14.0 SHOOTING
14.3 Basic game procedure applies to a three-point shot attempt with one exception: If the black die reads X, the shot is automatically not good.I've found that there are two problems with the three-point shot rules in the Advanced game; one is that players who attempted a low number of shots per 48 minutes (and have a lot of Replay results in their shooting columns to reflect this), but were proficient three-point shooters, have the ability to get WAY too many shot attempts per game by only attempting three-point shots.
2019 P.J. Tucker is a prime example. Tucker played 34 minutes per game, attempting only 9.0 FGA per 48 minutes, but 74% of his shot attempts where three-point shots, with a three-point shooting percentage of 0.377. Tucker has 26 Replay chances in his shooting columns, but also a 3-Pt. Shooting rating of 2-5, 11-12 and a 3-Pt. Replay on 10. So, a player who attempts 9 shots per 48 minutes, nearly 7 of which are three-point attempts, has just a 4% chance of getting a Replay result when attempting a three-point shot, but a 36% chance of a Replay result when attempting a two-point shot. Say what?!?! Yeah, that's right. Under the current three-point shooting rules, P.J. Tucker and other players like him can jack up 12 threes per 34 minutes played, conveniently ignoring all of those Replay chances in their regular shot columns, that are supposed to limit a players field goal attempts.
The second problem with the three-point shot rules in the Advanced game, since the proliferation of the three-point shot in the NBA, is the loss of fouls, and thus free throw attempts, in a game that has been producing low fouls and free throw attempts over the past 20-plus seasons. Even with the new Three-Point Foul Shot Attempts rule that was re-written by Strat-O-Matic just this year (located at the bottom of the 2018-19 roster sheet, on the Western Conference side), fouls and free throw attempts are still at unrealistically low levels.
So, in an attempt to rectify these short-comings in the Advanced game, I have re-written rule 14.3, as follows, in my game play:
14.3 Basic game procedure applies to a three-point shot attempt with two exceptions: if the black die reads blank, compare the result of the white dice to the shooters Outside shooting column; if the result is a Replay or an F(2) reading, then accept that result instead and no three-point shot is attempted. If any other result occurs, re-roll the two white dice and compare the result to the player's 3-Pt. Shooting section to determine if the three-point shot was made or missed (if the shooter has neither Replay nor F(2) results in their Outside shooting column, just accept the original result of the white dice for that player). If the black die reads X, the shot is automatically not good.Now, guys like P.J. Tucker, who only attempted 6 FGA per game in real life, can't fire away from three as if they were James Harden or Stephen Curry. In addition, players who have F(2) results in their Outside shooting columns won't be further diminishing fouls and free throw attempts in the game when shooting threes.
I've been using this revamped rule in my current 2019 NBA tournament play (http://www.stratfanforum.com/sffipb/topic/67317-2019-nba-tournament/) with very good results. I highly recommend giving this rule revision a spin in your games; I think you'll find that you like using it as much as I do.
Greetings! This is Derek. I commented under your Determining 3-Point Shot Attempts post the other day. Love your ideas but I am going to disagree here. No offense intended. SOM has done a really good job, as I will show, of closely replicating a player’s 3-point percentage. But that requires that 1/2 of a player’s 3-pt shots come as a result of rolling a blank, 1/3 from rolling a D and 1/6 from rolling X. I am going to use 3 2018-19 players and a 2018-19 team defense to show how closely SOM accurately delivers a player’s 3-pt shooting percentage and then I am going to use 2 of those players to show why your system doesn’t. The worse a player is at shooting 3s the more your system is off here.
ReplyDeleteLet me make the math easier by assuming there are no replays and no fouls on 3-pt shots. Using the SOM system we know you would roll:
(1) X 1/6 of the time and shoot 0% on those shots;
(2) D 1/3 of the time and, using the Utah Jazz defense, a team that gave up the league average 35.5% from beyond the arc, and shoot 53.19% on those attempts (5,6,8,9,12 are X and 2 is X 1-3, so 19.15 of the 36 combinations are X, 19.15/36 = 53.19%), and;
(3) a Blank, the player’s card, ½ the time.
Let’s take Steph Curry and again, let’s make it simple and ignore the 3-pt replay 8 on his card. He is 2-6,12. So he is 16/31 (we are not counting the 8 as a miss, that wouldn’t be fair, we are just going to pretend for simplification that we never roll it). That is 51.61%
Over an infinite number of attempts, Steph will shoot 0% 1/6 of the time, 53.19% 1/3 of the time and 51.61% ½ of the time.
