Odds and Log(Odds), Clearly Explained!!! 

NOTE: In statistics, machine learning and many programming languages, like Java, R and Python, the default base for the log function is 'e'. So log(0.17) = "log base e of 0.17" = -1.77. The natural log (log to base 'e') is used because it often simplifies the mathematics that underpins statistics. That said, you can use whatever base you would like as long as you are consistent. Also, at 10:00, I say that a histogram of the log(odds) has the shape of a normal distribution, but what I should have said is that the shape is *similar* to a normal distribution and is *approximated* with a normal distribution. Lastly, people often ask about how to generate the normal distribution: First, I randomly selected a number between 1 and 100 and I get 32. That means I will use 32 as the numerator for the odds. The denominator is then 100-32 = 68. Then I calculate the log(32 / 68) and get -0.75 (because I use log base 'e', but you can use any log base as long as you are consistent). Then I pick another random number between 1 and 100 and get 54. This means that the numerator for my odds is 54 and the denominator is 100-54 = 46. So I calculate the log(54 / 46)=0.16. Then I just repeat that process a bunch of times (100s) and draw a histogram of the log(odds) values. If I do this, I will get a normal distribution. Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/

GIVE THIS GUY A MEDAL!!! I understand more about logs than in the 4 years I studied for logs in my final exams for different levels of examinations!

thank you for helping me to spend my quarantine times effectively. the world is a much better place with mathematics!

NOTE: Odds are not probabilities. So if the definition of "odds" seems odd to you, just keep watching. It will all make sense in less than 2 minutes.

Some RU-vid channels really deserve an award. Thank you, Josh, for putting your teaching skills available to the world!

I have a really bad statistics professor who has made me want to give up on my way to becoming a data scientist. But you give me faith Josh, that really means something! I’m not giving up thanks to you

Fantastic video. A teacher who actually builds life-long intuition. Thanks, Josh!

The odds of learning something when watching your videos are very high!

Exactly how stats should be taught, intuitive explanation and then the math. Unfortunately, it is taught backwards, encouraging brute and route memorization without understanding the principles. Thank you for taking the time to enlighten us all. God bless u!!!

Thank you so, so much. I've been confused about odds & log(odds) for the past 3 years since learning about them. I finally understand them now.

statquest is just so freaking good. this and also your videos on regression, boosting and xgboost have given me more clarity on the topics than any other resource I've seen

I just found you a couple weeks ago and have already seen most of your videos. With you everything's clearly connected: from log(odds) to Xgboost. Thanks!!

Man. I'm really, really thankful with you. You no have idea how useful and helpful is your content to me and my job. Your work is amazing! Thanks!

I wish your videos existed during my years as a stat major :( you're really good at explaining things!! I appreciated my college lessons because of you. Thank you. Anyway, this would help me with ML concepts. My takeways: 1. Odds and prob are not the same 2. Odds can be calculated from prob 3. We use log odds to solve for assymetry

subscribed. I went through 4 years of psych stats without understanding what a logistic regression is... I just use it.. now I feel like I'm finally receiving a worthwhile education from you!

BAM!!!!! thank you so much for your great asset!!! I really happy to meet you and I've been improving my knowledge of statistic methods thanks to you!!!!!!!!!

You explained it like none other, its very easy to grasp the concept. Thank you, Josh!

It's crazy how intuitive and clear you make this. You're a remarkable educator. Considered doing just straight up mathematics lectures? That would be pretty sweet.

for this topic, I don't think if any other source could be as helpful as your video. Thanks a ton Josh!

Sir, you are a legend. I just discovered your RU-vid channel, it's a treasure to me. Thank you so much for your great videos.

Josh, you are a very talented teacher. Thanks so much for this video.

"Clearly Explained" should be "super clearly explained, so clear as if it is transparent" 🙂 Thank you! You are the best!

Greetings from Australia. I'm in an advanced research methods course and was struggling to understand log odds, probabilities, and the differences. I was mostly mixed up about the difference between odds and probabilities and didn't even realize it. Thank you so much! I'm sharing this with classmates. I wanted to let you know that this is making a difference for students literally around the world! :)

Probability and statistics never come easy to me, but this is so simple, enjoyable and informing at the same time! Thank you so much! :)

This channel is amazing. I think this is quality education! You will change the world! Can you imagine a world where most people would have access to teachings like those from Josh Starmer? Would people not make more informed decisions, would people not be better prepared for the future? Why don't we have this type of content on television?

Josh you were awesome. I have been teaching for the past 32 years (not stat or math but botany/biology) but it feels like it is still a long way to go when I watched such a splendid, extraordinary, marvelous.... well I don't have words for it.... explanation. It was simply magnificent. Needed the meaning of odds and the log odds for my Bioinformatics class (which I am also learning) and I stumbled upon your video. Problem solved to perfection. Looking forward to watching more...sorry can't buy your songs.

haha same here! Seriously what a boost to productivity it was finding Statquest. Thanks Josh! Excellent intro song to this one - one of my faves so far

You have a unique simple way of teaching. Thank you 👍🏻

Josh you're saving my life here with all your videos... thanks brother!

