Are We Relying Too Heavily On "The Lottery"?

[Steven43]

This seems fairly silly because it ignores two things.

1) Twos are also the lottery. There's this idea that threes are somehow a wildly bigger gamble than shooting twos, which most college teams don't exceed much more than 50% on. It's not like you have a 90% chance of making a two versus high 30s% on a good three-point shooting team.

2) It ignores that the bonus point means that you only need to hit 33.3% on threes to equal the equivalent 50% shooting percentage on twos. So shooting 38 or 39% from three is actually better than shooting 50% from two. Less "lotteryish," as it were.

I agree that our fortunes in March will depend on whether we make shots or not.

Just because people mimic the "live by the three, die by the three" meme as if it were a litany, it doesn't mean that open threes are some risky roll of the dice.

Thought-provoking take on the subject, Throatybeard. I hadn't really thought of your line of reasoning; probably because I have allowed myself to be influenced by constantly hearing the comment 'live by the three, die by the three'. However, I think what is perhaps a better way to play than hoping you can shoot 38 or 39% from three is to have a strong inside game, which should allow a team to shoot above 50% on two-point shots. I'd rather have a team approach that emphasizes scoring on the inside while mainly using the three-pointer as an added bonus. This is the way Carolina would like to play, but the fact that Pigeon would rather shoot jumpers than try to score on the inside hurts them, I think.

[FellowTraveler]

The high variance of 3's is a scary proposition come tourney time and the best way for Duke to avoid it would be to draw smaller teams like Mizzou or Marquette in regional games. If Duke ever plays a team like Kentucky of Syracuse, you can bet that close to if not more than half of Duke's shots will come from 3.

I basically agree with this.

[gus]

"Amazing" sure, whatever you want to call it, that's what I said... "great" big men, not standard. If Boozer shot 63% for a career, he had plenty of games where he shot 70% from the field!

He also had plenty of games where he shot below 50% (even games below 40%). Don't confuse outliers with averages. When discussing what is an effective strategy for maximizing the liklihood of winning, it's the latter that's important.

Bigs get fouled a lot more than 3 point shooters do... probably like 10 times more often. It doesn't matter if their FT % is lower than guards. A guard shooting 3s isn't going to the line in the first place!

Now you're making up numbers. Not a good way to support a statistical argument.

Look at Hans %age that you listed. No way he's the ACC leading scorer with just that shooting %age--he LIVED at the line, which isn't accounted for in that figure.

Why is the hack-a-shaq strategy effective? When a big man is fouled, it's generally stopping an otherwise high percentage shot, replacing it with a lower percentage (often) shot. It's not always effective: in Carlos's case, he was ~75% free throw shooter. Fouling him was a mistake. The Plumlees are not 75% FT shooters.

If you get cold from 3 you are in trouble. It's a lot harder to "get cold" shooting dunks and 2-4 ft shots.

This is where you're completely missing the argument. It's already been conceded that 3 point shooting has a higher standard deviation (getting "cold" is an misunderstanding of the probabilistic event that is shooting).

Dunks don't happen all that often? You're really losing me there. The Plums dunk every game, and they are not even elite, as you mentioned.

How many dunks a game are there? what are the Plumlees' shooting percentage when dunking?

I've heard the math just like everyone else who watches basketball. But the raw shooting %ages of 3-pt vs. 2-pt shots does not take into account factors like GETTING FOULED and GETTING YOUR OWN REBOUND. A big guy's overall offensive productivity is based on these factors, whereas a 3 pt shooters offensive productivity is just based on his shooting %age.

The use of caps is totally unnecessary, and it doesn't make you correct.

Ryan Kelly missed a three pointer, and grabbed his own rebound in last minute of the Carolina game. That's not a statistical argument of course, but missed three pointers also lead to offensive rebounds. Three point shooters do occasionally get fouled, and usually convert those free throws at a higher rate than inside players. In other words, your statement that "a 3 pt shooters offensive productivity is just based on his shooting %age" is completely false.

I don't think anyone is arguing that an emphasis on three point shooting is always the best strategy. Certainly no one thinks that only three point shots should be taken. If this team had two Carlos Boozers on it, we'd see far fewer three pointers. But we don't. I like the Plumlees, but they ain't Boozers.

