Big Man Switches onto Steph - UH OH!

Hey SOM fans, this is Derek Kraft. Chris has graciously allowed me to post on his blog. Here is the scenario I want to talk about: 2015-16 Steph Curry, the lethal break-the-game wizard at the height of his powers, has the ball. A pick is set and a big man is switched onto him. What should Steph do, step back and shoot the three, dribble behind his back and pull up for the midrange jumper, or put the big man to the test and attack the basket? There is a general answer (SPOILER ALERT-PENETRATE) but the better answer is, it depends. I will look at how well he does shooting the long ball, taking the outside shot and penetrating against 3 different teams (Utah, Atlanta and Phoenix) and 2 different players on each team (Derrick Favors and Rudy Gobert, Al Horford and Paul Millsap, and Tyson Chandler and Alex Len). In 4 of the circumstances, the answer is penetrate, but in the other 2 the long ball is the better option statistically.

The first thing to do is to outline the assumptions we are making about the game and how we play.

A “Switch…Any OPEN shot” result from the FAC (occurs 10x for Home and 5x for Visitor) is the scenario we are looking at. `

I treat the D-7 Penetration (and Inside for that matter) result on every team defense card and the Blank-9 Penetration (and Inside) result on the vast majority of player cards, including Steph’s, the same. When the defender is the Block Man, the shot is automatically missed. If the Block Man is not the defender, we look to see if the Block Man has blocked the shot. If he has the shot is missed but if he hasn’t the shot is good.  The official SOM rules treat the D-7 roll like that but not the Blank-9. I don’t see the point of rolling a 20-sided die (or checking the FAC for the split, for you old-school players) just to check for a blocked shot statistic that has no bearing on the game. I treat the Blank-9 the same as D-7 in that shots that are not blocked are made. Chris espoused this take in his infamous Expert Rules, and I believe he still plays that way.

I am using Chris’s Shooting Rule Adjustment 14.3 as outlined in his March 23, 2000 post. For our purposes, the effect is that on 3-Pt shots, all X rolls are misses and for Blank rolls we first consult Steph’s O column to see if there is a foul, and if not we re-roll the 2 6-sided die and look at his 3-Pt shooting.

Chris outlined an Offensive/Defensive Foul Adjustment in his April 14, 2020 post (and in the Expert Rules) and I use that, though I use the 20-sided die and not a separate colored 6-sided. Quickly, whenever an Offensive Foul reading occurs on the team defense card (Penetration rolls of 9 and 11 for our purposes), I roll the 20-sided and if the result is odd it is an offensive foul and if even then a defensive foul.

I am looking to see which shot results in the greatest number of points, not which shot results in the highest FG percentage. Steph has a replay in his 3-Pt shooting so, though it isn’t a missed shot, it doesn’t result in any points and thus is equivalent to one for our purposes. And c'mon, if you roll the 3-Pt replay in a Switch situation, you aren't gonna be happy. It's like rolling the X when you have a dominant player on the break. UGH!

For free throws, I am using Steph’s combos (he is 2-10 so 33/36), which results in .91667 and not his real life percentage of 90.8. As an aside, it astounds me that SOM can get a player’s 3-pt shooting to within a couple decimal places of accuracy (see my comments under Chris’s Shooting Rule Adjustment post), but with something as easy as free throws a player can be almost a percentage point off. That may be a topic for a future post.

I am using the Normal team defense cards.

Finally, I am assuming that the Block Man on each team is the player with the best block rating. So for Utah that is Gobert (1-14 rating), for Atlanta Millsap (1-10) and for Phoenix Len (1-7).

Ready for some number crunching?!?!? If this discussion gets to be too much, you can scroll to the bottom where I have inserted a chart that has all the numbers.

Let’s start with the basics. There are 36 combinations in each of the Outside, Penetration and 3-Pt shooting columns. If anyone wants me to explain this I will be happy to in the comments section. The Black die has 6 readings, 3 Blanks, 2 Ds and an X. This means that over an infinite number of rolls, 3/6 or ½ of the Black die rolls will be a Blank, 2/6 or 1/3 D and 1/6 X. This is important because once we figure out the number of combos per shot type and multiply by either 2 or 3, depending on whether it is a 2- or 3-pt shot, we then need to multiply our Blank columns by 3 and our D columns by 2 to account for the fact that these rolls are more common.

