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Topic: Anyone For Tennis? (Read 9286 times) |
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Noke Lieu
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Re: Anyone For Tennis?
« Reply #50 on: Sep 9th, 2007, 9:21pm » |
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on Sep 9th, 2007, 9:14pm, ThudanBlunder wrote:
I know what you meant, so did not type.
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SWF
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Re: Anyone For Tennis?
« Reply #51 on: Sep 9th, 2007, 9:23pm » |
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on Sep 9th, 2007, 6:54pm, ThudanBlunder wrote:
My formulae assume that the same person is always serving. So P(GAME) will be accurate, but not the others.
Similarly, 6.48 points per game ought to be accurate, but not the others. |
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I meant the assumptions of p=0.6 and ignoring the difference between serving and receiving are probably the main causes of the match set and match probabilities being so high. For comparable players, the better player might have probablity of winning a point of 0.75 when serving and 0.3 when receiving. Also, a good player would account for the game/set/match format in his strategy, and might even intentionally lose some points. So a fixed probability for each point does not tell the full story.
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srn437
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Re: Anyone For Tennis?
« Reply #52 on: Sep 9th, 2007, 9:30pm » |
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Intentionally lose points? This is tennis, I don't know what you think it is(golf perhaps).
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ima1trkpny
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Re: Anyone For Tennis?
« Reply #53 on: Sep 9th, 2007, 9:42pm » |
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on Sep 9th, 2007, 9:30pm, srn347 wrote:| Intentionally lose points? This is tennis, I don't know what you think it is(golf perhaps). |
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Sometimes, strategically speaking, taking some sort of loss will set up a situation that creates a net gain... take this situation for example: Let's say you're playing baseball (hopefully you are familiar with the rules, otherwise I will create a new scenario). If you have 2 runners on base and Barry Bonds comes up to bat, the smartest thing strategically to do would be to walk him. Essentially losing in that one encounter in order to avoid him hitting it out of the park and also to "load" the bases setting up double or even triple plays that would allow you to come out ahead in the long run. Think of it in terms of the old adage about losing one battle doesn't necessarily dictate the outcome of the war.
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srn437
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Re: Anyone For Tennis?
« Reply #54 on: Sep 9th, 2007, 9:51pm » |
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Walking in baseball I understand, but in tennis what is this "net gain" of losing points?
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ima1trkpny
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Re: Anyone For Tennis?
« Reply #55 on: Sep 9th, 2007, 10:20pm » |
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Well the game works of a "best of" either 5 or 7 (depending on male or female players) sets per match, etc
So lets say this is a best of 7. If you have won 3 and your opponent has won 1, and they are currently serving (in which they have a higher probability of winning), by allowing them to win that match, you allow them a victory to gain a point bringing it to 3-2, but you gain the serve. And the idea is that now you have the higher probability and can no go ahead to win with a 4-2 (no need to do the last one since you already have a winning majority), instead of wasting effort fighting the odds against you when it is their serve.
(If I have forgotten or left out any of the rules, etc please correct me as it has been a long time since I have played.)
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srn437
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Re: Anyone For Tennis?
« Reply #56 on: Sep 9th, 2007, 10:25pm » |
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Which is dependant on me already being ahead. Is there a way to use that when it's tied or I'm losing?
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ima1trkpny
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Re: Anyone For Tennis?
« Reply #57 on: Sep 9th, 2007, 10:37pm » |
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on Sep 9th, 2007, 10:25pm, srn347 wrote:| Which is dependant on me already being ahead. Is there a way to use that when it's tied or I'm losing? |
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Working on it... it has been a very long time since I played and my imagination begins to fade when it is late. I just gave the scenario that came to mind considering SWF's post about a good player with advantage... I will work on seeing if there is a way to take advantage of losing some points from a losing or tied relationship... however if someone else can think of anything or can add to my shaky knowledge of possible scenarios I would appreciate it.
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ThudnBlunder
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Re: Anyone For Tennis?
« Reply #58 on: Sep 10th, 2007, 4:11pm » |
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on Sep 9th, 2007, 9:23pm, SWF wrote: Also, a good player would account for the game/set/match format in his strategy, and might even intentionally lose some points.
