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Friday, January 29, 2010

Notes from the BDO Grand Slam

A good weekend for Ontario Juniors taking home both the Mens and Womens national titles. You had to feel for the Manitoba skip watching in agony as his last rock just shaved past the Ontario stone. To make matters worse, the missed shot meant I lost a “Provincial” bet with Steven Lobel. Steve, your frozen Bison steaks will be in the mail next week. At least I have Alberta going against Ontario in the Brier for 10 in a row this year.

A non-curling stat I heard a lot these past few weeks was “92% of teams with +2 turnovers win play-offs game in the NFL”. I was hopeful the Minnesota Vikings would be one of the 8% and head to the Superbowl, but alas, it was not to be. Perhaps next year…

On to some Curling thoughts from the BDO.

1. Glenn Howard vs Pat Simmons

In the 5th end, Simmons is up 3-2 with hammer. It is Glenn’s last rock.

Howard is yellow

This is the last end of the Middle Game (middle three ends) and they are about to start the End Game (final three ends).

CBC announcer Mike Harris says Glenn can’t afford to leave the Simmons rock in play. Can he?

Hitting: Glenn is most likely going to give up a single to Pat. There is some chance he could make a hit and roll, in which case Pat will most likely try a double and then there is some chance he could miss or jam and Howard steals. Let’s estimate that Glenn makes a good hit and roll 20% of the time and Pat misses 25% when that happens, leaving the chance of a steal as 5%. There is also some slight chance of a blank, but we’ll assume those odds as negligible.

WP = (.2)(.95) + (.35)(.05) = 21%

Guard: If Howard elects to play a guard, he brings a deuce into play.

WP = .07x + .2y + .35z

Where x is the odds of a deuce, y is odds for a single and z is odds for a steal.

The Howard stone was just back tee-line and likely a single will occur often. Let’s estimate a single is 60% and odds of a deuce or steal are each 20%. WP = 20%. If we estimate the odds of a deuce to be lower, say 10% and set z =30%, WP = 23%.

What at first appeared to be a simple decision now appears to be very close and, depending on our assessment of the situation, perhaps in favour of throwing a guard. I personally preferred the hit, due to ice conditions and the Howard stone being behind the tee-line. If the rock is top button and/or the ice is straighter with less finish, I would prefer the guard in that situation.

6th End, Glenn is now trailing by 2 with the hammer and faces this with his first rock:

Richard Hart drew to the Open side with his last rock and Simmons hit and rolled just out of the rings. Glenn’s first instinct was to replace that stone and play the end out for a deuce and be tied up playing the 6th end without hammer. The Howard front end then talked him and Richard out of the shot, and they elected to play a freeze on their shot stone frozen to the Simmons rock in the four foot. Glenn asks “what are the odds of us getting 3? Brent responds with “zero if we go open”. Glenn then comments “we’re getting a guaranteed two if I go open”.

I disagree that the open side gives them a “guaranteed deuce”. There is some margin for error and if they don’t come deep enough Pat may have a possible hit and roll into the four to make Glenn’s last more difficult. The margin for error on the freeze is slightly higher and the result showed having 6 inches too much weight left Simmons a chance to get out of the end.

If Howard scores two, WP=33% or 2-1 (on the border of Close and Control, per my past article here If Howard makes a great shot, Pat still has a possible chance of running his rock in the top twelve into the Howard rocks and killing one, holding them to deuce. If Howard does score three, their WP = 67%, flipping the odds against Pat Simmons to 2-1 against. If Glenn is forced to one (the actual outcome) their chances drop to 14%.

WP = .14x + .33y + .67z = .33

The actual outcome that occurred was, I believe, the least likely. Glenn made the surprising mistake of being heavy. If he is light, even third shot, a deuce for Howard remains the most likely outcome. A little heavier and there may not have been a chance for the double by Pat, leaving a deuce possible. Glenn’s rock happened to land in the worst possible spot and I’d suspect this would happen perhaps 10% of the time. If we assume x=.1, how often does Howard need to score three to make this the correct call?

z = .05 or 5%

If we estimate the chance of scoring a single as 20%, then z doubles to 10% and it becomes a questionable call.

I like the call but not the execution. It was a shot which had very little margin for error and probably would result in a deuce anyway. If this is the 7th end, there is no question it is the correct call. Because it’s the 6th end there is some argument to taking the nearly “sure” deuce and 2-1 odds instead of risking 14%.

2. Kevin Martin vs Mike McEwen – Quarterfinal

In the 4th End, Martin is up 4-2 and McEwen has the hammer. John Morris hits the open BJ Neufeld stone in the 12 foot. On Neufeld’s next rock, thirds last for the McEwen team, they choose to hit and roll rather than draw. Martin then has an open hit when the roll is not made. Mike Harris points out that McEwen may then be unable to play behind the guard based if Kevin hits on the nose. As it turns out, Kevin rolls to the four foot and Mike has to hit.

