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Why are the Warriors the best team in basketball? Probability and 3 pointers. We can calculate why they expect to win so many games.

Is it smarter to always shoot 3 pointers? Lets figure it out with math. What do you need to know?

1) What percentage of the time do people make 2 pointers? 55.6%

2) What percentage of the time do people make 3 pointers? 36.4%

Which one is better? This is where we need a new math concept called the Expected Value. The expected value is how many points you will make per shot, on average, after taking many many shots. So for 2 pointers we would get 2 points, 55% of the time. The expected value is 2 * .556 = 1.11 points. And of the 3 point shots? 1.09 points. Based on this math, should you shoot more 3 pointers or 2 pointers? 2 pointers! But the point of this lesson was that the Warriors were expected to win more games - so what's going on?

Steph Curry. I told you that the average player makes 36.4% of their 3 pointers. What do you think Steph Curry's percentage is? 43.6%. So what's the expected value of his 3 point shot? 43.6% * 3 = 1.31. 1.31 is way better than 1.09 or 1.11, and that's the key to why we can expect them to win the most games.

If you were a coach, what would you do once you were given this math lesson?

You should collect statistics on all of the shooting percentages of your players and bucket them by 2 pointers and 3 pointers. If you can get an expected value higher than 1.11, you should have those players take more of those kinds of shots. And if their expected value is below 1.09, you should probably have them take less shots overall.

How do we rank the best 3 point shooters of all time? Do you look at the number of 3 pointers made? Do you look at the percentage that they made? How should you combine both of those at the same time? Corey Wade (www.coreywade.com) came up with a great way to do this called the "3 point net gain" or 3NG. To compute this, we first need to see what the expected value is of a regular possession in basketball, whether the team makes a 2 pointer, 3 pointer, or misses completely. We have these numbers above, somewhere around 1.10 expected points per possession. Then you can say that if a player makes a 3 pointer, he's contributing an extra 1.9 points, but if he misses, he loses those 1.1 points. If you multiply the number of 3 pointers a player made * 1.9 and subtracted from that the number he missed * 1.1, you get the 3NG. Not surprisingly, Steph Curry leads the league in 3NG with 2.03 extra points per game. The next closest player in 2018 had 1.84 (Klay Thompson, also a Warrior). The cool thing about this metric is that you can use it to compare individuals, or teams, across one season or their entire career. For example, here's the list of the top career 3NG leaders:

Career 3NG Leaders

Career 3NG Leaders

Rank

Player

3NG

Stephen Curry

1.94

Klay Thompson

1.38

Kyle Korver

1.08

JJ Redick

0.91

Hubert Davis

0.83

Ray Allen

0.78

Steve Novak

0.76

Steve Nash

0.71

Peja Stojakovic

0.69

Dennis Scott

0.68

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A little shout out to number 8 on here, Steve Nash, as he's our neighbor in town

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