That's a heck of a lot of
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And I think I can understand square peases and cubical peases but I can't get my mind around a 7-dimensional pea. Does this have anything to do with the president of Brazil?
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Fargorate match odds puzzle
- Thread starter JC
- Start date
And I think I can understand square peases and cubical peases but I can't get my mind around a 7-dimensional pea. Does this have anything to do with the president of Brazil?
No. It was a Moscow hotel. And he wasn't president yet. Sheesh! This is how rumors get started.
If anyone is still confused on how to work out the math for multiple sets, here's an example.
Let's say Donny Mills and Siming Chen are gonna play another match,
but this time it's race to 50 per set, and first to win 3 sets.
Let's say you wanna figure out Donny's chances (you can pick either player) of winning the entire match.
Here's the steps you'd take:
---
1. Go to https://fairmatch.fargorate.com/ and click "find a player" and find Donny's rating.
Then look up Siming's. Remember them or write them down.
2. Refresh the page, or click "home", to get back to that same page. This time click "find match odds."
Put Donny's rating in the top left, and siming's in the top right. Or vice versa.
As of 3/20/19 that's 751 for Donny, 785 for Siming.
Now put in "50" for the race length, under both players, and click "Calculate".
So Fargo predicts that Siming's chances are 88%, Donny's are 12%.
That's for a single set.
3. So now we can use a "binomial calculator" to figure out the rest. That sounds complex but it's not,
because there's a website that makes this easy.
Go to this page: https://stattrek.com/online-calculator/binomial.aspx
Think of each set as a coin flip, except it's not a fair coin. It's weighted funny.
The coin comes up heads 88% of the time, and tails only 12% of the time.
We're talking about a race to 3 sets, which is the same thing as saying a best 3 out of 5.
So we're basically asking "what are the odds this coin will come up tails 3 out of 5 times?"
...for the sake of clarity, let's pretend they're gonna play out all 5 sets, no matter who wins each one.
4. So in the first blank, "probability of success on a single trial", we put in .12
(same thing as 12%... donny's probability of success, in a single set).
The "number of trials" blank should have 5, because we're talking about a best-of-5 series.
The "number of successes" blank should have 3, because we're calculating the odds of Donny winning 3 (or more) of these sets.
5. Click "Calculate".
----
So the rest of the blanks show you results.
The result we're interested in is the very last blank. This shows Donny's odds of winning at least 3 sets.
It's shown as a decimal instead of a percent, so it shows 0.0143188992.
That's the same as saying 1.43%.
The first blank is like the odds of doing a weird prop bet where you stipulate that Donny wins EXACTLY
3 sets... no more, no less. So that's your odds of hitting the "exacta" bet. Around 1.33%.
The 2nd and 3rd blank are Siming's odds of winning, but 2 slightly different cases -
The first is betting she wins MORE than 3 sets (so if she gets exactly 3, the bet would be a push). That's 98.56%.
The second is betting she wins at LEAST 3 sets. Her odds are a little higher here,
because she can win 3, 4, or 5 sets (whereas in the previous set, just winning 3 sets was a push).
The 4th blank is just the inverse of the previous one. So if she's 99.9% to get 3 or more sets... she's 0.1% to lose 3 or more sets.
Let's say Donny Mills and Siming Chen are gonna play another match,
but this time it's race to 50 per set, and first to win 3 sets.
Let's say you wanna figure out Donny's chances (you can pick either player) of winning the entire match.
Here's the steps you'd take:
---
1. Go to https://fairmatch.fargorate.com/ and click "find a player" and find Donny's rating.
Then look up Siming's. Remember them or write them down.
2. Refresh the page, or click "home", to get back to that same page. This time click "find match odds."
Put Donny's rating in the top left, and siming's in the top right. Or vice versa.
As of 3/20/19 that's 751 for Donny, 785 for Siming.
Now put in "50" for the race length, under both players, and click "Calculate".
So Fargo predicts that Siming's chances are 88%, Donny's are 12%.
That's for a single set.
3. So now we can use a "binomial calculator" to figure out the rest. That sounds complex but it's not,
because there's a website that makes this easy.
Go to this page: https://stattrek.com/online-calculator/binomial.aspx
Think of each set as a coin flip, except it's not a fair coin. It's weighted funny.
The coin comes up heads 88% of the time, and tails only 12% of the time.
We're talking about a race to 3 sets, which is the same thing as saying a best 3 out of 5.
So we're basically asking "what are the odds this coin will come up tails 3 out of 5 times?"
...for the sake of clarity, let's pretend they're gonna play out all 5 sets, no matter who wins each one.
4. So in the first blank, "probability of success on a single trial", we put in .12
(same thing as 12%... donny's probability of success, in a single set).
The "number of trials" blank should have 5, because we're talking about a best-of-5 series.
The "number of successes" blank should have 3, because we're calculating the odds of Donny winning 3 (or more) of these sets.
5. Click "Calculate".
----
So the rest of the blanks show you results.
The result we're interested in is the very last blank. This shows Donny's odds of winning at least 3 sets.
It's shown as a decimal instead of a percent, so it shows 0.0143188992.
That's the same as saying 1.43%.
The first blank is like the odds of doing a weird prop bet where you stipulate that Donny wins EXACTLY
3 sets... no more, no less. So that's your odds of hitting the "exacta" bet. Around 1.33%.