Martin is Red

At this stage in the Middle Game, Mike has a 21% WP (Win Percentage) if the end is blanked and 38% WP if he can score two. Even if Mike is forced to 1, the WP = 21%. This stat clearly shows that there is no need to play for a blank as an option, there is no advantage to do so. If we add the fact they are playing Kevin Martin, the odds may be more in favour of attempting a deuce. Martin historically is 49-7 (87.5%) when 2 up without hammer and 4 ends to play. Mike could consider that Kevin’s numbers have come against teams weaker than his own. That is a factor he needs weigh against the baseline statistics to then estimate his teams’ likely chance of winning in this situation.

In any case, I prefer the draw on third’s last rock when it was available. Perhaps others might disagree.

After the blank in the 4th End, Mike has another draw opportunity in the 5th End and chooses instead to attempt a hit and roll on Neufeld’s first.

Mike Harris mentions that, especially on this ice, the draw is much higher percentage shot. I would agree.

In the 7th End, McEwen is behind 6-3 with hammer but after a jam on Kevin’s run-back attempt, is looking at scoring 3 and possibly even 4. Mike makes a draw around the corner guard to sit four and Kevin, as expected, attempts a double on the two open McEwen stones. Martin surprisingly noses the top rock leaving yellow sitting two.

Mike Harris states there is a double for four if he wants to attempt it. He does and misses, scoring only two. If McEwen simply draws for three, WP = 25%. Per earlier analysis, Mike may believe it to be even less, given his competition. If he is able to score 4, they would be 1 up without hammer playing the final end and WP = 60%. Interestingly, Martin is 12-20 or 37.5% when down 1 with hammer in the final end; very much in line with the average. Needless to say, the triple does not have to be made often for this to be the correct call. The miss, however, needs to be thick to get three and as is often the case. I’ll spare the reader the formula, but even if McEwen makes the same mistake 30% of the time and only gets the double 10%, it is still a break even decision.

3. Kevin Martin vs Thomas Ulsrud – Semi-Final.
In the 4th End, a surprising call by Kevin. Tied 2-2 with hammer, he is about to throw skip’s first rock.

Martin is yellow

To the surprise of many, including me, Mike, Joan and likely Ulsrud, Kevin elects to draw to the back four foot with the out-turn, rather than play a double. Harris comments that perhaps Kevin doesn’t feel the double is an easy shot. Martin may have also believed the top red likely jams on his own yellow and, with the swing in the ice and long guard, Ulsrud could be left with a possible hit to lay two. An interesting call which could have backfired if his rock was not placed perfectly. As it happened, Kevin and John then discussed the outcome and Kevin appeared to be more focused on the risk of Ulsrud tapping while John saw the possible chap and roll into the centre which would make it difficult for Martin to score. Was Kevin possibly so focused on one outcome that he missed seeing the other risks in his call? Unfortunately for Thomas, his final shot racked on the top red and left a draw for three.

4. Kevin Martin vs Glenn Howard – Final.
Mike Harris mentions during lead rocks that if Kevin Martin gets a deuce in the first end they are tough to beat. Are they ever! Kevin Martin is 80-6 (93%) since 2003 when up two without hammer and 7 ends remain. Glenn can at least take solace in the fact the last time Martin lost in this scenario was the BDO Final last year when his squad was able to overcome an 0-2 deficit against Martin.

In the 1st End, Glenn, without hammer, is faced with some options on his last shot.

Martin is yellow

Glenn elects to try and hit and roll in front of the yellow stone in the back eight foot. This would force Kevin to try a delicate hit for two or possible he may draw for one if the shot is perfect. Surprising that Glenn does not choose to play a soft hit and try to flop behind the centre guard, Joan mentions this is her preferred call. Another option is to simply try the thin double. I’m not sold on the shot that was called and prefer either the hit and roll inside (if it’s possible) or a freeze. The rock is right on the pin hole and a freeze will leave no draw for two. Depending on the location, Kevin may have a big weight double to remove his own shot stone, keep his shooter, and score two.
It’s possible Glenn was not entirely certain of ice and weight, being the first end. However, the hit and roll had, I suspect, had a similar margin for error if not more than the other options. Given Kevin’s record when 2 up and 7 more ends to play, I believe Howard would be better suited to look at all options, even those that may appear too aggressive for the first end of a game, even a Grand Slam final.
Further to this theory, when down 2-1 without hammer in the 3rd End, Richard Hart misses on a run-back on his first and John Morris splits the rings.

