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Who has the best chance to serve out the match - Nerve van Steel or Brilliant Choker?

  • Brilliant Choker - there are more points played where this guy has the advantage

    Votes: 3 33.3%
  • Nerve van Steel - you always gotta win the last point, and van Steel has a major edge here.

    Votes: 3 33.3%
  • Ban OP - handing out difficult math exercises just for fun - this is a tennis forum for f*ck's sake.

    Votes: 3 33.3%
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Discussion Starter #1
I waited with this thread until the off-season, since there is a shortage of things to discuss. It might not be for everyone, though. An interest in math or in tennis betting is probably required to appreciate this topic. If you continue to read without meeting this criterion, be aware that you only have yourself to blame. :geek:

Now imagine this: In the distant future, let's say ten years from now, you have managed to get the job as a coach for one of the world's top tennis players. The ATP final is here, and your man will pass the group stage if he just serves out the match, leading 5-4 in the third. However, his group is extremely tight. Who advances depends on the game count with this single decisive game making all the difference (it is a three-way race with three players about to get two wins and the same win-loss ratio in the set count). If your player gets broken, he won't pass the group stage due to the game count, no matter if he wins 7-5* later on. To make matters even more thrilling, reaching the semi will likely suffice to give your player the year-end number-one spot. In your contract, there is a huge bonus if your man pulls that off. When your player steps up to the service line and bounces the ball, you can hear your heart beating.

And here is the tricky part - in our imagined scenario - the player you are coaching is one out of two possible options:

Either you train Brilliant Choker (his name is just a funny coincidence due to the parents not speaking English), perhaps the best player in the world, but with an unfortunate habit of getting tight when closing out matches. His chances of winning the points on serve are 80 % in this particular match-up. However, from painful experience, you know that his level drops dramatically if he gets a match-point. Whenever he has a match-point, his probability of winning the point on serve is just 40 %. Curiously enough, he can still play good in other tight situations, for example, deuce or break point down. Thus for all other situations, except having match-point, the 80 % win probability applies.

The other option is that you train another player, namely Nerve van Steel. He is also a good candidate for the world's best player. Recall that from our starting assumption, the top spot was on the line. However, unlike Brillant Choker, your man van Steel is a miracle of composure in this case. The win percentage on serve is the same independent of the score and is given by 70 %.

So who would you rather coach in such a situation? Both players are dominant on serve and have a good probability of succeeding, obviously. Thus your chances of getting the bonus are promising, no doubt, but who would you give the best odds? The math nerds can compute the probabilities, most likely, but it takes a little work (particularly the case of Brilliant Choker requires a bit of patience). The experienced betters might have a feeling for the right answer and could make a good guess without actually making the computation. Others could make a choice in the poll, depending on who you sympathize with. Federer fans that have been burned by this year's Wimbledon will probably refrain from voting. Note though, that this thread is not intended as a dig at the old man - and who knows, Brilliant Choker might be the guy with the best chance after all.

A bonus point is awarded to anyone that can give the correct probabilities for "Nerve van Steel" and "Brilliant Choker" to serve out the match for the given specifications.

* For this to make sense, actually 7-5 has to give an identical game count in the three-way split (6-4 gives a better ratio), and we assume that things come down to counting points, which is not beneficial for our hero.
 

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Given that the deuce-advantage scenario can occur an unlimited number of times in theory, is it possible to calculate an exact probability for the Brilliant Choker?

(No need obviously to reveal the answer: just a clarification of this point would be appreciated.)
 

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Great thread OP. Loving your ideas here. Re the question...having worked with both a lot, chokers will always choke once they choke once. The only way to stop is to be so good its not close. Which is unrealistic.

So i rather coach Nerv van steel. The dutch are good mentally plus if you are good you will improve them to get tp the big points.

