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View Full Version : Probability of us shooting so well from the line last night


gth816f
03-20-2010, 09:08 PM
Quick answer: 0.118 % chance of shooting 24/25 or 25/25, assuming I did this right.

Long answer:

Okay, this came up in the other thread: what was the probability of us actually shooting so well from the free throw line last night? Well, at first I was annoyed because I couldn't remember how to do it. But then I remembered(I think), and once I remembered I just had to do it.

Obviously when it got to the end, making/missing some of these free throws would have affected if we got the next ones, so we'll just operate based on the assumption that we were going to get that exact number of free throws from those specific players.

Someone check my math, because it's probably wrong...but here goes:

Lawal: 4 shots, .525 FT%
Favors: 2 shots, .629 FT%
Shumpert: 8 shots, .720 FT%
Rice Jr.: 1 shot, .529 FT%
Miller: 4 shots, .804 FT%
Oliver: 2 shots, .704 FT%
Peacock: 4 shots, .791 FT%

Basically, we should be able to figure out the probability of hitting 24/25 overall by figuring out the probability of missing the first then hitting 24 straight, missing the second and hitting the rest of the 25, etc., adding those 25 probabilities together, then adding in the probability of hitting all 25. We'll work with threesignificant digits and use conventional rounding.

So we might as well make the first step the easiest one. The chances of us hitting all 25 is simply the probabilities of each guy hitting all of his shots multiplied together. That is: .525^4 * .629^2 * .720^8 * .529 * .804^4 * .704^2 * .791^4 = 9.31 * 10^-5.

Now it gets a litle dicier. The basic math is still the same but there's a separate step for each shooter. I'll write out the first step to show what I'm doing. What we want to find out is the chance of Lawal hitting three out of four free throws. The probability of him missing the first then hitting three straight is .475 * .525^3.

Since multiplication is commutative, the chance of him making three out of four in each other order(miss second, miss third, miss fourth) is the same number. That means the overall probability of him hitting three out of four free throws is .475 * .523^3 * 4. Now we multiply that by the chance of the remaining players hitting every one of their free throws: (.475 * .523^3 * 4) * .629^2 * .720^8 * .529 * .804^4 * .704^2 * .791^4 = 3.33 * 10^-4

We have to do this for each player:

Lawal: (.475 * .523^3 * 4) * .629^2 * .720^8 * .529 * .804^4 * .704^2 * .791^4 = 3.33 * 10^-4
Favors: .525^4 * (.629 * .371^1 * 2) * .720^8 * .529 * .804^4 * .704^2 * .791^4 = 1.09 * 10^-4
Shumpert: .525^4 * .629^2 * (.280 * .720^7 * 8) * .529 * .804^4 * .704^2 * .791^4 = 2.90 * 10^-4
Rice Jr. = .525^4 * .629^2 * .720^8 * (.471 * .529^0 * 1) * .804^4 * .704^2 * .791^4 = 8.29 * 10^-5
Miller: .525^4 * .629^2 * .720^8 * .529 * (.196 * .804^3 * 4) * .704^2 * .791^4 = 9.08 * 10^-5
Oliver: .525^4 * .629^2 * .720^8 * .529 * .804^4 * (.296 * .704^1 * 2) * .791^4 = 7.83 * 10^-5
Peacock: .525^4 * .629^2 * .720^8 * .529 * .804^4 * .704^2 * (.208 * .791^3 * 4) = 9.79 * 10^-5

Whew. So now we have the probabilities of every possible combination of makes and misses that would get us to 24/25 or better. Now we just have to add them up!

Probability of us hitting 24/25: 9.31 * 10^-5 + 3.33 * 10^-4 + 1.09 * 10^-4 + 2.90 * 10^-4 + 8.29 * 10^-5 + 9.08 * 10^-5 + 7.83 * 10^-5 + 9.79 * 10^-5 = .00118, or 0.118%.