[dyedwab]

'. However, I think what is perhaps a better way to play than hoping you can shoot 38 or 39% from three is to have a strong inside game, which should allow a team to shoot above 50% on two-point shots. I'd rather have a team approach that emphasizes scoring on the inside while mainly using the three-pointer as an added bonus.

Not pick on you, but this quote is illustrative of the problem with the debate about 3's v 2's. You talk about "hoping" you can shoot 38 or 39% from 3, but that a strong inside game "should allow" a team to shoot above 50% on 2's. What this suggests, as Throaty has pointed out in his critique of the initial argument, is that making 3's is random, and making 2's isn't.

But if you look, players who consistently have high shooting percentages of 2's tend to be the same, and players who consistently have higher shooting percentages of 3's tend to be the same. My point? Making shots is a skill whether its 2's or 3's - and it isn't a randomly distributed skill. Thus the choice isn't between easy shots and harder shots...its a choice between which skills your team has.

K has recruited really good 3 point shooters - that's a strategy. Not randomly having everyone shoot three and see what hits.

Sorry for the rant - this argument has always seemed to me to be a math and personnel issue. Basically, if you have enough guys who shoot 3's at 35% or better, then the math says that you should maximize their opportunities to do so.

[UrinalCake]

If Boozer shot 63% for a career, he had plenty of games where he shot 70% from the field!

In that case, big men have statistical variation in how well they shoot too, just like outside shooters.

How many times have you seen a big guy "disappear" or "get shut down" for a game? Maybe their percentage is more consistent but their output can vary widely based on the defense and scoring pace for the game.

The other factor to consider is, how many great big men are there in college basketball? Maybe one per year coming out of high school would qualify as "great," and if he actually lives up to expectations then he'll be gone in a year. Conversely, there are probably 5-10 excellent three point shooters in each class. And Duke gets all of them So if you're going to build your program around a particular style of play, relying on three-point shooters is more "dependable."

Finally, if you look at past National Championship winners, they all have excellent talent obviously but you can't really make any generalizations as far as them all having a dominant big man, or all having a sharpshooter. I think having solid guard play is probably a safe rule of thumb, but in the end it's overall talent and team play that matter

[Kedsy]

"Amazing" sure, whatever you want to call it, that's what I said... "great" big men, not standard. If Boozer shot 63% for a career, he had plenty of games where he shot 70% from the field! Haywood had games where he went 70%.

This is a faulty argument. Do great inside shooters have games where they shoot 70% from the field? Sure, so what? Last night Andre Dawkins shot 67% from 3 (same as 100% from a 2-point shooter; how often does that happen?). He got fouled twice on three pointers (and he only made 4 of the 6 free throws, which was still 18% of his total points). He has had 9 games this year where he's shot 50% or better from threeland (32% of his games played) -- which of course translates to a 75% or better two-point percentage.

In contrast, this year Jared Sullinger (generally considered to be the best, or at least one of the best, big men in the country) has shot 70% or better four times this season (15% of his games played; and note that only two of those games were 75% or better). In those four games, 10 of his 83 points came on free throws (12% of his total points). I don't know how many of his points came on rebounds of his own misses, but since he didn't miss so much, probably not so many.

Which brings up another faulty element of your argument -- while it's true that three point misses go long, so you don't just grab your own miss and lay it in, your team can certainly get the rebound and put up another shot. Duke does this all the time. Sometimes it's even a player rebounding his own miss and putting in an easy 12 foot jumper, like Ryan Kelly against UNC and again last night.

Throatybeard is right -- the two point shot isn't really any more of a lottery than the three-point shot. Pomeroy may also be right, that the three is subject to more variability, but Duke's three-point shooters seem fairly consistent over the long haul, so I'm not sure how relevant Pomeroy's observation is in our case.

[snowdenscold]

Ryan Kelly missed a three pointer, and grabbed his own rebound in last minute of the Carolina game. That's not a statistical argument of course, but missed three pointers also lead to offensive rebounds.

As a side note - he did the exact same thing in the FSU game, only at the beginning: shot a 3, grabbed his own long rebound, then hit a mid-range jumper for 2 that swished through.