The math:
X shots = 0
D shots = 1/3 x .5319 = .1773
Blank shots = ½ x .5161 = .25805
0 + .1773 + .25805 = .43535 = 43.535%
Steph’s actual 3-pt shooting percentage for the season was 43.703%. SOM has come within 2/10s of a percent, That is ACCURATE.
Steph doesn’t have any Replays in his O column, and he does have a Foul. I am not opposed to your rule for a guy like him. Even with the SOM 3-pt foul adjustment in recent seasons (at one time there was no chance of a foul, then it became X12 I think was a foul, then if you roll X you look at the player’s O column and if it is a foul then it is a foul and if not a miss), we aren’t getting enough 3-pt fouls. Your system would increase that which is a good thing. But for players with a plethora of replays in their O column, your system does not maintain accuracy, especially as a shooter gets worse. The reason is because a greater percentage of their 3-pt shots come on a roll of D, which, as seen above, even for a marksmen like Steph, produces a higher percentage of makes. Steph shoots 51.61% on his card but 53.19% when he rolls on the league average defense. Imagine how that would affect a guy who shoots 37.73% or 28.48%.
Let’s look at your example, PJ Tucker, and another player, Draymond Green. Interestingly, their O columns are different but for purposes of your rule, statistically the same. Neither has a foul in their O column, Tucker has replays on 6-12 and Draymond has replays on 5-8 and 10-12. Under your system, each of these guys would attempt a 3-pointer only 27.78% of the time that they rolled a Blank. Of the 36 possible combinations, they would roll replays on 26 of them, and thus not shoot, and roll a non-replay/non-foul result only 10 times. 10/36 = 27.78%.
ReplyDeleteOn their own cards, Tucker is a 2-5,11,12 3-pt shooter with a replay at 10 (which, for simplicity’s sake, let’s ignore and pretend is never rolled) and Draymond 2-4,12 with a replay at 9 (you know the drill). On his card Tucker shoots 39.39% and Draymond 21.88%.
Using SOM’s system and not your adjustment, each would shoot 0% 1/6 of the time, 53.19% 1/3 of the time, and Tucker would shoot 39.39% ½ the time and Draymond 21.88% half the time.
For Tucker that gives us 0 + .1773 + .19695 (that is .3939 x .5) = 37.425%. In reality, Tucker shot 37.73%. SOM is only just over 3/10s of a percent off.
For Draymond that gives us 0 +.1773 + .1094 (that is .2188 x .5) = 28.67%. In reality, Draymond shot 28.48%. SOM is less than 2/10s off. REMARKABLE!
Here is where it gets a little complicated, Chris. Let me know if I am making an error here in my thinking.
Under your system, instead of Tucker and Draymond taking ½ of their 3-pt attempts off their own card, they will only be attempting 13.89% of their 3s from their own card. I got that number from taking the percentage of times they roll a Blank (50% of the time) and multiplying it by the percentage of time they actually shoot a 3 when they roll a Blank (27.78%). For the math there see above the paragraph beginning “Let’s look at your example, PJ Tucker…”
That means 86.11% of their 3-pt shots will be taken off the D and X rolls. D will be 2/3 of that, or 57.41% total, and X will be 1/3 of that or 28.7% total.
So for each of them
X roll will be 0 x .287 = 0
D roll will be .5319 x .5741 = .3054
For Tucker, when he gets to shoot off his card he is .1389 x .3939 = .0547
For Draymond, rolling on his card and getting to shoot he is .1389 x .2188 = .0304
Tucker’s 3-pt shooting under your rule would be 0 + .3054 + .0547 = .3601 = 36.01%. So Tucker in reality shot 37.73%, under normal SOM rules shoots 37.425% and with your adjustment shoots 36.01%. SOM was 3/10s off and you are almost 6x that off. Still, you are within 1.7%, it isn’t too bad. BUT…
Draymond = 0 + .3054 + .0304 = .3358 = 33.58%. Reality = 28.48%, SOM = 28.67%, your rule = 33.58%. That is more than a 5 percentage point difference. I am sure you agree that is not acceptable.
I may have mistyped something here. Sorry if I did that. The math should be right, excluding typos. What could be off is my understanding of how your rule affects the percentages of where shots are taken. I think I am correct though.
What is the solution then? This I haven’t done the math for. But I am pretty sure the way to maintain the accuracy of the game both in 3-pt shooting percentage and 3-pt volume (compared to 2-pt shots), is to decrease the 3-pt rating under Determining Three-Point Shot Attempts for players with replays in their O columns. Of Tucker’s 523 shots, 387 were from deep. Under your rating system he would be a 15. I don’t think we reduce his rating to the same as his O column such that we multiply 15 x 27.78%. I think that is too much. I have to think about it. But don’t want to do that until you confirm that I am correct in what I said.