Done! Now you people who actually know math can rip it apart and tell me I wasted the last hour of my life.

gtbuzz2011
03-20-2010, 10:09 PM
I personally would have taken the team's total FT % and set that as the probability, since it is already weighted based on who goes to the line the most in tandem with their FT %. From there, it is just a matter of finding Pr(X>=24), where X~binomial(n=25, p=whatever our teams season FT % is). I'd do it myself but I'm on my phone.

carober18
03-20-2010, 10:16 PM
just off the top of my head--peacock is not a 47% free throw shooter. closer to 80%

ND_jacket
03-20-2010, 10:34 PM
just off the top of my head--peacock is not a 47% free throw shooter. closer to 80%

Correct, according to the ramblinwreck.com stats page (http://ramblinwreck.cstv.com/sports/m-baskbl/stats/2009-2010/teamcume.html#TEAM.OCF). (It's actually 79.1%.)

ND_jacket
03-20-2010, 10:37 PM
I personally would have taken the team's total FT % and set that as the probability, since it is already weighted based on who goes to the line the most in tandem with their FT %. From there, it is just a matter of finding Pr(X>=24), where X~binomial(n=25, p=whatever our teams season FT % is). I'd do it myself but I'm on my phone.

That'd be a reasonable approximation. However, the distribution of who shoots how many free throws in any given game could be markedly different from the overall season average. It's certainly more accurate to do the analysis like gth did (assuming all the probabilities used are accurate).

gth816f
03-20-2010, 10:45 PM
Thanks guys, I fixed Peacock's FT%...accidentally used his FG %. And I think that a one game sample size is too small to get a good estimate of the probability, so I decided to do it with each shooter.

ND_jacket
03-20-2010, 10:55 PM
Thanks guys, I fixed Peacock's FT%...accidentally used his FG %. And I think that a one game sample size is too small to get a good estimate of the probability, so I decided to do it with each shooter.

It's a good decision (take this from the mathematician). I get something like 0.036% using the team's free throw percentage. An example of an important difference is that Gani shot 28.9% of our free throws for the season but only 16% against OK State.

jts1207
03-20-2010, 11:10 PM
Bored much?

BarrelORum
03-20-2010, 11:15 PM
Its **** like this why UGA fans not to mention everyone else, makes fun of GT fans.... and you know what? They're right.

gth816f
03-20-2010, 11:18 PM
Its **** like this why UGA fans not to mention everyone else, makes fun of GT fans.... and you know what? They're right.

Are these the same fans who were defecating in public before home games last year? Because if so, I can't say I'm too terribly concerned about their opinions on image.

And to answer the rhetorical question: yes, yes they are the fans who defecated in public last year. http://www.ajc.com/sports/uga/uga-tailgaters-warned-to-140564.html

The Jacket
03-20-2010, 11:20 PM
Its **** like this why UGA fans not to mention everyone else, makes fun of GT fans.... and you know what? They're right.

I don't give a **** what those morons think and neither do you. Sit back and enjoy the formula.

gtzulu
03-21-2010, 12:38 AM
Nice work. One thought: Players' free-throw percentages don't reflect how well they're doing at free throws at present, they reflect how they did over the entire season (or career). It's possible the players have gotten better over the season (through Hewitt's coaching, no doubt?) So it might be wrong to interpret the 0.118% as meaning we witnessed an approximately 1 in 1000 event. Not that anyone did this, just saying.

On the other hand, you could argue that there's more pressure in the NCAA tournament so it's harder to hit the FTs.

BarrelORum
03-21-2010, 12:55 AM
I don't give a **** what those morons think and neither do you. Sit back and enjoy the formula.

I'm too lazy to read it, I just like pointing out the obvious stereotype he just fell into.

TechSBP
03-21-2010, 01:07 AM
Its **** like this why UGA fans not to mention everyone else, makes fun of GT fans.... and you know what? They're right.