Rather than call a hit on Richard’s last, Glenn could have attempted a freeze and tried to escape the end. They instead try to roll to centre, to possibly set up a later attempt at a double on skips rocks. I believe the freeze was a better play, given the situation and score. Three down with 5 ends remaining WP=11% as an average and Kevin’s team is 67-3. On Glenn’s last shot he also elects to play a hit when a freeze may have been the more statistically correct call.
Incidentally, Glenn Howard is 87-12 when leading by 2 without hammer and 7 ends remain. No slouch either.

Some points in defense of Howard:
  • 25-23 (52.1%) when 2 down with hammer and 7 ends to play
  • 5-14 (26.3%) when down 3 with hammer and 5 ends remain. 
The question a team needs to ask is; given my strength vs the average team and my opponents strength versus the average team, and understanding these are small sample sizes, what will my outcome be against this opponent?  This answer involves adjusting the WP based on your team's ability and the strength of your opponent.  More on this in a future article.

Enough for tonight, I’m heading to sleep. Sweet dreams math fans. Mine are filled with nightmares of Favre throwing yet another play-off ending interception…..then I wake up and realize it wasn’t a dream.

Wednesday, January 13, 2010

The National…To tick or not to tick…BC Scotties 8th End

Greetings and Happy New Year to all. Many items to dig into this month so let’s get right to it….

1. Grand Slam - Swiss Chalet National

Semi-Final: Brad Gushue vs. Glenn Howard
A rematch of the 2007 Brier final.  That game included an interesting decision by Gushue which I analyzed here

One of the more interesting decisions in this rematch was the 1st End. Tied (naturally) without hammer, Gushue was faced with an option on his first rock to be aggressive and attempt a steal but instead chose to peel out the Howard stone protecting his rock in the four foot. This shot call forced Howard to a single rather than giving Gushue a chance at a possible steal.

Gushue is Red

Down 1 with hammer and 7 ends remaining WP = 47%.
Down 2 with hammer and 7 ends remaining WP = 26%

Assuming the most Howard will take is two, how often does he need to estimate a deuce occurs for the Gushue call to be correct?

We will assume that if Gushue peels Howard will always take 1. Chance of a blank is assumed negligible.

x = Gushue steal
y = Howard scores 1
z = Howard scores 2
.47 = .53x + .47y +.26z

Simply looking at the equation, if x =0 than the correct decision is to peel. Let’s choose x as 25%.
.47= (.25)(.53)+(1-z-.25)(.47)+z(.26)
Solving for z = 7%

Would appear the decision which at first seemed conservative is very prudent, given the estimates we have chosen. Hard to believe that with the Gushue rock behind the button that Howard will fail to prevent a steal at least 75% with two rocks to come. Even if Howard never scores a deuce and Gushue steals 50% of the time, he only increases his WP from 47% to 50%.

Finals: Brad Gushue vs. Randy Ferbey

3rd End
Game is tied, Ferbey has hammer. Gushue places a centre guard with the first stone. Marcel places his stone in a high position, biting the eight foot. Gushue elects to play a runback on his own rock, which he is entitled to do under the 4-rock Free Guard Zone rules. Not a play we see very often. Teams commonly play a corner freeze regardless of the placement of this stone. I think this type of play could be used more often.

What is interesting is, tied with 6 ends remaining, a team chooses to place a guard without hammer – while two ends previously they commonly put it in the rings.

This leads to a question a poster on CurlingZone asked: “If you have hammer in the first end of an eight end game and your opponent places a rock in the rings, should you hit with desire to blank the end and have hammer in the second?”

The odds do not change from 8 ends to 7 ends remaining. Beginning eac end, probable outcome for Tied with hammer WP= 61%, one down with hammer WP=43% and down two with hammer WP=26%.  These ends are considered the Early Game, which I explained in this past article:

Possible reasons for choosing this play:
  • If your opponent is stronger you may want to shorten the game.
  • You want to conserve time by playing a quick end early
  • You are unfamiliar with ice and/or rocks
There may be other considerations I haven’t addressed. I prefer aggressive play as outlined in a previous article:

However, taking into account other considerations could lead a team to the decision to play an open end for a blank. As always, understanding the numbers is a first step but situational analysis must always be considered as well.

4th End
Ferbey is up 2-1 without hammer. It is Nedohin’s last rock of the end.

After much discussion, the Ferbey rink decided to play a freeze to shot stone in the four foot, forcing Gushue to make a difficult shot for multiple score or possibly even steal. Dave makes a great shot but not quite perfect and Gushue is left with a run back for three, which he makes.
Gushue is Red

Gushue is Red

At one stage, the Ferbey team discussed hitting the half open Gushue rock in the eight foot, conceding a deuce. Randy mentioned he was unsure of the ice, though I ‘m surprised given it’s the 4th end and the final game of the event. The question I had is, if they could be assured of conceding a deuce, how often does Dave’s rock need to be perfect to make the shot call they attempted?

