Comments on: Is it better to play your strength or your weakness? Finding the right mix http://mindyourdecisions.com/blog/2009/01/27/is-it-better-to-play-your-strength-or-your-weakness-finding-the-right-mix/ Articles on game theory and personal finance Thu, 29 Jul 2010 12:43:59 -0500 hourly 1 http://wordpress.org/?v=3.0 By: Frank http://mindyourdecisions.com/blog/2009/01/27/is-it-better-to-play-your-strength-or-your-weakness-finding-the-right-mix/comment-page-1/#comment-5574 Frank Sun, 06 Sep 2009 05:40:36 +0000 http://mindyourdecisions.com/blog/?p=1230#comment-5574 Presh, Glad to have found your blog. I am reading the Dixit book right now and am very interested in his tennis example. You did a nice job recreating it, although I want to point out a very convenient calculation method to determine the optimal mix strategy. For the server's perspective, take the difference between the two possible payoffs he receives when aiming to the forehand, and do the same for when he aims to the backhand. Make a ratio out of these two values, this ratio is the optimal serve strategy to the backhand:forehand side. Note that you have to reverse the ratio if you want the forehand:backhand. For this example, to get the forehand:backhand ratio you would see that for forehands nadal gets 70 or 50, difference of 20, and for backhands he gets 80 or 50, difference of 30. So his ratio of forehands:backhands is 30:20 or 60:40. I think this is a really cool method that has illustrates the mechanism of whats going on. It shows us that the larger the difference is between the payouts of our opponents options in response to our strategy, the less often we should use that strategy. Presh,
Glad to have found your blog. I am reading the Dixit book right now and am very interested in his tennis example. You did a nice job recreating it, although I want to point out a very convenient calculation method to determine the optimal mix strategy.

For the server’s perspective, take the difference between the two possible payoffs he receives when aiming to the forehand, and do the same for when he aims to the backhand. Make a ratio out of these two values, this ratio is the optimal serve strategy to the backhand:forehand side. Note that you have to reverse the ratio if you want the forehand:backhand.

For this example, to get the forehand:backhand ratio you would see that for forehands nadal gets 70 or 50, difference of 20, and for backhands he gets 80 or 50, difference of 30. So his ratio of forehands:backhands is 30:20 or 60:40.

I think this is a really cool method that has illustrates the mechanism of whats going on. It shows us that the larger the difference is between the payouts of our opponents options in response to our strategy, the less often we should use that strategy.

]]> By: Ivar Källblad http://mindyourdecisions.com/blog/2009/01/27/is-it-better-to-play-your-strength-or-your-weakness-finding-the-right-mix/comment-page-1/#comment-5199 Ivar Källblad Sat, 25 Apr 2009 11:57:01 +0000 http://mindyourdecisions.com/blog/?p=1230#comment-5199 In some matches the server wins a higher percentage of the points after the first serve included the faults of that serve than he does on the second serve that is 100 percent in. What does game theory say of the solution of only hitting first serve strokes on the serve. In some matches the server wins a higher percentage of the points after the first serve included the faults of that serve than he does on the second serve that is 100 percent in. What does game theory say of the solution of only hitting first serve strokes on the serve.

]]> By: Presh Talwalkar http://mindyourdecisions.com/blog/2009/01/27/is-it-better-to-play-your-strength-or-your-weakness-finding-the-right-mix/comment-page-1/#comment-4558 Presh Talwalkar Fri, 06 Feb 2009 07:10:49 +0000 http://mindyourdecisions.com/blog/?p=1230#comment-4558 The mix must be random, as you point out <b><em>Scott</b></em>, or else it will lose out as opponents learn the patterns and respond in kind. Thanks for the excellent analog in football <b><em>Drobviouso</b></em> The mix must be random, as you point out Scott, or else it will lose out as opponents learn the patterns and respond in kind.

Thanks for the excellent analog in football Drobviouso

]]> By: Ravi Grover http://mindyourdecisions.com/blog/2009/01/27/is-it-better-to-play-your-strength-or-your-weakness-finding-the-right-mix/comment-page-1/#comment-4499 Ravi Grover Fri, 30 Jan 2009 04:44:41 +0000 http://mindyourdecisions.com/blog/?p=1230#comment-4499 Rnadomness is important -- I remember reading a study that found that the top tennis players had serve patterns that were indistinguishable from randomness, while worse players did not Rnadomness is important — I remember reading a study that found that the top tennis players had serve patterns that were indistinguishable from randomness, while worse players did not

]]> By: Drobviousso http://mindyourdecisions.com/blog/2009/01/27/is-it-better-to-play-your-strength-or-your-weakness-finding-the-right-mix/comment-page-1/#comment-4498 Drobviousso Thu, 29 Jan 2009 21:41:12 +0000 http://mindyourdecisions.com/blog/?p=1230#comment-4498 This is very similar to the run/pass balance problem in the NFL, which has bedeviled both of the participants of the superbowl this year. For 'zona, they have a fantastic passing game and a comparatively abysmal running game. They have made a conscious effort to run a lot, in order to keep the opposing team's defense honest. This is a big problem against very good run stuffing teams that can stop the run from the nickle (the set with more resources to stop the pass than the run). Their Superbowl opponent Pittsburgh is capable of doing this. For Pittsburgh, their offensive coordinator wouldn't know a random play call if it put his cat in box that may or may not release poison gas. I believe (but don't have proof) that they run more Run-Run-Pass pattern of plays than any other team in the league. Thus, opposing teams can stack the box (the set with more resources to stop the run) on first and second, and then focus on the pass on 3rd down. http://smartfootball.blogspot.com/2008/06/runpass-balance-game-theory-and-passing.html (go Stillers!) This is very similar to the run/pass balance problem in the NFL, which has bedeviled both of the participants of the superbowl this year.

For ‘zona, they have a fantastic passing game and a comparatively abysmal running game. They have made a conscious effort to run a lot, in order to keep the opposing team’s defense honest. This is a big problem against very good run stuffing teams that can stop the run from the nickle (the set with more resources to stop the pass than the run). Their Superbowl opponent Pittsburgh is capable of doing this.

For Pittsburgh, their offensive coordinator wouldn’t know a random play call if it put his cat in box that may or may not release poison gas. I believe (but don’t have proof) that they run more Run-Run-Pass pattern of plays than any other team in the league. Thus, opposing teams can stack the box (the set with more resources to stop the run) on first and second, and then focus on the pass on 3rd down.

http://smartfootball.blogspot.com/2008/06/runpass-balance-game-theory-and-passing.html

(go Stillers!)

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