History of the SOM 3-Pt Rule

Time for more ‘Stache Talk! I don’t think I am revealing top secret information when I say I am a bit obsessed with 3-Pt shots. I want players to shoot threes in the proper ratio with the clearly inferior 2-Pt shot. I want them to maintain the accuracy they demonstrated in reality and which SOM worked so hard to simulate. Heck, I regained my love for the NBA and SOM when the Warriors exploded with their 3-Pt barrage in 2014-15. So it should be no surprise when I say that Chris’s recent Basketball Roster Post got me thinking about the Rodman Rule. Wait, no, it got me thinking about three-pointers! More specifically, it got me wondering about the history of SOM’s 3-Pt rule. So I looked at the roster sheets for every one of the “yellow box” seasons to determine when the rule changed. I found it interesting and hope you do too.

The 1980-81 roster sheet, labeled as “1981-82 STRAT-O-MATIC 23 TEAM BASKETBALL ROSTERS,” (as a side note, the roster sheets listed the SOM season, the season of the release, not the NBA season, which was the prior season, until the 1991-92 season) had no mention of the 3-Pt shot. The NBA introduced the long gun the season prior, and teams put up an average of 2.8 attempts per game that maiden season, led by the San Diego Clippers at 6.6. Shot attempts fell to 2 per game in 1980-81, with the Clippers again firing away at the highest clip (5 per game).

The 1981-82 roster sheet had one sentence relevant to the 3-Pt shot: “For realistic results, Campy Russell of the New York Knicks should only attempt one 3-point shot per game.” Why single out the 30-year old Russell? Well, he led the league in 3-Pt percentage, shooting 43.9% from deep. But it was on only 57 attempts in 77 games played, so less than an attempt per game. His card has him as a 2-7, 12 3-Pt shooter, pretty awesome! So you can see why he should be restricted. But then why not limit Andrew Toney, who took only two more 3-pt shots in the same number of games, and shot nearly as well at 42.4%? He is a 2-7 3-Pt shooter on his card. Doesn’t make sense why he is not restricted as well. The story gets sadder for Campy when you realize he missed the next two seasons with a knee injury then returned in 1984-85 to play just three final games for his original team, the Cavaliers. Campy wasn’t especially proficient in the seasons prior to 1981-82, so his accuracy that season may have just been a fluke, but we will never know.

The next season, 1982-83, SOM players are advised to limit both Trent Tucker, a legendary gunner from distance who shot 40.8% for his career on an average of 1.9 attempts per game (peaking at 3.7 attempts in 1988-89), and Kevin Grevey, who made a three on opening day of the 1979-80 season, to a single 3-Pt attempt per game. As for everyone else, bombs away apparently.

Teams averaged 2.4 3-Pt attempts per game in 1983-84 and SOM saw fit to implement the following instruction on the roster sheet: “Please note that all players except the following may only take one 3 pt. shot per game. The following players may take the amount found in parentheses below.” Ten players are listed, all allowed to take a pair of 3-pt shots except for Darrell Griffith, who was allowed a maximum of four. Dr. Dunkenstein led the league in 3-Pt accuracy as well as attempts, shooting 36.1% from behind the line. His card has him as a 2-6, 11 3-Pt shooter, which seems a little high but the team defense cards were much stingier against three-pointers back then.

1984-85 is notable for being the first of four consecutive seasons that Larry Bird shot 40% or better from downtown. He shot 42.7% on 1.6 attempts per game in 1984-85. His peak attempts per game in this run was in 1987-88 when he hoisted 3.1 per game, though he would attempt 3.3 in the 1990-91 campaign. The roster sheet has the same language as the prior season but now lists twenty-one players who may take more than one attempt per game but not more than the number listed. Griffith again is allowed the most attempts with four. Darrell averaged 3.3 attempts per game, so limiting him to four will probably allow him to shoot about the right amount over the course of an entire season. But the problem with the early SOM approach is that in real life players often took more than this limit and this rule doesn’t allow for the variation that actually happened. For example, Griffith launched six three-pointers on five different occasions that season and in three games he attempted seven 3-Pt shots. He failed to shoot a three-pointer in seven games.

Twenty-one players again are listed in the 1985-86 roster sheet as allowed to take more than one 3-Pt shot in a game. Three attempts is the most any player can take and that includes Larry Bird, World B. Free and Dale Ellis. Seven players shot better than 40% that season, led by Tucker and Craig Hodges, another 3-Pt legend, who each shot 45.1%. Each has a card reading of 2-7, 12. It is worth noting that Ernie Grunfeld, in his final season, is a 2-7 3-Pt shooter. He put up 61 attempts over 76 games, which was four times more attempts than he had ever previously had. Wannabe Grunfeld gunners would be saddened to learn he was not listed as an exception and thus was limited to a single attempt per contest. Teams were still only averaging 3.3 attempts per game.

