part two to my original coverage of the Canadian Open, but one commentor suggested perhaps I was to lenient in my assesment of these decisions.  It is possible.  As a good Canadian I naturaly avoid confrontation and only bury critism underneath pleasantries like "perhaps they might have" or "possibly she could have considered" instead of just calling out skips for being dead wrong.

Much of my strategy analysis is based in data, but I also believe what my childhood stats hero Bill James would protest

"there are so many things that none of us know, no matter how detailed the statistics".

A skip is always making a strategy decision based on many factors, most of which cannot be analyzed with statistics.  Even stats which are available need to be adjusted based on the conditions, the opponent, their team, and their own skills.

Warning to those right brain thinkers, we're going to dig a little further into the numbers than in our first pass.

Note: if you haven't read the original article, please go there first.  Otherwise this will make even less sense.   I wrote both and am still not sure what I'm talking about.

Situation 1:  Steve Laycock

Steve has a choice between draw to the full four foot for 1 point or a hit and roll for 1 point.  Let's estimate his odds at the draw are 95%.  Let's estimate a steal of 1 is 3% and a steal of 2 is 2%.  We'll use the WE chart for 4 rock FGZ (it's all we have for now) but increase the chance of a team 2 down with hammer to win by 3%.  This is slightly better than just a wild ass guess.  We do have a small sample of data from the 5 rock events which indicate that teams score threes about 3% more often.  We need a couple of years more data to be more accurate but it seems like a reasonable start.  We won't expect 1 down with hammer to change under 5 rock FGZ because thus far ends appear to play out identical as with 4 rock FGZ.

Win Expectancy (draw) = (.95)(.86)+(.03)(.79)+(.02)(.41) = .8489 or 85%

Estimate the hit and roll by Steve is made for 1 point 1/4 the time.

Win Expectancy (hit) = (.75)(.79)+(.25)(.86) = .8075

So these numbers indicate it's a 5% mistake.

What if Steve knows his lead makes the tick shot 80% of the time and when they make both ticks they win 100%.  When they don't make both ticks they still win 70%.  This would channge his WE when tied with hammer from .79 to:

WE = (.8)(.8)+(.7)(1-.64) = .892 or 89%

That's higher than our estimate for 2 up!

Replace .79 above in our equations with .89.

WE(draw) = 85.2%

WE(hit) = 88.3%

What looked originally to be a 5% mistake becomes a 3% advantage, if Steve's assessment of the ability for his team to execute the tick shot and finish the game tied with hammer is correct.  And what if Steve doesn't expect to make the draw as high as 95%? Yes, a lot of IFs, but as we get more recent data on elite teams, we may see numbers which look closer to these results.  Recall the previous chart (with a small sample size) shows recent Grand Slams (from 2012-13 Season to today) WE of 87% for tied with hammer in the final end.

Situation 2: Rachel Homan

Rachel can make the double for a blank (WE=.872) or will miss and give up a steal (.7).

Even more so than with mens data (for an up and coming team like Laycock), I'm willing to give Team Homan credit for having numbers which well exceed these averages for womens play.  It's fair to say Rachel wins much more than 70% of the time when tied in the final end, and higher still when 1 up with hammer.  In fact, Homan is 39-5 (88.6%) tied in the last or extra end and 11-1 (91.7%) 1 up with hammer in the final end. They are 19-1 (95%) when 2 up without hammer in the last end.

We could spend time trying to pull in data from other top teams and then use regression analysis to create a more confident estimate,  But I don't have that much time on my hands.  

Homan lead Lisa Weagle is so good at the tick shot they've started naming it a "weagle".  Using the same formula as above for Laycock: assume she makes the tick shot 85% of the time (Rachel may even have these exact stats).  Assume they also win 100% of the time both tick shots are made.  When one or both ticks are missed, let's guess that Homan wins 60% of the time.

WE = (.85)(.85)+(.6)(1-.7225) = .889 or 89%  

You may notice this is very close to their actual results.

The arguement now boils down to Homan's expected WE for the other conditions (1 up with and 2 up without hammer).  89% is higher than the womens averages for both these situations and if we use them the hit becomes an obvious decision.  It seems obvious that as one of the top 3 teams in the world, Homan is well above the average, but how much?  

It's late and I feel like I'm repeating myself.  I think we get the idea.

One thing we find in both these decisions is it is closer than initially thought and when a team is in this dominant position, the wrong decision won't be that big of a mistake.  Trying to decide whether you chose to have an 88% chance to win or an 90% is not a large error, especially given these numbers are not absolute for a particular team and situation.

I've talked before about the problem with "average" in our data and the elite teams.  When I've run samples of different levels of teams (at least for mens), what stands out is that most numbers look fairly consistent, except for tied with hammer, where the team with hammer has a 4-5% advantge.  The reason is the position of tied with hammer is less influenced by the skill of the opposing team and a large impact based on the ability of the team with hammer to clear free guards and draw for a point.  Given the  improvement by elite leads to make the tick shot most of the time, this gap is only getting larger.