Steph’s card is truly awesome. The only outright miss he has in the Outside column when he is open is a 4, and he has a chance to score on every Penetration roll unless the Block Man is on him or the Block Man is a dominant shot-blocker. I will try and limit the math but let’s do it for Steph’s Outside column just so we can see how it is done. He has an X or O on rolls of 2,3,5,7,8,9, and 10. That is 25 combos right there. He has an X 1-10 at 11 (so that is .5 x 2 = 1 combo) and O 1-13 at 12 (.65 combos). Finally he has an F(2) at 6. For that we multiply 5 combos x 33/36 which equals 4.58333 combos. Adding them up we have 25 + 1 + .65 + 4.58333 = 31.23333 combos. We multiply that by 2 because each combo is worth 2 points. That gives us 62.46666 points. Finally, we multiply that by 3 because Blank rolls are 3x more likely than X rolls. Our final total for Steph’s Outside column is 187.39998 points. That is how many points he will generate on 108 rolls on his Outside column (36 combos x 3). Another way of looking at that is that for every Blank roll on an Outside shot, Steph will generate 1.735185 points.

For a Penetration shot on a Blank roll, we do the same thing, except now we have to account for the Block Man on 9 and the X+ F(1) roll on 10. For the X+, we multiply Steph’s free throw rating (33/36) by the number of combos, 3, then multiply by ½. We have to multiply by ½ because he is only getting 1 free throw and not 2. So the X+ itself is equal to 4.375 combos. Assuming Steph has the Block Man switched onto him, and thus the 9 roll is an automatic miss, Steph has a total of 31.54167 combos or 63.08333 points, which we multiply by 3 to get 189.25 points. That is the baseline. That is how many points he will score on 108 Blank rolls Blank against Gobert, Millsap and Len.

When the Block Man is not switched onto Steph, we need to look at the Block Man’s rating, determine the decimal of shots that are NOT blocked, and multiply that by the number of combos (4), the number of points per combos (this is a 2-pt shot so 2) and then by 3 to adjust for the propensity of rolling a Blank. Gobert is a 1-14 block, so .3 (6/20) of Steph’s Blank-9 shots will be good. 4 combos x .3 x 2 x 3 = 7.2 pts. We add 7.2 to the baseline to get the number of points Steph scores when he is guarded by Favors on a Penetration shot with a Blank roll, 196.45 points. Len is a 1-7 block so when Chandler guards Steph the total is 204.85. Millsap is 1-10 so when Horford switches onto him Steph scores 201.25 points.

Rolling a Blank on a 3-Pt shot brings an extra complication because we first are looking to see whether there is a foul. Steph has an F(2) (which is an F(3) here) on 6 in his Outside column, which comes to 5 out of 36 combinations. This is important because when we calculate Steph’s final 3-Pt score on a Blank roll, we need to account for that fact. Those free throws come out to 4.58333 combos, or 13.75 points (remember 3 free throws and not 2) x 3 which equals 41.25 points. Steph is a 2-6,11 3-Pt shooter, which is 17 combos or 51 points x 3 = 153 points. We can’t just add those point totals together because you don’t get both. You get the Foul 5/36 of the time and a chance on his 3-Pt shooting column only 31/36 of the time. So we multiply his 3-Pt points, 153, by 31/36 then add 41.25 to get a total of 173 points. Steph scores 173 points on 108 Blank 3-Pt opportunities.

So on Steph’s card, even the baseline Penetration shot, where the defender is the Block Man or when the Block Man is 1-20 block, is the best at 189.25 pts, compared to 187.39999 for Outside and 173 for a 3-Pt shot. As many of you probably surmise, it is on the team defense card where the 3-Pt shot makes its comeback.

On the team defense cards, it is the Outside shot that is the weakest. On Utah’s card, Steph sinks the jumper on only 11.2 combos. You multiply that by 2, the number of points an Outside shot is worth, then multiply again by 2 because D rolls are worth twice what X rolls are worth. So Steph gets 44.8 points on 72 shots on Utah’s Outside column. Similarly, against Phoenix he scores a total of 46.8 points Outside and against Atlanta a measly 35.8 points.

As well as the F(2) foul on D-4, we have to deal with the offensive/defensive fouls on D-9 and D-11 on Penetration shots. There are a total of 6 foul combos then, 3 for the D-4 roll, 2 for D-9 (4 combos x ½ because 2 are offensive fouls) and 1 for D-11 (2 combos x 1/2 because 1 is offensive). And then we have the D-7 Block Man roll. If the Block Man Gobert switches onto Steph, the D-7 roll is always missed and Utah’s team defense card gives up 14.25 combos, or a total of 56.5 points. If Favors switches onto him, Gobert blocks D-7 20-sided rolls 1-14, but gives up the bucket for 15-20. So .3 x 6 combos = 1.8 combos x 2 x 2 = 7.2 pts. We add that to 56.5 to get 63.7. Against Phoenix he scores a total of 58 pts when Len is switched onto him. Against Chandler and with the 1-7 Block Man Len, a shooter tallies 73.6 pts. Against Atlanta and Millsap, Steph gets 52.6 points. Against Horford and with 1-10 Millsap behind him, you get 64.6 points. So the baselines were 56.5, 58 and 52.6  against Utah, Phoenix and Atlanta respectively, but 63.7, 73.6 and 64.6 with the Block Man called into duty as Block Men. As a solid Block Man Rudy allowed only an extra 7 points while Len as a poor Block Man allowed more than 15 extra points.

