Hey Folks! Derek
here again for a little more [let’s see if this catches on] ‘Stache Talk! I’m
feeling a little frisky. So cue the Barry White, dim the lights, cuddle up
close and let’s talk about one of the most titillating facets of Strat-O-Matic…free
throws! What, you don’t think free throws are sexy? You’ve obviously never seen
John Stockton in his short shorts at the line.
Before I forget,
thank you to basketball-reference.com for the stats. That is my go-to stat
site. Whenever I cite stats here it will likely be from that site.
In my comment
under Chris’s Shooting Rule Adjustment post, I showed how SOM comes within
3/10ths of a percentage point in replicating a shooter’s 3-pt accuracy. Yet, as
I pointed out in my recent Big Man Switches onto Steph post, SOM can be more
than a whole percentage point off on a player’s free throw percentage. This is
because the two 6-sided die system only results in 36 combinations. Thus, the
difference between one combination (let’s say 32/36) and the next (33/36) is
2.78 (to make things easy I am mostly going to round to the hundredth decimal
place). So for 2015-16 Steph Curry, the
player I used in my post, his actual free throw percentage for the season was
90.75%. But his SOM card has his free throw shooting at 2-10, which is 33/36 or
91.67%. That is almost a full percentage point off.
SOM’s 36-combo
system results in 37 different free throw rating/percentages of 0, 2.78,
5.56…83.33, 86.11, 88.89, 91.67, 94.44 etc. So for 2014-15 Steph, the choice
was between 88.89 and 91.67, and because his actual percentage of 90.75 was
closer to the latter, he was assigned that. It makes sense. But there is a
better way to do it, a way where we can replicate a player’s free throw percentage
to the decimal place.
I examined some
players from the 2018-19 season, two in particular who had less than a decimal
point difference in free throw percentage, but who fell on opposite sides of
the halfway marker between one rating and another, and thus were assigned
different ratings with a difference of 2.78. So in reality there was less than
a .1 difference between their free throw shooting percentages but in SOM the
difference between their ratings was 2.78. I want to correct that.
On the bottom of
LaMarcus Aldridge’s card, in the 2018-19 Statistics section, his free throw
percentage is listed as 84.7%. If we divide his makes by attempts and round to
the hundredth decimal place we get 84.71%. Jamal Murray’s free throw percentage
at the bottom of his card is 84.8% and if we do the math on him we get 84.75%.
The halfway point between the SOM free throw ratings of 83.33 and 86.11 is 84.72. As
we can see, LaMarcus falls on one side of it, and is assigned a free throw
rating of 2-9 (83.33%) and Jamal falls on the other, and is assigned a rating of 2-9, 12 (86.11%). The difference
between their free throw shooting in reality is less than 1/10th of
a percent, but the difference in their SOM free throw shooting is 2.78%.
I did not invent
the solution to this problem. I read about it on somhoops.com. Unfortunately, that
website is currently down so I can’t give credit to the person who posted the
idea. I don’t think it was the person who runs the site, Jason Blaze, but it
may be. Anyways, the solution is to use three 10-sided dice of three different
colors (I am going to use red, white and blue, which can be for American
patriotism or to honor the ABA, the American Basketball Association (not the
American Bar Association, that is on you to figure out how to honor them),
whichever you choose). You roll all three and you read the red die as the first
number, the white as the second and the blue as the third. If the three-digit
number is less than or equal to the player’s free throw percentage listed on the
bottom of his SOM card, the free throw is good. If it is greater it is a miss.
It took me a
little while to wrap my head around this. I actually had to pick up
a 10-sided die to really understand it. Each die has 10 sides from 0 to 9. For
2015-16 Steph Curry, a 90.8% shooter, he should make just over 90% of his free
throws. The way I think about is that the red die rolls of 0 through 8, which
is 90% of the rolls, are automatically good. It is the other 10%, the 9 rolls,
that are at issue. And of those, the vast majority, almost 90%, are going to be
misses. He needs the second die, the white die, to be a 0 in that situation for
his free throw to be good, and even then he needs the blue die to not be a 9.
For LaMarcus and
Jamal, they each need rolls of 84.7% and 84.8% or less, respectively, for their
free throw to be good. The difference in real life between their free throw
percentages is only .04% and here we will still have a .1% difference, but to
me that is marginal and significantly better than the 2.78% difference the SOM
system generates.
Now, there is one
exceptional circumstance. I know some of you have been thinking it the entire
time. What about a roll of 000? That is a hundred and for me that means that
ANY PLAYER misses it. Even guys like the 2018-19 Gary Clark of Houston and
Lorenzo Brown of Toronto, each of whom shot 100% from the line (and have SOM
ratings of 2-12, check out their cards!!!). Why should a player who never
missed have a possibility of a miss? Because the guys who didn’t miss shot
hardly any free throws, no one has ever gone a full season and shot a decent
amount without missing and there should be a statistical possibility of a miss (it
is only 1 in a thousand by the way). Clark shot only 7 free throws and Brown
only 3. Clark actually shot the most free throws of any player who did not miss
in the 2018-19 season. I think it is fair to say that it wouldn’t take many
more attempts for him to get a miss.
I’ve gone back to
the 2013-14 season and from that point forward the most free throws shot in a season without a
miss by far was 25, by 2017-18 Koby Simmons of Memphis. That’s pretty impressive. But
I would still assign him a miss. I don’t know where I would draw the line
exactly as the point where I would not assign 000 as a miss, but 25 is
certainly not close to it. I think qualification for the NBA season free throw
percentage leader is the minimum, and no 100% shooter has ever qualified. José Calderón has the best single
season at 98.05% in 2008-09 (he made 151 of 154 btw). Calvin Murphy is second
but more than 2 percentage points less. I don’t think it is something we need
to worry about.
We could get
really pedantic and talk about the extremely unlikely situation of a 0% free
throw shooter who rolls 000. But that isn’t sexy, and we want to keep the vibe
going. :) Until next time…
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