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I don't see how it can ever be advantageous for a player to lose the next point, but here is an interesting quirk:
Let p = the probabiity that the server wins a point, and q = 1 - p, (0 < p < 1)
Let P(X - Y) be the probability that the server wins the game when the server has X points and the non-server has Y points.
Using your previous method
P(40 - 40) = pP(40 - 30) + qP(30 - 40)
P(40 - 30) = p + qP(40 - 40)
P(30 - 40) = pP(40 - 40)
This leads to
P(40 - 40) = p2/(p2 + q2)
and
P(40 - 30) = p + [p2q/(p2 + q2)]
In a similar fashion we can derive
P(40 - 15) = p + pq + [p2q2/(p2 + q2)]
and
P(30 - 15) = p2(1 + q) + pq + [p2q(pq + 1)/(p2 + q2)]
and
P(0 - 0) = p4(1 - 16q4)/(p4 - q4)
Btw, this gives the unexpected identity p4 + 4p4q + [(10p4q2/(1 - 2pq)]  p4(1 - 16q4)/(p4 - q4)
P(0 - 0) > P(40 - 30) simplifies to 8p3 - 4p2 - 2p - 1 > 0
which is true for p > 0.9196...
and
P(0 - 0) > P(30 - 15) simplifies to 8p2- 4p - 3 > 0
which is true for p > 0.9114...
So we are led to the inescapable conclusion that it is possible for a player to be ahead during the game and yet have less chance of winning than before (s)he started!
For example, when p = 0.95,
P(0 - 0) = 0.9999077...
and
P(40 - 30) = 0.999862...
And conversely,
P(30 - 40) > P(0 - 0) when p < 0.0804...
and
P(15 - 30) > P(0 - 0) when p < 0.0886...
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| « Last Edit: Sep 11th, 2007, 5:15pm by ThudnBlunder » |
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srn437
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Re: Anyone For Tennis?
« Reply #59 on: Sep 10th, 2007, 6:59pm » |
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p<1 It also works at p=1. Or at least the original formula(p^4+q^2+10p^4q^2/1-2pq) does.
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ThudnBlunder
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Re: Anyone For Tennis?
« Reply #60 on: Sep 10th, 2007, 7:08pm » |
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on Sep 10th, 2007, 6:59pm, srn347 wrote:| p<1 It also works at p=1. Or at least the original formula(p^4+q^2+10p^4q^2/1-2pq) does. |
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Obviously if p = 1 there is no more point in playing than there is in reading your posts.
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| « Last Edit: Feb 1st, 2009, 6:29am by ThudnBlunder » |
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SWF
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Re: Anyone For Tennis?
« Reply #61 on: Sep 10th, 2007, 7:15pm » |
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Although I didn't check the math, that is an interesting conclusion, ThudanBlunder.
Within this probabililty model, I can't see an advantage to intentionally losing points. I was referring to reality. If for example, a player leading the match 2 sets to 1, but is losing the fourth set of the US Open 5 games to zero, and he is worn out from the summer heat, his joints ache, and he doesn't think he can play his best for much longer, even though he is a better player than his spry young opponent. He might intentionally lose the the game to end the set he is likely to lose anyway. Then he can get on with the last set before he is worn out. The other player might similarly try to lose some points to counter this strategy and wear down his opponent before the last set.
It is not strange to see a player lose the fourth set 6-0 or 6-1, and then win the match in the fifth set. Of course this doesn't prove he tried to lose some games, and I bet few pros would admit doing so.
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mikedagr8
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Re: Anyone For Tennis?
« Reply #62 on: Sep 11th, 2007, 3:45am » |
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I agree with that about losing intentionally to gain advantage. SWF makes very good points for tennis, and from my own experiences in soccer and various other sports it is true.
E.g. Soccer; Instead of taking on a team from defence, clear the ball into the other half as far as possible, and then work from there. It is quite common when a team is being pressured.
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| « Last Edit: Sep 11th, 2007, 3:46am by mikedagr8 » |
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srn437
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Re: Anyone For Tennis?
« Reply #63 on: Sep 12th, 2007, 8:23pm » |
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In fact, I've played ayso soccer for a year, I'm a defender, and clearing it to the other half of the field is what I usually do.