The 1986-87 season saw teams increase their 3-Pt output to 4.7 attempts per game. Kiki Vandeweghe only attempted one per game but he shot a remarkable 48.1% from 3-Pt land. His SOM card has him as a just-as-remarkable 2-7, 10 marksman. Not a lick of defense or rebounding. I jest of course. I love peak mid-80s Kiki. The number of players listed on the roster sheet who can take more than one 3-Pt attempt per game grew to thrity-five. Bird, Ellis, Tucker and Hodges were among those who could launch up to three from deep.

The list of players who could take more than one 3-Pt shot had swollen to forty-two for the 1987-88 season, led by Danny Ainge and Michael Adams, each of whom could take up to five shots from distance. Hodges changed teams but was still deadly from downtown, connecting on 49.1% of his attempts, which SOM correlated to a 2-7, 12 rating.

The 1988-89 season is notable for (1) team 3-Pt attempts jumping from 5 per game to 6.6; (2) players who attempted 200 or more 3-Pt shots increasing from four the prior season to sixteen, including a CENTER Jack Sikma; AND, perhaps most importantly, (3) SOM changing the 3-Pt rule, though it is not clear from the roster sheet to what. If there was a 3-Pt system for this period, I don’t think it was the “super advanced” rule, which, based on the information on the roster sheets, did not appear until the 1990-91 season.

Okay, so here is what the 1988-89 roster sheet tells us: “When attempting a 3-Pt. Shot, if the dice roll is listed in 3-Pt. Replay – follow normal replay rules. Otherwise, 3-Pt. shooting rules apply.” That’s it. There is no longer anything about limiting to one attempt per game or listing players who are allowed to take more. And there are no numbers after each player so I don’t think the Automatic Three-Point Shot rule that would take place soon after, and which is still in place today, happened yet. So, SOM added replays to 3-Pt shooting, and took away the rule limiting attempts but replacing it with apparently nothing. I don’t know. I believe there may have been a change in the rule book but I don’t know that for a fact. I would love to hear from someone who knows.  For me, this is the dark age of SOM three-pointers.

Same for the 1989-90 season. The roster sheet just reiterates the replay statement and nothing else. Sikma came up one attempt short of 200. Sad days. In 2015-16 Steph Curry would MAKE 402 3-Pt shots, more than anyone but Michael Adams (432) ATTEMPTED in 1989-90.

An Enlightenment occurs for the 1990-91 season! Hallelujah! The roster sheet provides that “we are enclosing Super Advanced Rules for the basketball purist.” Each player on the roster sheet has a number after his name, which “refers to their three-point frequency. Please refer to automatic three-point shots found under Super Advanced Rules to use this system.”

I have a copy of what are entitled “SOM BASKETBALL SUPER-ADVANCED RULES.” I believe they are the rules referred to in the 1990-91 roster sheet. I say that because there is a chart entitled “ADDITIONAL THREE-POINT SHOTS ALLOWED CHART.” And the roster sheet from the 1991-92 season announces a “REPLACEMENT RULE FOR ‘ADDITIONAL THREE-POINT SHOTS ALLOWED’ CHART.”

Regardless, this is the rule with which all modern SOM players are familiar. All players are given a three-point frequency rating between 0 and 6, and when the FAC reads “outside shot only” you roll a six-sided die and if the result is less than or equal to the player’s frequency rating, he takes a 3-Pt shot. Furthermore, “[w]hen using this rule, teams may not take any other three-point shots except ‘half-court’ three-point shots (described above), and three-point attempts allowed on the ‘Additional Three-Point Shots Allowed Chart.’” The half-court shot is allowed under Super Advanced Rules when a team gets a defensive rebound on the last action card of a period and the Normal Control section lists a position and not a pass. That player heaves the ball, you roll the six-sided dice and if the total is 12 the shot is good. Personally, I have revised that rule a bit and combined it with the buzzer beater shot referred to in Chris’s Expert Rules, but let’s not get into that. The chart, which again is rescinded the following season, tells you when you may take unlimited 3-Pt shots based on how much time is left and how many points you are trailing by (though in final two minutes of the game you can take unlimited 3-Pt shots regardless of score).