Wednesday, December 17, 2014

ATH, 12/17/14: Just Before Festivus

Jordan, Gerry and Kevin catch-up just before the holidays to discuss the recent Canadian Open, thoughts on the "tick" shot, the progress of Team Stoughton, report on early playdown results and share news on the new Asian Curling Tour.

Check out this episode!

Monday, December 15, 2014

Giving Away Points at the Canadian Open

Eve Muirhead won her first Canadian Open and Brad Gushue won his second Grand slam of the year.  This year the Open added a women side to the bracket and also had a bracket.  Instead of a round robin format, qualifying came through a triple knockout format.  Unlike in a round robin where an 0-4 team still has to finish all their contests, this ensured no team would be playing without some chance of still winning the event.  By qualifying in the A side, teams were awarded hammer for the quarter finals.  Three qualifiers came from a B event (where teams had lost 1 game) and three more from the C side (teams which had lost two games).  This also meant half the field qualified for the championship rounds (16 of 32 teams).  A small wrinkle that makes the event somewhat different without really impacting the actual games.  

Another wrinkle that continues to introduce never-before-seen strategy decisions is the five rock free guard zone.  The semi-finals were all played during the same Saturday evening draw.  In the span of a few minutes, Steve Laycock and Rachel Homan both appeared to concede a stolen point in the 7th end.  Each of them were one up with hammer and rather than draw to go two up heading to the last end, chose difficult hits which were highly probable to give away points to their opponent.

In the case of Laycock, he had a possible draw to full four foot (blue line) but instead chose a hit and roll that, to score one, needed to land in an area of a few inches (green line).

Laycock is Red

Everyone in the booth was questioning this decision.  His opponent Brendan Bottcher was possibly pleased. Steve is from Saskatchewn and historically teams from that province tend to hit more often than draw (sadly, I could not find a Bob Pickering photo on the internet), but that was in the old days of curling.  These days, most any Grand Slam level skip would draw.  

Rachel Homan had a possible chance at a blank.  Facing a simple draw for one (blue line), she instead chose to try a double (green line) that could result in a blank to hold hammer one up heading to the 8th end, but also could be a likely steal.

Homan is Yellow

Team Homan was being coached by Richard Hart.  He came out and encouraged Rachel to make the call she wanted to make.  They discussed that whether she is down one or tied in the final end, she'd need to make the same draw.

Laycock and Homan ended up with victories and trips to the finals, where they both lost.  So what do I think of these calls?

Looking at 4 rock FGZ numbers (2003 to 2014), in the final end, mens teams win 76% when tied and 90% when up two without hammer.  Womens teams win 70% when tied with and 86% when up two without.  The 76% is deceiving because it includes games including weaker teams.  If we look at only Grand Slams, it's closer to 79%.  Still, not 90%.  Women's results don't show this type of difference for elite play.

So, the question is whether adding a 5th guard for a team down 2 is significant enough to overcome the gap (11% and 16%) in WE.  In the case of a tied game, the rule has no impact.  When up 2 without hammer, a team now needs to decide if they will try tick shots on corners or pile up rocks in the house or even put up a centre guard (common if they are up 1).

There could be some over thinking with both of these shots.  Both Steve and Rachel called shots which if executed would NOT result in a steal.  A made shot by either (however slim their chances) would benefit them. Their calls both removed any chance of a steal of two and in the case of Rachel, perhaps even still get a blank.

We do not have enough data yet to specifically state that the WE of a team 2 up without hammer in the final end in 5 rock FGZ is closer to the 79% or 70% WE of being tied with hammer.  We could start to look at odds to score deuces and threes in 5 rock, but that will take me too much time and I'd still rather wait until we have more data.

Let's look at the notion of tied with hammer.  The ability to make the tick shot has improved dramatically just in the past 2-3 years.  Let's look at recent data:

These are very small sample sizes (around 100 situations each) but it is clearly showing a trend for teams at the elite level.  Reason to be wary of small sample sizes: the data from 2010-2012, taken from the most elite events, is actually 10% BELOW that from Playdowns (78% from Provincial, Brier and Worlds), games which include many "B" level teams.  

If these trends hold up for larger samples, it's fair to say, for Laycock the decision was either a small mistake or fairly close to equal (with the 5 rock rule), and for Rachel given some chance at a blank, possibly close to an even decision. Given their proficiency with the tick shot, she likely expects her WE to be above 80% tied with hammer.

Top skips will almost always err on the side of having hammer.  Even when the numbers indicate otherwise, skips will make a decision that includes having the last shot.  I often argue, as in the case of "two-hammers-to-one" its importance is sometimes over emphasized.  Because of our validation of the numbers when 1 up without hammer in the final end (60% to 40%), many teams altered their strategies in the later ends. 

