Wednesday, April 15, 2015

Korver Faces Tough Odds to Reach 50/50/90 Level

The Atlanta Hawks' Kyle Korver should be familiar to aficionados of hot shooting. The 6-foot-7 shooting guard once had a streak, spanning the 2012-13 and 2013-14 seasons, of making at least one three-pointer in a record 127 straight games (I analyzed Korver's streak here, when it was at 98 games).

During the 2014-15 season, Korver has sought out further frontiers of shooting accuracy. As Ian Levy pointed out back on February 13, Korver was threatening to record the unprecedented feat of hitting 50 percent on all shots from the field, 50 percent from three-point land, and 90 percent on free throws, a so-called 50/50/90 season.

As the Hawks enter their regular-season finale tonight at Chicago, Korver is slightly below all three milestone levels, with a .487 field-goal percentage, .493 three-point percentage, and .897 free-throw percentage (Korver stats page).

It's not even clear how much -- if at all -- Korver will play tonight, as the Hawks rested Korver and other key players last Sunday at Washington, although he played 34 minutes Monday vs. New York. However, assuming he plays tonight, what kind of shooting numbers will he need to post to reach each of the three criteria?

I plotted some equations for how many shots without a miss Korver would need to make to reach .500 on overall field goals and treys, and .900 on free throws. Even if Korver missed a shot of a given type, it would be mathematically possible for him to still reach the milestone, but far more makes and attempts would be necessary than if he never missed.

Let's take three-point shooting, where he enters the game 219 out of 444 (.493). Assuming no missed shots, the number of attempts is equal to the number of makes. We can thus define the equation:

y = (219 + x) / (444 + x)

where y represents Korver's three-point shooting percentage and x represents each new attempt (which is always made). In other words, each new attempt raises his number of attempts beyond the current 444 and each new make raises his number of makes beyond the current 219. By how many attempts (and makes) must x rise to bring y to .500? One can type an equation, such as the one above, into Google, which will automatically generate a plot. Here are the resulting plots for Korver in all three shooting categories (you may click on the graphic to enlarge it).

We see in the upper-right graph that Korver's three-point shooting line (blue upward trend) crosses the .500 threshold (black horizontal line) at six attempts. Six more made threes (again, without a miss) would give him 225, which would be half the new number of attempts, 450. Alternatively, Korver could hit the .500 threshold with a 7-of-8 performance behind the arc, resulting in (226/452). As I said, each miss progressively increases the number of shots he would need to make.  Making 6-of-6 on threes is not terribly likely. Given that his three-point percentage is very close to 50%, let's imagine coin-tossing. Korver would have to flip heads six times in a row, which has a probability of 1-in-64.

Finishing at .900 on free throws should be relatively easy. Korver just needs to make at least three free throws without a miss. If he's not perfect, he would have to make 12 of 13 to reach .900 (117/130).

Lastly, we have overall field-goal percentage. To reach .500, Korver would need a 16-for-16 night (resulting in 305/610) or, alternatively, 17-of-18 (306/612).

Clearly, Korver has his work cut out for him. At the college level, Christian Laettner's performance against Kentucky in the 1992 regional final comes to mind; not only did he hit the turnaround buzzer-beater, but he also hit 10-of-10 from the floor and 10-of-10 from the stripe. Also, Bill Walton hit on 21-of-22 field goals in the 1973 final. That's the kind of game Korver's looking at.

UPDATE: Korver went 3-of-6 from the floor at Chicago to finish the regular season with a .487 field-goal percentage; 2-of-5 on three-pointers for a final percentage of .492 beyond the arc; and 1-of-1 from the free-throw line to finish at .898 from the stripe (box score; final regular-season statistics).

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