The important thing here is that in 1990-91 SOM gave us the 3-Pt frequency rating and “outside shot only” rule which is still in effect today. I’m sure that rule made sense and adequately reflected 3-Pt frequency at that time. In the 1990-91 season, teams averaged 7.1 3-Pt attempts per game, with Denver leading the league at 12.9. But in 2018-19, the last full NBA season, teams averaged 32 3-Pt attempts per game, with Houston leading the Association with 45.4. Now, it should be noted that the vast majority of players were nowhere near being assigned a 3-Pt frequency rating of 6 in 1990-91. In fact, ten of the twenty-seven teams had ZERO players who were assigned a 6 and another eleven teams had only one such player. Only two teams, Portland and Indians, had three prolific 3-Pt shooters. In 2018-19, there are literally entire teams, such as Toronto and Atlanta, where every single player, including additional players, is assigned a 3-Pt frequency of 6. Still, that doesn’t allow for enough 3-Pt shots. Not in today’s game. The rule is and has been for quite a while outdated, and that explains why Chris came up with his own rule (detailed in his Determining Three-Point Shot Attempts post), why I am trying to improve on that rule slightly, and at least partially why I am obsessed with the long gun (thanks also to George Blaha, longtime Piston play-by-play announcer).

In 1991-92 we get the “REPLACEMENT RULE FOR ‘ADDITIONAL THREE-POINT SHOTS ALLOWED’ CHART.” This change allows for unlimited 3-Pt shots in the following circumstances: (1) any time a team trails by 10 or more points; (2) in the fourth quarter when a team trails by more points than there are minutes left (the example given is down by 6 with 5 minutes to go); and (3) in the final 2 minutes of the game, regardless of score. SOM notes that a player must “ALWAYS be positioned outside in order to take a three-point shot.” The replacement rule is very similar to what was on the chart, with only minor differences. I will note that the aforementioned Rodman Rule, which concerns rebounding and not 3-Pt shots, was also announced for this season.

There were no 3-Pt rule changes in the 1992-93 and 1993-94 seasons. Thunder Dan Majerle led the league with 503 3-Pt attempts and 6.3 attempts per game in 1993-94, connecting on 38.2% of them. His card  rating is  2-5, 9 with a replay at 10. In that same season Reggie Miller was 18^th in attempts per game with 3.7 but found the bottom of the net 42.1% of the time, more than anyone with more attempts per game. SOM graded him as a 2-6, 12 with a replay at 8 3-Pt shooter.

The 1994-95 season saw the NBA shorten the distance of the 3-Pt line from 23’9” (and 22’ in the corner) to a uniform 22’ all around. It is also saw SOM introduce the 3-Pt foul, which occurred on X-12 dice rolls. If you rolled X-12 on a 3-Pt attempt you would then “[r]oll the two white dice again and if a 7 occurs the basket is good (possible 4 point play). If any other number occurs attempt three free throws.” Whether it was the change in distance or the addition of a SOM 3-Pt foul, the result was clear – more 3-Pt shots were attempted than ever before! In the 1993-94 season teams averaged 9.9 3-Pt attempts per game while in 1994-95 the rate increased by more than 50% to 15.3 attempts per game.

From 1995-96 through 2011-12, no changes were made to SOM’s 3-Pt rules. It is interesting to note that in 2011-12 teams took an average of 18.4 3-Pt attempts per game. That is only 3 more attempts than occurred in 1993-94. That marginal increase seems crazy by today’s standards, influenced by advanced analytics and Steph Curry. It can partially be explained by the fact that the line was moved back after the 1996-97 season. With the reversion teams attempted an average of only 12.7 attempts per game in 1997-98. I also find it interesting that accuracy dipped only from 36% in  the final season of the shorter line to 34.6% the following season. Even more amazing to me, in 2018-19 the average 3-Pt shooter connected on 35.5% of his attempts. Players haven’t improved that much, if at all, from behind the line in the past twenty years, yet are attempting more. Analytics, man!

For the 2012-13 season, SOM made a change to the “REPLACEMENT RULE FOR ‘ADDITIONAL THREE-POINT SHOTS ALLOWED’ CHART.” They removed the third situation where additional 3-Pt shots were allowed. But they didn’t do it explicitly; they didn’t tell us they were doing it, they just included the rule in the roster sheet as they have since they introduced it but without the third situation. AND they made a mistake doing it, which they have not corrected. Let me include the new rule verbatim: “Additional three-point shots are allowed as follows (ignore  the chart, found in the Super-Advanced rules in the instruction book): (1) Any time a team trails by ten or more points they may take unlimited three-point shots; (2) In the last ten minutes of the game if a team is trailing by more points that time left (for example, down by six with five minutes to go), they may take unlimited three-point shots, regardless of the score.” Regardless of the score?!??!?! What?!?!?! That doesn’t make sense. The team had to be trailing by more points than there are minutes left. Whether they can take unlimited 3-Pt is dependent on the score.