When 1 down with hammer and 4 ends remaining WP = 41%

If Ferbey attempts the freeze, 4 outcomes are possible: steal, Gushue takes one, two or three. This leaves a lot of possible outcomes to examine.
WP = .79s + .62x + .41y + .21z

Let’s examine extreme case where Gushue scores three 60% of the time, deuce 20% and 10% forced to one and 10% a steal.
WP = 35%
If z becomes 30% and a deuce (y) becomes 50%, WP = 41%.

It’s very likely if Nedohin’s shot curls 2-3 inches more the play for three is not even possible. I’d suggest Ferbey’s estimation of David placing the rock perfectly would lead him to believe giving up three is not likely higher than 30% and is certainly not 50%.

What we don’t know is, if Dave’s rock had been short, leaving Gushue sitting one, would Gushue simply draw for two anyway, rather than attempt the hit for three?

7th End
Tied without hammer, Ferbey has a long off centre guard and a Gushue stone in the wings. It is Nedohin’s first shot.

Gushue is Red

They could choose to play around the guard and attempt to steal or force Gushue to one at the risk of a possible deuce. They instead choose to hit and increase the likelihood of a blank, which occurs, and then need to steal in the final end to win (WP=25%).

Compare this decision with their choice to risk a difficult double for two to go one up against Howard in the Olympic Trials, rather than take a single and be tied without coming home.

Here they take a very different approach. Perhaps it was their competition, thinking the chance at a steal was better than in the previous situation. Instead it could have been the ice conditions and the length of the guard led Ferbey to believe a deuce was simply too likely. In either case, a somewhat surprising call given Ferbey’s aggressive nature. Looking at the numbers, assuming a draw attempt will result in no blank, if we assume Ferbey never steals, he will need to successfully force a single by Gushue at least 45% of the time to make it the correct decision.

2. Tied with hammer “To tick or not to tick”
I recently read Russ Howard’s book “Curl to Win”. In it, he discusses the situation of tied with hammer in the final end. His preferred strategy is to play both leads rocks into the top of the rings, allowing your opponent to place two centre guards.

I noticed this weekend that both Gushue (against Ferbey in the final) and Koe (against Murdoch in the quarterfinal) adhered to this philosophy. Ferbey, in his round robin game against Gushue chose the alternate strategy of playing tick shots to remove both guards. Interestingly, Russ’ brother Glenn used the tick strategy during the Olympic Trials against Koe.

Both Gushue and Koe won their games, but both had tense finishes in which their opponent had chances to perhaps pull out a victory.

I can appreciate Russ’ approach, but prefer the tick strategy for a few reasons, one of which he mentions in his book.

  1. If the first tick is missed, you can choose to draw around on your next shot. I believe a well placed rock has nearly as much benefit as placing two stones, and still provides an option to make the tick shot.
  2. At this level, teams should be able to succeed at the tick shot. It would surprise that top teams would not be extremely proficient at making the tick shot a high percentage of the time.
  3. If you could walk down to the end of the sheet and place the stones, what would you do?. The obvious answer is open the front of the rings by moving the guards. So if you can’t move the rocks correctly by throwing them, practice until you can.
  4. More rocks give the team behind more options.  This is a general concept that does not clearly translate to all situations, and does not have sufficient data to defend, but may have some validity in these scenarios.
I suspect over time the tick will become the more common play, but for now the “draw twice” strategy appears to have some followers.

3. BC Scotties - Kelly Scott vs. Kelly Law
Several posts on CurlingZone related to Kelly Scott’s decision to draw for a single point in the eighth end of the BC Provincial final. Rather than blank and start the 9th end 2 up with hammer, Scott chose to be three up without and two ends remaining.

The numbers actually indicate the decision is equal, a team’s WP =7% whether they are down three with or two without hammer. I would support either decision as it was made based on any number of other factors such as ice conditions or opponent.

To those posters who state that Scott made a horrible decision and it almost cost her the game due the outcome which almost occurred in the 9th end: you are wrong. Basing how a single end plays out and what occurs is irrelevant to how a decision is reached beforehand. Even if you argued Kelly made a wrong decision that her competition and/or conditions should have led her to blank, it simply is not a big enough “mistake” in that case to have a substantial impact. For example, if she was 100% wrong (and she wasn’t), Law’s chances only increase to 14%, still a Dominant position for Scott.

Congratulations to all the Scotties Provincial Winners. Also, congratulations once again to the Lobel Team for gaining a third straight trip to the Provincials in Ontario. 

Until next time, remember to keep your numbers in mind before placing your broom.