I was thinking, "Hmmm, new go-to move for Kelly?" =)

[mkirsh]

A few different arguments on this thread:

1) Is it more efficient to shoot 3's at 40% or 2's at 60%? One side of the argument states that expected value is the same at 1.2 points per attempt, while the other side states that it excludes other factors such as foul shots, etc. In the last few years of the ACC we've seen probably the best 2 case studies around - Hansbrough scored 2872 points on 1752 shots (1.6 pps), compared to JJ who scored 2769 points on 1906 shots (1.45). While this includes the impact of higher FT rate for inside players, it is not perfect as it does not adjust for level of competition, quality of teammates, and travels/offensive fouls not called, and also does not factor in other benefits of shooting more 2's (higher player and team fouls for opponents, etc) or more 3's (stretches defense, momentum plays, etc). Although imperfect, it does seem that 2's are likely more efficient way to score. The dynamic holds for this team as well, as Mason and Miles are averaging 1.45 and 1.56 points per shot respectively, compared to Curry and Dawkins at 1.4 and 1.34 respectively. However for this Duke team, our bigs are turning it over at a higher rate than our guards, so if you adjust for turnovers by adding TO's to shot attempts, the guards drop to 1.1 and 1.2 and the bigs drop to 1.1 and 1.2 as well. Basically, Duke should take the best look it can get as interior and exterior offense seems to be a wash - ie doesn't matter if we shot 25% of shots from 3 or 50% of shots from 3, efficiency should be the same (assuming no diminishing returns in quality of shot at either extreme).

2) Is a team that shoots more 2's less prone to variation as teams that shoot 3's? I don't have the standard deviations for 3's vs 2's, but would feel safe guessing that 3's have higher variability. However, I think the point of this debate is really about March - is a team that relies on the 2 better suited for a single elimination tournament? I think the best case study here is Kansas, the ultimate "Live by the 2, die by the 2" team. Since Bill Self took over in 2005, Kansas has consistently been ranked in the top 30 for 2 point shooting percentage (average 53.3% from 2, average national ranking of 26, no years below 50%) and one of the least frequent 3 point shooting teams (just under 30% of shots from 3, average national ranking of 241) - basically, the anti-Duke offensively. Over this period, Kansas did win a title in 2008, but has not been a model of consistency, and has seen some prolific upsets. Again shooting more or less 3's is probably a wash, as March is a crap shoot for everyone and no one formula for success exists.

So back to the original point, 3's are the "lottery" in March, but so is everything else.

[Wander]

2) It ignores that the bonus point means that you only need to hit 33.3% on threes to equal the equivalent 50% shooting percentage on twos. So shooting 38 or 39% from three is actually better than shooting 50% from two. Less "lotteryish," as it were.

Having a 33% chance to get 3 points is more lotteryish than a 50% chance to get 2 points. Maybe even a 38% chance to get 3 points is more lotteryish than a 50% chance to get 2 points, depending on what the statistics show. That's the point. Taken to an extreme example, you'd consider a 0.01% to win a million dollars more lotteryish than a 100% to win a hundred dollars, wouldn't you? Even though both cases give the same average return. Expected value isn't everything.

[weezie]

Seems to be the flavor of the moment, examining the impact of 3s on the game. ESPN mag did a big spread and all the talking heads regularly expound upon the concept. Defense is also examined and dissected as some kind of 'new' idea whereas Duke completely changed the game when K's reign began.

[Matches]

All teams rely on being able to make shots, be they 2 pointers, 3 pointers, layups, whatever.

Perimeter oriented teams MAY be more prone to "going cold" or may be more streaky than teams that rely more heavily on post play. I'm not sure history really bears that out but it makes sense from a common-sense POV.

With that said, good teams play to their strengths. Our strength offensively is on the perimeter. So long as we're not just chucking up threes without attempting to run offense or move the ball around, I don't care how many we take.

[gus]

Having a 33% chance to get 3 points is more lotteryish than a 50% chance to get 2 points. Maybe even a 38% chance to get 3 points is more lotteryish than a 50% chance to get 2 points, depending on what the statistics show. That's the point. Taken to an extreme example, you'd consider a 0.01% to win a million dollars more lotteryish than a 100% to win a hundred dollars, wouldn't you? Even though both cases give the same average return. Expected value isn't everything.

