trig shots
- Thread starter demonrho
- Start date
That was a really interesting find.
If I read it right:
As a player approaches more and more perfect accuracy, the hardest straight in shot gets closer and closer to right in the middle of the table... the famous "harder than hitting a dime at 100 yards" long diagonal straight in shot. Closer to the shooter means that whatever imperfection the shooter has in accuracy is minimized. Closer to the pocket means more room for error on the shoot, so the slightly imperfect hits still go in.
When you approach the other end of the scale, where the shooter is getting less and less accurate (but not a complete spaz who will miss the ball entirely)... the hardest possible distance is when the CB is 1.618 x the distance between OB and pocket.
My initial thought is "why shouldn't 2.0 x the distance or greater be more difficult than 1.618? More distance = harder shot." But then I remembered the "can't miss the OB entirely" restriction. So if we're just talking about someone who's definitely gonna get a hit, that's the sweet spot where they're gonna have the hardest time sinking the shot.
I'm trying to extrapolate something useful out of this but so far coming up dry.
If I read it right:
As a player approaches more and more perfect accuracy, the hardest straight in shot gets closer and closer to right in the middle of the table... the famous "harder than hitting a dime at 100 yards" long diagonal straight in shot. Closer to the shooter means that whatever imperfection the shooter has in accuracy is minimized. Closer to the pocket means more room for error on the shoot, so the slightly imperfect hits still go in.
When you approach the other end of the scale, where the shooter is getting less and less accurate (but not a complete spaz who will miss the ball entirely)... the hardest possible distance is when the CB is 1.618 x the distance between OB and pocket.
My initial thought is "why shouldn't 2.0 x the distance or greater be more difficult than 1.618? More distance = harder shot." But then I remembered the "can't miss the OB entirely" restriction. So if we're just talking about someone who's definitely gonna get a hit, that's the sweet spot where they're gonna have the hardest time sinking the shot.
I'm trying to extrapolate something useful out of this but so far coming up dry.
Anybody else notice our very own Dr. Dave quoted on page 2?
-Andrew
-Andrew
Sorry, guys, I'm not a mathematician by a long shot so the numbers don't do much for me. What I see in this article is an egghead telling us that shots where the cue ball and object ball are close together, or if the object ball is close to the pocket are the easiest shots. Then, if I'm not mistaken, he's saying that from the middle of the table, with some distance between the OB and the CB, that any errors will be magnified over the distance to the pocket. Sorry, I thought that was pretty much common knowledge amongst pool players.
MULLY
MULLY
Nice article. Thanks for sharing it.
I don’t necessarily disagree with the 1.618 part, but it’s clear that the professor has some more work to do. A complete formula would have indicated what all pool players already know. That the most difficult straight-in shot is when you’re in a strange pool room, down 8-1 in a race to nine for (as you've just discovered) $50 more than your wife left you when she raided your wallet this morning, you’re jacked up over so many balls that the only bridge you can make is an “air” bridge, the tip just flew off your playing cue, so you’re having to finish the set with a house cue that looks like it’s been used as a melee weapon (which would go a long way toward explaining the object embedded in the butt that looks eerily like an upper incisor), and the guy you’re playing looks like he belongs on the short list of potential perpetrators of said “tooth extraction”.
Aaron
Aaron
I have the original article from The College Mathematics Journal in case anyone is seriously interested.
For a simpler summary including how you might actually use the difficulty of shots on the table, see this article.
As mentioned in another recent thread about the earliest pool instruction book, Edwin Kentfield in 1839 discussed how the difficulty of a shot varies with distance from the pocket, including pointing out that the difficulty is greatest when the object ball is half way to the pocket (for a given cue ball position).
I seem to recall that there is a chart in the book "The Science of Pocket Billiards" that shows the margin of error allowed for straight in shots from 1 diamond distances between the CB/OB and OB/Pocket all the way to 4 diamonds between each and every variation in between. It basically shows the same thing, that the hardest shot is when the OB is right in the middle. So, there's really nothing new about that part of the report.
1.614
I have no idea how it relates to billiards, but the ancient greeks discovered that 1.614..... was the ratio of the distance between the outstreched fingers and the height of ideal human.
others including Leonardo da Vinci made the same discoveries later on.
The greeks then extrapolated this ratio and used it to build the parthanon.
I have no idea how it relates to billiards, but the ancient greeks discovered that 1.614..... was the ratio of the distance between the outstreched fingers and the height of ideal human.
others including Leonardo da Vinci made the same discoveries later on.
The greeks then extrapolated this ratio and used it to build the parthanon.
I think that was the point of the whole article, the connection to the golden ratio... 1:1.614. It's creepy how the number comes up everywhere.
I think I get it but I have difficulty putting it into words that make sense.
But basically, imagine a straight in shot X distance from the pocket. Now imagine a shooter who sees fine but his mechanics are horrible, his cue ball might go off several inches. We're gonna line up ball in hand for him and set the cue ball on the straight-in line too. Forget about pocketing the ball, we want him to miss the shot (for some reason). But we don't want him to foul and miss the whole ball. So basically you want to find a distance where... if he's aiming dead center, his ugly stroke will send the cue ball at WORST a half ball off to the left (by the time it arrives at the OB it barely thins the left edge of the ball) or to the right. You want to bring the cue ball as far away as possible without going so far that he misses the ball. That distance will always be 1.618 * distance-to-pocket. Any further and he can miss entirely and foul. Any closer and he's a greater threat to make the ball.
I still can't quite get my head around it but that's what I think I'm seeing... 1.618 is a sweet spot between sure-hit but least-possible-chance-to-make.
I think I get it but I have difficulty putting it into words that make sense.
But basically, imagine a straight in shot X distance from the pocket. Now imagine a shooter who sees fine but his mechanics are horrible, his cue ball might go off several inches. We're gonna line up ball in hand for him and set the cue ball on the straight-in line too. Forget about pocketing the ball, we want him to miss the shot (for some reason). But we don't want him to foul and miss the whole ball. So basically you want to find a distance where... if he's aiming dead center, his ugly stroke will send the cue ball at WORST a half ball off to the left (by the time it arrives at the OB it barely thins the left edge of the ball) or to the right. You want to bring the cue ball as far away as possible without going so far that he misses the ball. That distance will always be 1.618 * distance-to-pocket. Any further and he can miss entirely and foul. Any closer and he's a greater threat to make the ball.
I still can't quite get my head around it but that's what I think I'm seeing... 1.618 is a sweet spot between sure-hit but least-possible-chance-to-make.