The former rule had three unlimited three situations. The language for the second situation ended with “they may take unlimited three point shots.” Then the third situation was “(3) In the last two minutes of the game, both teams can take unlimited three-point shots, regardless of the score (emphasis added).” SOM took out the third situation but forgot to remove that final phrase. And to this day they have not fixed it. It is still there in the 2018-19 roster sheet. Is it possible they didn’t intend to remove the third situation at all? Sure, and a piece of evidence pointing in that direction is SOM's failure to include an "and" between the ONLY two situations where additional 3-Pt shots are allowed. If there are only two situations there should be an "and" between them. But if there are intended to be three, and somehow most of the third situation got chopped off in a copy and paste disaster, then not having an "and" between situations one and two is correct. Oh boy! I am not crazy about these unlimited situations to begin with, and I don’t see why there should be a rule for threes that is then ignored during the final two minutes of the games. So I think they intended to make a change and just inadvertently failed to delete that final phrase.

The most recent rule change, an excellent one, occurred in 2017-18. It replaces the X-12 rule. Now, when you roll an X on a 3-Pt attempt, you look to the shooter’s O column, and if the result is a foul, then the player was fouled attempting a 3-Pt shot. If the roll is any other result, the shot is missed. And, just like the X-12 rule, if the player was fouled you roll again to see if you get a 7 and a 4-point opportunity. I like this rule but I advise that for players who do not have a foul in their O column, that X-12 be a foul. I believe that there should be a possibility of a foul for every 3-Pt shooter.

That is the history of the SOM 3-Pt shot rule. And I think we should mostly scrap it. The "outside shot only" rule worked well for a time but no longer, not when teams are shooting three-pointers on more than one-third of their field goal attempts. In my next post I will detail my approach for remedying the situation. 

X Files Section

I've added a new X Files section to the blog, which can be accessed via the X Files link located on the menu below the site heading.

The first files I've made available are Excel worksheets for keeping season replay statistics for you team. I created these a number of years ago to keep stats for my Boston Celtics replays. I plan on adding more files in the near future, and will post to let you know whenever I've added to files to the section.

Basketball Roster Sheets

You've just scored the 1987-88 season cards off eBay, but it did not include a roster sheet. What is one to do? Where can you get the roster sheets for past carded seasons for the Strat-O-Matic basketball board game? Well, you're in luck, because Strat-O-Matic has made rosters sheets available, for every previously carded season, on their Website. The thing is though, they can be hard to find if you don't know where to look.

In order to find the Roster Sheet Archive section on the Strat-O-Matic Website, you have to click on the site menu icon, and then click on the 'STRAT-O-MUSEUM' link, to get to the 'ROSTER SHEET ARCHIVE' link. From there, you click on the 'Read More' link under the "Basketball Rosters" heading. Not very intuitive, for sure, but they are there to be had. Not only can you print the roster sheets directly from the Website, but you can also download them as well (they're in PDF format). I have included a direct link to the basketball roster sheet section of the Strat-O-Matic Website at the bottom of this post.

As some things can be hard to find on Strat-O-Matic's Website, I'm also including this tip on how to search Strat-O-Matic's Website (or any Website, for that matter), using Google, or your browser's search box:

Type site:www.website.com search term in the search box and hit Enter. For example, if you enter site:strat-o-matic.com basketball roster sheets you will get a direct link to the page with the Strat-O-Matic basketball roster sheets at the top of your search results. Pretty nifty!

As promised, here is the direct link to the basketball roster sheets on the Strat-O-Matic Website:

http://www.strat-o-matic.com/basketball/basketball-rosters/

Free Throw Problem & Solution

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 1/10^th 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…

Variable Rest (Basic/Advanced)

As I've mentioned previously, I use the Basic/Advanced rest rule when I play the game. I'm just not a fan of Super-Advanced Playing Time Chart. To me it just seems like too much micro-managing of minutes for EVERY player in the game, and results in wasted time spent trying to figure out how many two-minute intervals everybody can play in each half.

On the other hand, using the Basic/Advanced game rest system can easily result in players getting way more minutes than they did in real life, especially if you're also using the Super-Advanced "Playing Safe" rule in your games. For example, you could easily get a player who averaged 34-minutes per game in real life averaging 40 to 42-minutes per game in your Strat basketball games.

So, I've come up with a simple method of better controlling playing time, which is kind of a happy medium between the Basic/Advanced and Super-Advanced game's rest rules. What I've come up with  is this:

Variable Rest 

Prior to the start of a game, roll a six-sided die for each player in the starting lineup. If the result of the die roll is 1-3 then use the player's original Rest rating for that game. If the result of the die roll is 4-6 then downgrade the player's Rest rating one level (2 to 6, 6 to 12, 12 to 18, and 18 to 24) for that game.

It is recommended that the Variable Rest rule be used only within a season replay, or when playing games that represent a regular season match-up between teams. When playing playoff or tournament games, you should use the original Basic/Advanced game rule as written, as this will allow the playing of extended minutes by starters, which you would normally see in playoff or tournament games.

I really like the unknown factor that this rule brings to my regular season match-ups; will Jayson Tatum be able to give the Celtics 36 minutes, or does he only have 30-minutes in the tank tonight?

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…