AAAAAAAAND why do we care? If they think stuff like this is bad, fine. We can do math. Which comes in handy. If we are nerds for doing math I can deal with that.

Now, if they are making fun of a GT fan who rushes in to correct any real or perceived slight against GT anywhere on the internets? Then I'm with you on telling that GT fan to STFU. Thats the nerd stereotype I hate (like my Dook friends being, seriously, shocked to find out the guy wearing the GT helmet in the stands wasn't, in fact, retarded--to be frank I was too).

Here, not so much. Pretty much it boils down to this:

U[sic]GA fan, taunting: "You know how to do math! NEERRDSSSS!"

GT fan: "You flip burgers for a living. Redneck."

U[sic]GA Home ec grad: That's not true. I work at Zaxbys.

gth816f
03-21-2010, 09:45 AM
Nice work. One thought: Players' free-throw percentages don't reflect how well they're doing at free throws at present, they reflect how they did over the entire season (or career). It's possible the players have gotten better over the season (through Hewitt's coaching, no doubt?) So it might be wrong to interpret the 0.118% as meaning we witnessed an approximately 1 in 1000 event. Not that anyone did this, just saying.

On the other hand, you could argue that there's more pressure in the NCAA tournament so it's harder to hit the FTs.

That's true. I think the way to test this would be to come up with a graph of each player's free throw percentages per game and see if there is an upward or downward trend, or if the distribution is random.

But I'm not going to do that :). This was just a fun little thing which there were a lot of people wondering about.

gthog61
03-21-2010, 10:49 AM
Thanks for the analysis. I knew somebody would know how to do it.

yellowbritchies
03-21-2010, 11:44 AM
Quick answer: 0.118 % chance of shooting 24/25 or 25/25, assuming I did this right.

Long answer:

Okay, this came up in the other thread: what was the probability of us actually shooting so well from the free throw line last night? Well, at first I was annoyed because I couldn't remember how to do it. But then I remembered(I think), and once I remembered I just had to do it.

Obviously when it got to the end, making/missing some of these free throws would have affected if we got the next ones, so we'll just operate based on the assumption that we were going to get that exact number of free throws from those specific players.

Someone check my math, because it's probably wrong...but here goes:

Lawal: 4 shots, .525 FT%
Favors: 2 shots, .629 FT%
Shumpert: 8 shots, .720 FT%
Rice Jr.: 1 shot, .529 FT%
Miller: 4 shots, .804 FT%
Oliver: 2 shots, .704 FT%
Peacock: 4 shots, .791 FT%

Basically, we should be able to figure out the probability of hitting 24/25 overall by figuring out the probability of missing the first then hitting 24 straight, missing the second and hitting the rest of the 25, etc., adding those 25 probabilities together, then adding in the probability of hitting all 25. We'll work with threesignificant digits and use conventional rounding.

So we might as well make the first step the easiest one. The chances of us hitting all 25 is simply the probabilities of each guy hitting all of his shots multiplied together. That is: .525^4 * .629^2 * .720^8 * .529 * .804^4 * .704^2 * .791^4 = 9.31 * 10^-5.

Now it gets a litle dicier. The basic math is still the same but there's a separate step for each shooter. I'll write out the first step to show what I'm doing. What we want to find out is the chance of Lawal hitting three out of four free throws. The probability of him missing the first then hitting three straight is .475 * .525^3.