Hope this provides some food for thought :)
Thank you for your comments Derek. You are exactly right; the system that I use to limit three-point attempts based on Replay results from a player's Outside shooting column will increase the three-point shooting percentage for players who have a lot of Replay results. As to whether or not that increase is acceptable, I will leave that up to individual players of the game to decide. If you find it acceptable, then use the rule, and if you find it unacceptable, then don't use my rule, or adjust it to something that works best for your sensibilities.
DeleteAnytime you create a rule such as this, it's going to break something else in the game. So there is always a trade off. The trade off I'm making with this particular rule is that players who did not attempt many shots per 48 minutes, will be limited in regard to three-point shot attempts as well, even though it may adversely affect the three-point shooting percentage of those players.
I would add though, that in my current testing of my home-brewed rules (though not yet complete), I'm finding that team totals for three-point shot attempts, makes, and percentages have been dead-on. Over the course of 12 games from 2019 thus far (781 three-point shots taken), I have attained the following per game results vs. the 2019 per game league totals:
3PM: 11.6 in my games vs. 11.4 NBA.
3PA: 32.5 in my games vs. 32.0 NBA.
3P%: 0.357 in my games vs. 0.355 NBA.
From these preliminary results, it seems that my rule for Determining Three-Point Shot Attempts, in conjunction with my Shooting Rule Adjustment rules, are doing exactly what they were intended to do, even if individual player statistics may be out of whack for certain players who have a high number of Replay chances in their Outside shooting columns.
Again Derek, you are exactly correct in your calculations and conclusions regarding the this rule, as it pertains to three-point shot percentages for players with a high number of Replay results in their Outside shooting column. I welcome more comments from you on the subject, and if you come up with your own alternative rule(s) please let me know. I would be more than happy to post your rule(s) on the site for fellow board gamers to consider using in their own games (or that I might consider, to replace what I'm currently using). That's the great thing about the board game (as opposed to the computer game), we all get to make it our own, with either our own home-brewed rules, or with rules created by others; there is no right or wrong way to play YOUR game.
Thanks again for your comments, and I look forward to hearing more of your thoughts on this subject, or others, presented on my site.
Thanks for the reply, Chris! Cool you are getting the ratios you want. Let me just jump right in.
ReplyDeleteThe method for determining 3-point shot attempts is simple yet brilliant: you divide the player’s 3-pt attempts by his total FG attempts then multiply the result by 20. Then every time he has an opportunity to shoot (with limited exceptions) you roll the 20-sided die and if the result is less than or equal to the player’s 3-pt rating, he shoots a 3, and if not a 2. The system works great for most players, but for players who have a large number of replays in their O column, it skews them towards a higher frequency of 3-pt shots than they had in reality. Chris formulated a nice system to rectify this but as I pointed out, it results in a higher 3-pt FG percentage for players with replays, with the worst shooting players receiving the most benefit. Here is how I would resolve it.
There are 2 formula’s here, which makes it a little more complicated.
First we have the above formula which is
(3-pt attempts / total FG attempts) x 20
We need to change one factor, total FG attempts, to total FG attempts including unattempted 2-pt shots (which I will refer to as Z). These are the shots that resulted in a replay on the player’s O column.
And to figure out Z, we need to use another formula. That formula is a little tricky because it is player dependent. We know that half of the rolls for a 2-pt shot will result in either a D or an X, which we will assume always results in a shot attempt (ignoring the occasional D Outside column that has a turnover). So ½ of our 2-pt rolls always result in a shot. Then we have the other half, the rolls of Blank, which do not always result in an attempt for the players we are concerned with, the replay guys. We need to look at their O column and determine how many of the 36 combinations result in FG attempts, then divide that number by the total combinations. So for Tucker who has misses on 2-5 and replays 6-12 (Draymond is statistically the same), he is 10/36 or .2778. Half of his shots, the X and D rolls, always result in a shot, so the number there is .5. And for the other half of his shots, the Blank rolls, .2778 of those result in a shot, so we multiply .5 by .2778. The math
(.2778 x .5) + .5 = .1389 + .5 = .6389
Now the tricky part. This had me fooled for a while. We don’t multiply total shot attempts by .6389. Instead. We divide 2-pt FG attempts by .6389. Then we add that number to 3-pt FG attempts. That will give us Z. Tucker had 136 2 pt FG attempts and 387 3-pt FG attempts. So Z =
(136 / .6389) + 387 = 212.8659 + 387 = 599.8659
Now, we insert that number back in Chris’s formula for determining 3-pt shot attempts. Tucker had 387 3-pt attempts and Z is 599.8659. So his adjusted 3-pt rating is
(387 / 599.8659) x 20 = 12.9029. We will round that to 13.