While we're here, let's look at recent results (again, small sample sizes) for these top events for 1 up without hammer.  We see not much has changed and results are in line with historical numbers.

Given a close decision, I understand why an elite skip wants to have the last shot: if they thought otherwise, they wouldn't be the best in the world.  In both of these situations, the odds were probably very close, we can't argue much with their preference to have hammer in the last end.  

As teams improve even further at the tick shot, I expect we may reach a point where elite level games are above 90% for tied with hammer.  There's been some discussion about potential rule changes to thwart this type of result. A "no-ticks-allowed" rule might be just around the corner. 

Of note, at some point during the mens final broadcast we were told Sundays draws were a sell out.  That is nice to hear but the chairs still appeared just over half full.  I have hope that one day a Grand Slam will be standing room only and fans will cheer loudly throughout.

Until next time...

Thursday, December 11, 2014

A Quick One from the Canada Cup

Why?  My wife asked this question when I told her I was headed 90 minutes away to Camrose, Alberta to watch the 2014 version of the Canada Cup.  I have a longer, more wordy and less Mathy article coming out in the next digital edition of The Curling News that elaborates on this question.  With that effort and the Canadian Open starting this week, I have little time to dig too deep into the play over the last weekend.  But I wanted to touch on the return to 10 ends, the Classic version of a free guard zone and blanking.

Ten ends seemed long.  Am I right?  It can only be a matter of time until the move to 8 ends for all events.  If not for the sake of the players than for the sake of the television viewer.  3+ hours is a long time to sit on a couch.  

The four rock free guard zone was noticeable in subtle and obvious ways.  Teams appeared to be adjusting to a more conservative approach when up without hammer.  Suprisingly, several gambling web sites had the Over/Under Totals for mens and womens games at 12.5 points.  This was a clear betting opportunity as historically we've seen mens games (and Rachel Homan's games) at 11.5 for 10 end contests.  16 of 23 mens games were under.  A $100 bet on every under could have netted around $600 return.  However, I missed out.  I didn't realize until mid-way through the event, then missed betting some later draws because of work and managed to get caught in 3 of the overs with the five bets I was able to place.  I'd be shocked if this type of opportunity comes again.

There were also more blank ends than we've seen recently.  Two in particular where rather dramatic.  During their Semi-Final, both Mike McEwen and Glenn Howard both made what could be considered "risky" attempts at a blank.  TSN announcers Russ Howard, Cheryl Bernard and Vic Rauter all shared their surpise in each case.  Where they correct decisions?

In the 3rd End, McEwen is tied with hammer, 0-0.  Glenn makes a hit and role with his last shot and Mike faces a difficult draw-tap (blue line) to get his one point.  

McEwen isYellow

The guard is long enough that he instead chooses a board weight hit and roll out (green line) to blank.  He makes the shot with a few inches to spare, but it introduced risk that Howard might steal a single point.  At this stage, a blank has a Win Expectancy (WE) of roughly 61% and taking taking one drops McEwen to about 57%.  A steal will result in a WE of 43%.  The decision appears reckless except that the shot for one is no piece of cake either.  Mike added some difficulty to the shot but as long as he get the "right miss" and ensures he removes the Howard stone, the worst outcome is taking the single point.  Hard to estimate exactly the additional risk Mike was taking, but the way he's been playing this season, you can't fault McEwen for believing it's the right call.

In the 7th End, Howard is down 3-1 with hammer and facing a McEwen stone buried in the twelve foot ring out on the wings.  

McEwen isYellow

Rather than choose the simple draw for one point (blue line), they decide to try the soft weight hit on the McEwen stone and attempt to role out for the blank (green line).  This shot does add some additional risk but they only needed to move their opponents stone a short distance, so it appeared much easier than what Mike had tried earlier.  Still, with the corner guard in front and risk of either crashing or sailing wide, it was clearly more difficult than the draw for one.  If Howard takes one their WE will be 16.5%.  By blanking they increased their odds to 19.1%.  A steal and they drop to a dismal 7%.  At first glance it looks like a poor decision but the risk in actuality seemed rather low.  Glenn should be able to remove the stone most of the time and the common miss would be sticking around for one, the same as the draw.  I've also noted before, a 2.6% difference might seem small, but as your odds decrease, every chance to increase WE has a greater advantage.  Similar to how chips in a poker tournament are worth more as you have fewer, the same situation for WE.  Another way to consider the situation.  A 2.6% increase over 16.5% is 16% improvement.  That same 2.6% change in McEwen's WE only amounts to about 3% difference.

I enjoy 5 rock FGZ and 8 end games, but that semi-final (and Howard versus Koe in the round robin) were fantastic games with tension throughout.  Maybe there's room for more than one type of game. Maybe we could even go back to a 3 rock event, or even a no guard zone but all teams need to use corn brooms.  The possibilities are endless.

Next stop, The Canadian Open.