Since multiplication is commutative, the chance of him making three out of four in each other order(miss second, miss third, miss fourth) is the same number. That means the overall probability of him hitting three out of four free throws is .475 * .523^3 * 4. Now we multiply that by the chance of the remaining players hitting every one of their free throws: (.475 * .523^3 * 4) * .629^2 * .720^8 * .529 * .804^4 * .704^2 * .791^4 = 3.33 * 10^-4

We have to do this for each player:

Lawal: (.475 * .523^3 * 4) * .629^2 * .720^8 * .529 * .804^4 * .704^2 * .791^4 = 3.33 * 10^-4
Favors: .525^4 * (.629 * .371^1 * 2) * .720^8 * .529 * .804^4 * .704^2 * .791^4 = 1.09 * 10^-4
Shumpert: .525^4 * .629^2 * (.280 * .720^7 * 8) * .529 * .804^4 * .704^2 * .791^4 = 2.90 * 10^-4
Rice Jr. = .525^4 * .629^2 * .720^8 * (.471 * .529^0 * 1) * .804^4 * .704^2 * .791^4 = 8.29 * 10^-5
Miller: .525^4 * .629^2 * .720^8 * .529 * (.196 * .804^3 * 4) * .704^2 * .791^4 = 9.08 * 10^-5
Oliver: .525^4 * .629^2 * .720^8 * .529 * .804^4 * (.296 * .704^1 * 2) * .791^4 = 7.83 * 10^-5
Peacock: .525^4 * .629^2 * .720^8 * .529 * .804^4 * .704^2 * (.208 * .791^3 * 4) = 9.79 * 10^-5

Whew. So now we have the probabilities of every possible combination of makes and misses that would get us to 24/25 or better. Now we just have to add them up!

Probability of us hitting 24/25: 9.31 * 10^-5 + 3.33 * 10^-4 + 1.09 * 10^-4 + 2.90 * 10^-4 + 8.29 * 10^-5 + 9.08 * 10^-5 + 7.83 * 10^-5 + 9.79 * 10^-5 = .00118, or 0.118%.

Done! Now you people who actually know math can rip it apart and tell me I wasted the last hour of my life.
I applaud you're effort,however, probably only 3-4 posters have any idea what you did, including me!!

Pantone874
03-21-2010, 12:56 PM
Saw this on Twitter after the game:

RT @vegaswatch: Odds of a team that shoots 64.2% from the line (GT) making 24+ out of 25? 1 in 4,338.

cantSpellConvictWithoutVT
03-21-2010, 01:25 PM
good work gth816f.... but two things i don't believe you're capturing:

(i) your computation assumes 25 FT attempts, but IMO you need to focus on number of FT opportunities - that is, factoring in 1-1's where you need to hit the front end. I think the one miss we had (Shump) was on a shooting foul, so we hit every front end. Thus I think your prob is overstated.

(ii) are FT attempts really independent? I don't know, but I would suspect not (except with Gani). I would conjecture the prob of hitting your second would be higher if you hit your first.

in any event, i applaud your work!

and as far as the nerd stereotypes - I say bring it on. It's orders of magnitude better than the VThug, U[sic]GA, or any SEC school sans Vandy.

chilidogking
03-21-2010, 01:28 PM
Nerds! Nerds! Nerds!

gth816f
03-21-2010, 01:29 PM
good work gth816f.... but two things i don't believe you're capturing:

(i) your computation assumes 25 FT attempts, but IMO you need to focus on number of FT opportunities - that is, factoring in 1-1's where you need to hit the front end. I think the one miss we had (Shump) was on a shooting foul, so we hit every front end. Thus I think your prob is overstated.

I know about that. That's why I put in this paragraph: Obviously when it got to the end, making/missing some of these free throws would have affected if we got the next ones, so we'll just operate based on the assumption that we were going to get that exact number of free throws from those specific players.

I suppose I could have done the math for the 1&1 front ends but...that would have been a little too much work :biggthumpup:.

(ii) are FT attempts really independent? I don't know, but I would suspect not (except with Gani). I would conjecture the prob of hitting your second would be higher if you hit your first.

in any event, i applaud your work!

That depends on who you ask. I am the camp that they are completely independent. There have been many studies on this(the so-called "hot hand" effect) and I believe most of them conclude that shots are all independent of each other. We just tend to focus on the streaks that arise naturally and mistakenly attribute them to a hot hand or being in rhythm.