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Tuesday, February 17, 2009

Scotties Decision by Team Canada and Middle Game Strategy

Jennifer Jones’ Team Canada rink made some interesting decisions in their round robin game against Ontario at the 2009 Scott Tournament of Hearts (Scotties). During the 6th end, Team Canada (TC), one down without hammer, could have chosen a more aggressive route during the latter part of the end. Instead of drawing around their opponent’s stones in front of the rings, they instead chose to hit the Ontario stone towards the back of the rings and play out the end as a blank. Was this the correct decision? Recall:

Notice that if the end is blanked, TC has a 24% chance. At the beginning of the 6th they had a 22%. In fact, their odds get slightly better if the end is blanked.

If they play aggressive and steal, they increase their chances to 40%. Holding Ontario to one is 22%. In fact, a blank appears to be 2% better than actually forcing Ontario to a single point! It appears the risk of attempting a steal at this stage is not necessary.

What about in the next end? If it had been the 7th instead of 6th end, the decision is very different. Now, entering the 8th end when 1 down without hammer, the odds are only 18%. Holding Ontario to a single gives a 21% chance. A steal in 7 instead of 6 still leaves them 40% - no change. It would be more tempting to play the final rocks aggressively if it were the 7th end. If the 7th were to be blanked and TC is one down without hammer playing 8, it is imperative to either score a steal or force opponent to a single. When entering the final two ends 1 down without hammer, a teams chance drops to 16% - but more importantly, a steal in 9 gains less. A steal in 8 would produce a tie and a 39% chance, but a steal in the 9th to tie the game is only 30%.

The 5th and 8th Ends
Recall my previous article on Early, Middle and End Game. The Early Game is the first 4 (or 2) ends. At this stage, most top teams will play aggressive attempting to take control or dominant control as soon as possible. In the End Game (final 3 ends), teams will play the scoreboard more closely, attempting to be tied with hammer or two up without hammer in the final end of a close game. So what is Middle Game Strategy?

Middle Game is the 5th through 7th ends in a ten end game (or 3-5th in an 8 end game). Recalling my previous description, statistical changes start to appear in the middle game. Trends appear for each situation (tied with hammer, 1 up without, etc). So what are some considerations when determining our Middle Game Strategy?

The first decision is whether to continue aggressive play. This is usually the case early in each end, but as the end develops a team will choose shot calls based more on scoreboard and ends remaining before the End game. So to start discussion on Middle Game strategy, let’s start by examining which scenarios are more favorable in the End Game.

I will use a 10 end game from now on, the reduce complication. To transfer this analysis to an 8 end game, just subtract 2.

In the 9th End, one down with hammer is a disadvantage greater than any other point in the game. In fact, only the scenarios starting the 9th and 6th ends have tied without hammer the same (less than 1%) as one down with hammer. In all other cases, one down with hammer is preferred position. If we have the hammer in a close game the ends previous (5th and 8th), it allows us to take some additional risk with less penalty for being forced to a single point. Recall a Close game is one in which a team is down one with hammer anytime or tied prior to final two ends.

One down with hammer:
In the 5th and 8th ends we can aggressively play for two or three and if we are forced to one, our chances are actually the same as if we had blanked the end. If we instead are one down with hammer in other ends, if our aggression results in being held to one, we are worse than if we blanked the end.

One up without hammer:
Conversely, forcing our opponent to one in this situation (5th or 8th end) gains no advantage over blanking the end. The risk of playing aggressive to force our opponent to one, which may result in a deuce, provides no advantage – a steal is required to gain any advantage. Stealing in the 5th puts us at a 76% winning probability (Control). Stealing in the 8th an 85% chance (Dominant Control). Blanking 5 and then stealing in the 6th in fact gives us now an 80% chance. I’d suggest a sensible play is to tempt our opponent into blanking the 5th end and force our position without hammer in the next end. Blanking the 8th was discussed in our last article and is more open to debate.

Tied without hammer:
If we force our opponent to a single, we again gain no advantage to blanking. However, a steal is a significant advantage over our current position. For the 5th end, in our previous example (one up without) a steal takes us from a 61% chance to 76%. If we are tied and steal, we move from 39% to 61%. Using our analysis from the last article, switching from 39 to 61 is 50% better, whereas 61 to 76 is only 25% better. For the 8th end we go from 34 to 65 (91% better). It would appear we are more inclined to attempt to steal in this scenario. However, stealing is always difficult and we risk our opponent making a multiple score. We are forced to be more aggressive because of our position but being one down with hammer gives us an ability to be aggressive without the same risk.

Tied with hammer:
Being forced to one in the 5th or 8th end is no mathematically disadvantage. In all other ends, being held to one is a disadvantage over a blank. Again, per situation one down, we can be very aggressive at the risk of being held to one. However, as pointed out above, a steal is very bad for us in this position. In fact, a steal is very bad for us every time in this position. It is most critical in the 9th where we drop from 74% to 38%.

In every case, having hammer appears to be a greater advantage in this position. We can be aggressive without any risk of being “held to a single” as it is virtually no different mathematically from a blank.

So…what is our finding? In a close game, we’d prefer to have hammer in the 5th and 8th ends. We may in fact make decisions in the ends previous which will force this situation. For example, if we are tied playing the 4th with hammer and have an opportunity to blank, we are more inclined to take this route. If we are one up in the 4th or 7th, we should force our opponent into scoring, even at the risk of a deuce, in order to have hammer in following end. Eight end games become interesting because the advantage exists in the 3rd end. A team may even choose to tempt a blank if they are without hammer in the first end, to force their opponent to score in the second end, in order to have hammer in the third. This seems drastic and I’d suggest the advantage is not significant enough to “drop an end”. But further analysis might disprove my initial thinking.

Some readers may have noticed that there are two ends between the 5th and 8th. This means, without a blank or a steal, if we have hammer in one of these ends, our opponent has hammer in the other end. For example, say having hammer in the 5th when one down results in a deuce. We are now one up. If our opponent is held to one and then we are held to one, we are now one up without in the 8th end. However, if our opponent ties us in the 6th and we instead manage a blank in the 7th, we are now tied in the 8th with hammer.

I would not suggest this analysis should be a factor in how a team begins play in and end. The modern game does not allow a team to force a blank end at will. However, as an end develops we may be more inclined to “bail out” of certain ends in order to better position us in ends where we have greater advantage with hammer in a close game.