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ThudnBlunder
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Re: Anyone For Tennis?
« Reply #64 on: Oct 1st, 2007, 5:41pm » |
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on Sep 12th, 2007, 8:23pm, srn347 wrote:| ...I'm a defender, and clearing it to the other half of the field is what I usually do. |
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You mean you just blindly boot it up the field?
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mikedagr8
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Re: Anyone For Tennis?
« Reply #65 on: Oct 1st, 2007, 5:47pm » |
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on Oct 1st, 2007, 5:41pm, ThudanBlunder wrote:
You mean you just blindly boot it up the field?
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Yes. That's the general idea. Of course, there's a lot more of a fine art when you have skill, as to where you kick it. If you are skillful, you can generally set it up in a way to benefit your team, by putting the ball in a position where your attackers can run onto the ball.
Note Before: I've been playing for close to 10 years now, I was a reserve for Australia (don't bother looking me up, you wont find me) in Futsal, and have represented Victoria in soccer as well. This is not coming from an ignorant opinion.
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| « Last Edit: Oct 1st, 2007, 6:47pm by mikedagr8 » |
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sm347
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Re: Anyone For Tennis?
« Reply #66 on: Oct 1st, 2007, 6:42pm » |
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what is your position, left outside?
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mikedagr8
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Re: Anyone For Tennis?
« Reply #67 on: Oct 1st, 2007, 6:43pm » |
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on Oct 1st, 2007, 6:42pm, sm347 wrote:| what is your position, left outside? |
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Depends where I am required in a team. I'm very versatile. My preffered is CDM, but being ambidextrous, I can play anywhere.
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ThudnBlunder
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Re: Anyone For Tennis?
« Reply #68 on: Oct 1st, 2007, 6:50pm » |
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on Oct 1st, 2007, 6:43pm, mikedagr8 wrote:
Yes, we have a CDM in our team and he Cannot Do Much either. 
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| « Last Edit: Jan 3rd, 2011, 2:17am by ThudnBlunder » |
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mikedagr8
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Re: Anyone For Tennis?
« Reply #69 on: Oct 1st, 2007, 6:51pm » |
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on Oct 1st, 2007, 6:50pm, ThudanBlunder wrote:
Yes, we have a CDM in our team and he Cannot Do Much either. |
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LOL. That's a description not a position. That position is Left Back.
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ThudnBlunder
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Re: Anyone For Tennis?
« Reply #70 on: Feb 1st, 2009, 8:25am » |
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on Sep 9th, 2007, 2:27pm, SWF wrote:Here is an attempt at comparing the game/set/match approach to a match to just playing until a certain number of points are scored. To keep it simple, ignored difference between serving and receiving probability and also ignored using the tie breakers for sets...
For a fair comparison to a match being a fixed number of points, need to find how many points are in a typical match. For 0.6 probability of winning each point, I come up with an average of 6.48 points per game... |
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Just finished watching Federer - Nadal. There were 347 points (174 -173 to Federer) comprising 51 games.
That is 347/51 = 6.804... points per game. 
Not a bad fit, considering these two are more evenly-matched than most opponents.
(No, I didn't count the points.)
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ThudnBlunder
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Re: Anyone For Tennis?
« Reply #71 on: Feb 3rd, 2009, 4:01am » |
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SMQ, what was your argument that the tie-break system confers no advantage to either server?
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SMQ
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Re: Anyone For Tennis?
« Reply #72 on: Feb 3rd, 2009, 10:24am » |
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Hmm, I don't recall making that argument. I'm fairly sure the only real tennis discussion I've had was in this thread, and there I argued mostly from "feel" rather than from mathematical probability since the question I was trying to answer was a "what would you prefer" question.
As to the question of a tiebreak advantage, if we assume that the players are evenly matched (a reasonable assumption since they have played to a tie) and so have the same probability p of winning a point on service (and so a probability of 1 - p of breaking service), the exact probability of winning a tiebreak should be a tractable problem.
I'm working on a program...
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ThudnBlunder
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Re: Anyone For Tennis?
« Reply #73 on: Feb 3rd, 2009, 11:31am » |
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on Feb 3rd, 2009, 10:24am, SMQ wrote:| Hmm, I don't recall making that argument. --SMQ |
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Oh, maybe it was Grimbers. Sure I read one somewhere.