The 2nd and 3rd blank are Siming's odds of winning, but 2 slightly different cases -
The first is betting she wins MORE than 3 sets (so if she gets exactly 3, the bet would be a push). That's 98.56%.
The second is betting she wins at LEAST 3 sets. Her odds are a little higher here,
because she can win 3, 4, or 5 sets (whereas in the previous set, just winning 3 sets was a push).
The 4th blank is just the inverse of the previous one. So if she's 99.9% to get 3 or more sets... she's 0.1% to lose 3 or more sets.
JC
Coos Cues
Using the binomial calculator and the numbers from my original post it comes up with just about exactly the number Bob Jewett came up with using the fargo rate calculator alone in post #2 of this thread.
Or as Bob said maybe the player who keeps outrunning the math odds and defeating the other guy has his number psychologically. Fargo rate after all is the average play of people against all opponents. There are still the dynamics of individual match ups to consider. Maybe one person's average fargo rating is lower in games he doesn't really care if he wins or not. Like league games for instance, which shapes a guys fargo greatly if he doesn't get out much.
In my own case I notice every time I play in a tournament my fargo goes up and eases back down once league play is my main input. In short league play has lost it's new car smell.
So next time you play someone and get drilled and you think they may be under rated you may be right. Their average play could consist of a bunch of games they didn't care too much if they won or lost for a variety of reasons. But they do care about the game you're playing with them. Maybe play more safeties instead of reckless offense.
I would make a small bet that if you took just my own history and split it out into two categories, league play and tournament play it would look like two different players fargo wise. Maybe as much as 30-40 points.
Wish I could do this but I can't. Mike can. I think the result would be interesting.
JC
It is far more complicated than needed.
Simply use the FargoRate tool to find the rating difference for two players that gives the better player an 88% chance of winning a single game. That turns out to be (after a few guesses) a 288 point rating difference. Change the match to race to 3 and you immediately get the result -- 1.4% for the weaker player.
JC
Coos Cues
My guess is the same math is behind the software of both methods fargorate just has it streamlined.
JC
You can also type it into the google search window.
bar box the great equalizer
fargo rate has its place in our sport and deserves kudos for the work involved. the problem with most amateur competition is its played on bar tables, shorter shots with less stroke to huge pockets that gobble balls. to much luck on small tables. diamond smart tables are a great improvement.. play great everyone.:wink:
fargo rate has its place in our sport and deserves kudos for the work involved. the problem with most amateur competition is its played on bar tables, shorter shots with less stroke to huge pockets that gobble balls. to much luck on small tables. diamond smart tables are a great improvement.. play great everyone.:wink:
Well, in my defense, my process boils down to: open a new tab, type numbers into 3 blanks.
It only looks complicated because I wrote 3 pages for a 20 second process.
I think it's actually slower to do it all within fargo because you gotta trial-and-error repeatedly to come up with that rating gap that produces 88% chance of winning.
On the one hand, that's entirely possible. Maybe a guy shoots like a 700 in some situations,
and 740 in others, so "720" is not really the most accurate predictor of how they'll play.
But if you had to boil down a complex thing into just a single number, that 720 number is
probably the best you can do.
On the other hand, I think people may also overestimate how much their gameplay varies
for league vs. tournament. Or big table vs. small table, or whatever.
I know a lot of people who use "I wasn't really bearing down" as an excuse, but I don't know a lot of people
who literally just don't try very hard (in a rated match) and then only show their real game in limited situations.
I think most players with ratings that are worth caring about (i.e., not the Fargo 400's) are competitive about pool,
and will not voluntarily tolerate losing, say, 10% more often than they have to. Even if it's "just league".
Fargo Rate
Tournament/gambling versus league/practice is an interesting idea.
Without a doubt my best pool has been played when it means the most to me. But then again, sometimes I dog my brains out. The same emotional arousal that can bring me into the zone can sometimes take me right out of it. Meanwhile when I practice I don't have either the benefit or hindrance of that sort.
It could be that my FR has a higher top gear but also a wider range. It could be that overall it does average more than my practice FR. Or it might be closer than I think.
I've learned that when I practice the same shots I dog because I'm "not bearing down" are often the shots I dog when I'm under a lot of pressure. In fact, this helped me take practice much more seriously. Even though I'm dogging shots for different reasons, it still shows me where the weak links in my game are.
Tournament/gambling versus league/practice is an interesting idea.
Without a doubt my best pool has been played when it means the most to me. But then again, sometimes I dog my brains out. The same emotional arousal that can bring me into the zone can sometimes take me right out of it. Meanwhile when I practice I don't have either the benefit or hindrance of that sort.
It could be that my FR has a higher top gear but also a wider range. It could be that overall it does average more than my practice FR. Or it might be closer than I think.
I've learned that when I practice the same shots I dog because I'm "not bearing down" are often the shots I dog when I'm under a lot of pressure. In fact, this helped me take practice much more seriously. Even though I'm dogging shots for different reasons, it still shows me where the weak links in my game are.
Back when I played handicapped nine ball, I would show up for the weekly tournament tired after work and usually hungry. For tournaments I'd usually be better rested and fed.
As for doing the calculation for a match, if I want detailed info I use a spreadsheet that I made. Here is part of the sheet for the above example. It shows the percentage for each possible score in the race to 3, so the weaker player has a 0.17% chance to win 3-0. You only fill in the yellow squares. If anyone wants a copy of the spreadsheet, just ask. The translator of rating difference to percent wins is just a convenient separate tool and not related to the main calculation.
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