Thanks at ton!! The fine difference between ODDs and Probability is a concept often not clear for many!! This is was really helpful

thank you so much for making this video, it is so clear and helpful for me since i don't have any previous knowledge of it

This is the most useful and straight-forward explanation video I have found. Thank you!

Josh, you are simply excellent. You make concepts so simple and explain it with lots of visuals. Odds are no longer odd for me :)

It is just excellent your explanation! Thank you so much for such a qualified video!

Brilliant explanation as always, couldn't get through this master's degree without you!

This channel is a pedagogical gold mine

Excellent! Much better than my teacher! Thanks!

This video series is fantastic - keep up the good work.

I am 30 years old, and finally because of you I have understand it... I'm grateful

If only my high school teaching was this simplified, thank you very much.

I dont know how to thank you enough, I am passing my finals because of you.

Oh snap. I always conceptualized odds and probability as exactly the same thing. I am now in an existential crisis. The world around me no longer makes sense. Why oh why did I come here … :(

Wow really amazing explanation. I recently completed the machine learning course by Ng, now this video just made everything click!

precisely the video that I needed! This is like the third time I am leaving a comment on youtube. Thank you StatQuest!!

Thanks Buzz Lightyear for another amazingly well explained video! Particularly your lead up and explanation of the log(odds), brilliant!

Awasome man, your are explaining everything very clearly. I want to say this thanks for responding to everyone's comment, This is the first time I seeing in RU-vid.

I came here from your logistic regression details 1....and NOW the logit fxn makes so much sense. Josh, thanks for going slowly and step by step...it really helps in understanding. I like how you explain everything. So few textbooks do that...and so you have a very imperfect understanding...just rote learning. Thanks!

INFINITY BAM!!! I think I just found a gold mine!!! Subscribed!!!

Love you 3000 BAM!!! Josh for making learning so easy. Thanks a lot Sir!

I wish your videos were available during my undergrad, could have achieved much good GPA. Keep up the good works!

this guy is so good at explaining

Why did I take so long to find this channel? Congrats.

Congratulation. It is an amzing video; I understodd many things that always remain a little bit obscure in statistic courses.

sir, you and your videos are truly awesome.

I just randomly click into this video, didn't expect that I will understand the intuition behind a logit function!!

You are the bombb! Sir Starmer... Thanksss a million!

Very beautifully explained! Thank you so much! 🎉

I love your videos so much. I have my statistics exam in two days, and if it weren't for your videos I wouldn't be able to prepare at all!! So easy to understand. Thank you so much!

Incredibly good explained !

I love you! You literally perfectly describe everything.

Josh, thank you so much for your work. I have learned so much from your awesome videos. They have been a great help in refreshing my statistics and learning new methods! Could you do a video on survival functions? :)

That intro alone has be hooked

Thank you so much, helped me clarify a lot

Simple explanation. Anybody can understand it. Thanks a lot.

The BEST explanation. Thank you!!!

Brilliant explanations! Thx Josh, I finally get it😁

The intro tune on this is one of my faves

BAM!!! I just become a member :) The odds and log(odds) were indeed clearly explained.

I struggled to understand this a computer science student :') You are sent from heaven. Thank you!

9:46 Simulate the distribution of the log of odd (log prob_happen/prob_not_happen) 1. Randomly pick a pair of numbers between 0 and 1. 2. If they sum up to 1, then keep them, else drop. So that the number pairs retained would be [0.x, 1 minus 0.x]. The ratio between the two numbers is an odd. 3. Plot histogram of log(odd), using all the number pairs. The distribution will be normal.

That DOUBLE BAM moment was worth 100 BAM !!

you, sir, are a genius at explaining things. Thanks

This is the best of RU-vid

The explanation cannot get better!

Thanks Josh. COVID-19 has helped us become more productive. I appreciate greatly the work you guys at StatQuest do. Thanks alot.

This video was extremely useful. Thanks for sharing

YOU ARE LIFE SAVER! I can't say THANK YOU enough

Superb explanation!

Great work all the time.thank you so much

thank you a lot this video explained what i needed :)

You are the best stat person ever!!!! Super Bam!!!

What my tutor could not make me understand in 3 lectures, you did it in 11 minutes! This video itself deserves Quadruple BAM!!! (Thanks)^'e'

this is excellent! thank you sir

The explanation at 9:30 is the whole point of this video. Thank you.

Excellent explanation

You are the best, man! Thank you so much.

EXCELLENT ...THANK YOU SO MUCH

This is so great Thank you

Thanks for explaining so well. Where were you and your teaching all these years? sad could not find you earlier.

Excellent explaination sir☺️🤜🤛 You are the Best😊

Amazing, thank you!

Can't thank you enough !! God Bless.

This is shockingly clear.

This is truly clear!

Thank you very much! 十分谢谢！

Good thanks

REALLY AWESOME!!! A BIG THANK YOU

very clear thank you

Very clearly explained

I finally get it, which I did not get even after 4 years of college. Best teacher🙏