Honestly, I was surprised how many points the team defense cards give up on 3-Pt shots. Against the Jazz, the long ball is good on 19.45 combos or a total of 116.7 points after multiplying by 3 for the number of points each basket is worth and times 2 to account for the D rolls. Phoenix gives up a total of 128.7 points and Atlanta 105.3 on the 3-Pt shot.

Quickly, just looking at Utah, they give up 44.8 points on the Outside column, between 56.5 and 63.7 points if you Penetrate and 116.7 points on the 3-ball. A 3-Pt shooter rolling a D against Utah has a 54% of hitting the shot (19.45 combos / 36). At 2-6,11 with a replay at 7, Steph shoots just under 57% from downtown on his own card. So even for a sharpshooter like Steph a D roll isn’t bad, but for your average 3-Pt shooter YOU SHOULD WANT to roll a D.

Finally, the X roll. All 3-Pt shots are automatic misses so 0 points against all 3 teams and 6 players. Utah’s Gobert and Favors have the same O and P X columns, 12 combos or 24 points on Outside shots and 24 combos or 48 points on Penetrations. Both Phoenix defenders give up 24 points on Outside chances and Len gives up 60 points on Penetration shots while Chandler gives up 48. Millsap is an excellent one-on-one defender, giving up only 12 points Outside and 36 Penetrating.  You score 24 point shooting Outside against Horford and 48 penetrating. The key takeaway here is probably self-evident – the big man doesn’t do well when he is backpedaling.

What does all this tell us? Well, against Utah and Favors, penetrating is about 18.5 points better than shooting a 3-Pt shot. Against Gobert it is only 4 points better. If Horford switches, Steph is 35 points better attacking the rim. But against Millsap, whose X column is 12 points better and, because he is the Block Man , all those D-7 and Blank-9 rolls are now misses, the long ball is the slightly better option, by about ½ a point. If up against Chandler, attacking is almost 25 points better, but against Len the Block Man the 3-Pt shot is 7 points better. This is because when Steph penetrates against Chandler, Len is a weak Block Man, but those same shots are automatic misses when he switches onto Steph, so the 3-Pointer becomes the better option.

Look below at the Blank numbers, especially against the Block Men. The P column is less than 2 points better than the O column and 16 points better than the 3-Pt shot. Against the non-Block Men the P shot does better, and gets better and better the worse the Block Man is. The 3 gains a ton of points against all the team defenses, but the Penetration outperforms the Outside shot. And then there is the X roll where P is clearly superior.

	Outside	Penetration	3-pt
Blank v Utah Favors	187.39998	196.45	173
D-Utah v Favors	44.8	63.7	116.7
X - v Favors	24	48	0
TOTAL	256.19998	308.15	289.7
Blank v Utah Gobert (BM)	187.39998	189.25	173
D-Utah v Gobert	44.8	56.5	116.7
X - v Gobert	24	48	0
TOTAL	256.19998	293.75	289.7
Blank v Atl Horford	187.39998	201.25	173
D-Atl v Horford	35.8	64.6	105.3
X -v Horford	24	48	0
TOTAL	247.19998	313.85	278.3
Blank v Atl Millsap (BM)	187.39998	189.25	173
D-Atl v Millsap	35.8	52.6	105.3
X -v Millsap	12	36	0
TOTAL	235.19998	277.85	278.3
Blank v Pho Chandler	187.39998	204.85	173
D-Pho v Chandler	46.8	73.6	128.7
X -v Chandler	24	48	0
TOTAL	258.19998	326.45	301.7
Blank v Pho Len (BM)	187.39998	189.25	173
D-Pho v Len	46.8	58	128.7
X -v Len	24	48	0
TOTAL	258.19998	295.25	301.7

What conclusions can we draw here? Because we can’t do this kind of math during the game when you only have 24 seconds to get a shot up! For a lethal scorer like Steph who gets buckets in every column, the choice comes down to penetrating and shooting the 3 when a big man switches onto him. And from there I would look to see who the player is on him (is he the Block Man, how good is his X column?). If a wing switches onto him I would think usually the decision is still between a Penetration and 3-Pt shot, but I can certainly envision a situation where you have a Manute Bol-type Block Man and an undersized guard whose O X column is weak but whose P column is strong, and an Outside shot may be the answer.

Another consideration of course is foul trouble, If Steph picked up a couple of early ones we probably wouldn’t want to risk him getting an offensive foul by penetrating.

Let me end by saying that if we changed the scenario to the final shot of the game and the Warriors down only 1, we would want to look at which shot produces the greatest number of combos, and not necessarily points, because a 3-Pt shot has more misses and, assuming you aren’t a betting man, it doesn’t matter whether you win the game by 2 points or only 1. The possibilities are endless. Until next time…