Off the top of my head, I would say that the 2nd player has a miniscule advantage as, if every point goes with serve (the most likely scenario, albeit highly improbable), he gets to set point (at 5-6) first. Unfortunately, the absolute expected deviation from this scenario is not zero, as at 5-6 they have not had an equal number of serves.
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| « Last Edit: Feb 4th, 2009, 5:43am by ThudnBlunder » |
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SMQ
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Re: Anyone For Tennis?
« Reply #74 on: Feb 3rd, 2009, 3:56pm » |
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Assuming I haven't made any programming errors, the tiebreak is mathematically fair.
Call the player serving first in the tiebreak A and the player serving second B. Let A win a point on service with probability p, and B win a point on service with probability q. Clearly, then, A wins a point returning B's serve with probability 1-q, and likewise B wins a point returning A's service with probability 1-p. There are three possible outcomes from the first 12 points: A wins 7-x, B wins x-7, and deuce at 6-6.
P(A wins before deuce) = -462p6q6 + 1512p6q5 + 1260p5q6 - 1890p6q4 - 4536p5q5 - 1260p4q6 + 1120p6q3 + 6300p5q4 + 5040p4q5 + 560p3q6 - 315p6q2 - 4200p5q3 - 7875p4q4 - 2520p3q5 - 105p2q6 + 36p6q + 1350p5q2 + 6000p4q3 + 4500p3q4 + 540p2q5 + 6pq6 - p6 - 180p5q - 2250p4q2 - 4000p3q3 - 1125p2q4 - 36pq5 + 6p5 + 360p4q + 1800p3q2 + 1200p2q3 + 90pq4 - 15p4 - 360p3q - 675p2q2 - 120pq3 + 20p3 + 180p2q + 90pq2 - 15p2 - 36pq + 6p
P(B wins before deuce) = -462p6q6 + 1512p5q6 + 1260p6q5 - 1890p4q6 - 4536p5q5 - 1260p6q4 + 1120p3q6 + 6300p4q5 + 5040p5q4 + 560p6q3 - 315p2q6 - 4200p3q5 - 7875p4q4 - 2520p5q3 - 105p6q2 + 36pq6 + 1350p2q5 + 6000p3q4 + 4500p4q3 + 540p5q2 + 6p6q - q6 - 180pq5 - 2250p2q4 - 4000p3q3 - 1125p4q2 - 36p5q + 6q5 + 360pq4 + 1800p2q3 + 1200p3q2 + 90p4q - 15q4 - 360pq3 - 675p2q2 - 120p3q + 20q3 + 180pq2 + 90p2q - 15q2 - 36pq + 6q
P(deuce is reached) = 1 - P(A wins before deuce) - P(B wins before deuce)
= 924p6q6 - 2772p6q5 - 2772p5q6 + 3150p6q4 + 9072p5q5 + 3150p4q6 - 1680p6q3 - 11340p5q4 - 11340p4q5 - 1680p3q6 + 420p6q2 + 6720p5q3 + 15750p4q4 + 6720p3q5 + 420p2q6 - 42p6q - 1890p5q2 - 10500p4q3 - 10500p3q4 - 1890p2q5 - 42pq6 + p6 + 216p5q + 3375p4q2 + 8000p3q3 + 3375p2q4 + 216pq5 + q6 - 6p5 - 450p4q - 3000p3q2 - 3000p2q3 - 450pq4 - 6q5 + 15p4 + 480p3q + 1350p2q2 + 480pq3 + 15q4 - 20p3 - 270p2q - 270pq2 - 20q3 + 15p2 + 72pq + 15q2 - 6p - 6q + 1
(Note that I chose the order of the terms to make it clear that the equations are symmetrical w/rt p and q, i.e. swapping p and q also swaps P(A wins before deuce) and P(B wins before deuce) and has no effect on P(deuce is reached)).
From deuce a player must win two points to win the set. Since deuce can only occur after an even number of points, the next two points will always be served one by each player. To win the set from deuce, then, a player must always win one point serving and one point receiving, and so the probability of winning from deuce is independent of who serves first. Together with the above observation this is sufficient to show that the game is fair.
--SMQ
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