At least that player will win when supposed to. Its horrible to lose when you should wim
 
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Probabilities of victory:
van Steel: 0.7^4 + 4*0.3*(0.7^4) + 10*(0.3^2)*(0.7^4)/(1-2*0.3*0.7) = 0,900788966
Choker: out of memory error = 0,945712889

Thus I would choose Choker.
 

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Discussion Starter #8
Probabilities of victory:
van Steep: 0.7^4 + 4*0.3*(0.7^4) + 10*(0.3^2)*(0.7^4)/(1-2*0.3*0.7) = 0,900788966
Choker: out of memory error = 0,945712889

Thus I would choose Choker.
Yeah, that is the same formula I got for van Steel. For Choker I rounded off the numbers to three digits, but they do agree. Come to think of it, it was a mistake to like your post. My intention was not that the right answer should be revealed this quickly. :sneaky:
 

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Probabilities of victory:
van Steel: 0.7^4 + 4*0.3*(0.7^4) + 10*(0.3^2)*(0.7^4)/(1-2*0.3*0.7) = 0,900788966
Choker: out of memory error = 0,945712889

Thus I would choose Choker.
Thanks for doing this. I wanted to myself but was too lazy and knew someone would soon come around :p

Anyway, though Choker might win this math exercise, in reality he would also get tight on BPs, deuce points, etc. Especially knowing how much depends on the result of this match. So the real odds favor van Steel the closer the match is and definitely in this case.
 

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Yeah, that is the same formula I got for van Steel. For Choker I rounded off the numbers to three digits, but they do agree. Come to think of it, it was a mistake to like your post. My intention was not that the right answer should be revealed this quickly. :sneaky:
Unfortunately there's always some nerd who spoils the party :geek:
 

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Discussion Starter #13
Given that the deuce-advantage scenario can occur an unlimited number of times in theory, is it possible to calculate an exact probability for the Brilliant Choker?

(No need obviously to reveal the answer: just a clarification of this point would be appreciated.)
Supercell gave the right answer (unfortunately very quickly :mad:). The possibility of an infinite number of points is not a problem due to a recursive relation, which leads to the denominator of the last term in Supercell's expression for van Steel. The same type of reasoning works also for Brilliant Choker, but the larger number of terms makes it more practical to give a rounded expression.
 

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Anyone who was ever a fan / coaching team / related to a choker will answer that in a flat second. Chokers ruin you so much it's like torture sometimes.
 

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Supercell gave the right answer (unfortunately very quickly :mad:). The possibility of an infinite number of points is not a problem due to a recursive relation, which leads to the denominator of the last term in Supercell's expression for van Steel. The same type of reasoning works also for Brilliant Choker, but the larger number of terms makes it more practical to give a rounded expression.
Actually I don't even know the formula for Choker: to do it quickly I used dynamic programming (calculating probabilities of various states of game in excel table based on previous states - recursive relations) plus obviously finite sum of geometric series (that you mentioned) from deuce on.

Even though choker is better at the end, coaching him would increase the likehood of heart attack (longer game duration). So maybe it's a bad choice after all :D
 

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I'd choose dull van faker. Two mental beasts combined would make a giant impossible to beat. That would be the easiest job in the world.
 

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Van Steel obviously

Strokes are easy to teach, guts are not

Brilliant Choker will obviously choke brilliantly

I'd rather have Ferrer than Kohlschreiber
Pretty much this, coaching physical parts of the game is much easier than coaching mental parts which a lot of times, never really improve and ultimately hinder players’ careers despite having the physical potential of a great player (Monfils, Verdasco).
 

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Honestly you can take your numbers and shove it

Tennis is played with guts, not calculators
But the question is who you would rather coach.

So mister Calculator de la Gymnast is exactly the kinda player I want to coach (more than both Brilliant Choker and Nerve Van Steel), because De La Gymnast will do exactly whatever new trick I tell him to adopt and experiment. If it fails he will easly move on to trying something else. Ideal for a coach.
 
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