Using Chris’s original formula for determining 3-pt shot attempts, Tucker would be a 15. He took 387 3-pt attempts out of a total of 523 FG attempts. We are only reducing him to 13. That will allow him to take the proper ratio of 3s to 2s without losing/gaining any 3-pt accuracy.
Let’s do Draymond, who takes a smaller percentage of 3-pointers. He had 257 2-pt FG attempts and 165 3-pt FG attempts for a total of 422 FG attempts. Because Draymond’s O column is statistically equivalent to Tuckers, we can use that same .6389 number. Dividing Draymond’s 2-pt FG attempts of 257 by .6389 we get 402.2539. We add that to his 3-pt FG attempts of 165 to get 567.2539. We then divide his 3-pt FG attempts of 165 by that number to get .2909. Multiply that by 20 to get his 3-pt rating of 5.8175 which we round to 6. Under the basic formula Draymond would have been an 8. Like Tucker, we are reducing his rating by 2.
Can we just determine 3-pt shots as Chris outlined then subtract that number by 2 to get a player’s 3-pt rating? I think it depends on the number of replays and fouls on a player’s O column. Let’s see if it holds up for 2018-19 Andre Iguodala, who is statistically equivalent to Tucker and Draymond, having Replays in his O column from 2-8, and shot attempts and not fouls 9-12. So he would be 10/36 and doing all that math we would arrive at .6389 as the number we divide his 2-pt attempts by for the adjustment
ReplyDeleteThe basic formula for Iggy would give us a 10 as his rating ((144 3-pt attempts / 302 total FG attempts) x 20). With the adjustment, Iggy is an 8 (158 2-pt attempts / .6389, then we add that number 241.0393 to the 3-pt attempts of 144 to get 385.0393, and finally we divide 144 by 385.0393 and multiply by 20 and round).
Let me look at 3 other players who take 3s but have replays in their O columns, Austin Rivers, Iman Shumpert and Daniel House, all of the 2018-19 Rockets. To make it easier, I will put the player’s name then his 2-pt FG attempts, his 3-pt FG attempts, and his total FG attempts. As an aside, though I do not advocate violence, if you told me I could punch one person in the face without recrimination, that person would be one of these 3 players. I just hate his face that much…
Rivers 245 327 572
House 74 178 252
Shumpert 173 273 446
All take more 3s than 2s with House taking the largest percentage of 3s, more than 2 to 1. This should be interesting.
Without the replay adjustment, River’s 3-pt rating is 11, House (a man I have no strong feelings for) has a rating of 14 and Shumpert’s is 12.
Rivers has 25/36 combos in his O card resulting in shots, for a number of .6944. House and Shumpert each have 22/36 combos for a number of .6111
For Rivers, we take 245 2-pt attempts, divide by .6944 to get 352.8226. We then add that number to 3-pt attempts of 327 to get 679.8226. Finally we divide 327 by 679.8226, multiply by 20 and round to get 10. So his rating only drops by 1.
For House, we take 74 2-pt attempts, divide by .6111 to get 121.0931. We then add that number to his 3-pt attempts of 178 to get 299.0931. We then divide 178 by 299.0931, multiply by 20 and round to get 12.
So for House, the adjustment to his 3-pt rating is 2.
Finally, for Shumpert, a man who once had a crazy hair style but inspired no thoughts of violence, we take 173 2-pt attempts, divide by .6111 to get 283.1424. Add that number to his 3-pt attempts of 273 to get 556.1424 hypothetical total shots. Divide 273 by that number, multiply by 20 and round to get to 10. So for Shumpert we also reduced his rating by 2.
I think the key here is that Rivers didn’t have as many replays/fouls on his O card. I would guess that for players with even more replays/fouls than Tucker/ Draymond and Iguodala, their adjustment might be 3, and for players with even less replays/fouls than River, there may be no adjustment needed.
It should also be noted that Dazzlers, Switches and actual 2-pt FB shots will change the ratio of 3s to 2s a bit. All of these Houston players will receive the benefit of Dazzlers from Chris Paul and James Harden (less so if you use Chris’s Dazzler adjustment, and let me say that my wife would kill me if I took Dazzlers away from her when we play (“I love me my Dazzlers”)). Instinct tells me that for replay guys who shoot a decent percentage from 3, you would almost always choose to take a 3 in a Switch situation. For guys like Steph Curry, who are lethal if open in their O ad P columns, I am not so sure. Anyways, the game isn’t perfect but this is an attempt to get reasonably closer to perfection.