If there is a strategy for making 100% of our field goals with the same expected point total and holding our opponents to a field goal of 0.01%, I think we'd all agree that's the right strategy.

[Jderf]

What are the Plumlees' shooting percentage when dunking?

It's incredibly unfortunate that this is actually a meaningful question in this debate. Thunder dumbs...

[Troublemaker]

I've mostly been on the "we shoot too many 3s" bandwagon ever since Duke started emphasizing the 3-pter more in the mid-90s. But with this particular team, I don't believe that to be true at all.

We have such amazing shooters and we need to use them to be at our peak. We are successfully utilizing those deadly weapons by getting them open looks off penetration and offensive boards/tapouts. Everything we do is sound. It's not like we just give the ball to Andre Dawkins and have him go 1-on-1 beyond the arc. We collapse the defense and create shots for our shooters. Fundamental basketball. (Only Austin has the green light to create 3s for himself, but that's with good reason. He's very good shooting off the dribble and is great at using jab steps and head/shoulder fakes to create space.)

As for Pomeroy's conclusions, I'm not concerned. Statistical conclusions can often falter when dealing with extremes. And this Duke team is an extreme data point; we are probably the best 3-pt shooting team in the country. There may be other teams that rank higher than Duke in 3-pt percentage nationally, but they wouldn't rank ahead of us if they had played our schedule. This isn't to say Duke couldn't have a bad shooting day. Of course we could. But I find it hard to believe that Duke would win more games by having this group of shooters shoot less. We're doing what we have to do with the roster we have.

[Jderf]

It took about an hour (I should probably be working or something...), but to aid the discussion, I went ahead and actually calculated the standard deviation for Duke's 3-point shooting from game to game this season. I got .100581, or just about 10%. The numbers are below if anyone wants to double check. I'm going to follow that up soon with the standard deviation for 2-pt shots. I figure that having both will give us a much clearer picture.

Total: 236-602 (.3949)
Bel: 9-19 (.474)
Presb: 8-16 (.500)
MSU: 10-21 (.476)
Davi: 5-13 (.385)
Tenn: 7-18 (.389)
Mich: 11-21 (.524)
KU: 11-25 (.440)
OSU: 3-15 (.200)
CSU: 7-21 (.333)
Wash: 5-17 (.294)
UNCG: 10-21 (.476)
WMU: 14-27 (.519)
Penn: 9-20 (.450)
Temple: 6-14 (.429)
G-Tech: 6-22 (.273)
UVA: 5-20 (.250)
Clem: 8-23 (.348)
Wake: 3-16 (.188)
FSU: 10-23 (.435)
MD: 3-16 (.188)
SJU: 7-19 (.368)
V-Tech:8-18 (.444)
Miami: 9-31 (.290)
UNC: 14-36 (.389)
MD: 9-24 (.375)
NC-State:8-29 (.276)
BC: 10-22 (.455)
FSU: 13-28 (.464)

[UrinalCake]

Regarding offensive rebounds, I think you have a better chance at rebounding a missed three than a missed two. When you put up a two, the defense is in a better position to get the rebound since they're closer to the basket, so they're more likely to rebound a miss. But when you miss a three, it's more like a 50/50 ball. And the shooter has some idea of how the shot is off, so he has a little bit of an advantage there. Part of why we rebounded so well offensively in 2010 is that we shot a lot of threes and then had good size at every position (well, except for Nolan).

Would love to see some statistical analysis on the rebound percentage of missed twos versus missed threes. Someone get on that right away!

[No Cute Name]

Matches hit on this a little. I think this is kind of a bogus argument. It's about getting good shots, wherever they are. All 3-pt shots or all 2-pt shots are not created equal. If we run our offense and Dawkins is open in the corner, he should shoot it. What's the alternative? He passes up a good shot just because he happens to be behind the arc?

Saying "we shoot too many threes" isn't really valid. However, you could say some particular threes we took were not good shots because a) we didn't work the ball around, b) the shooter was not set, c) the right person is not shooting (you know who you are), etc.

[iragsdale]

One thing I think this argument is missing is the effect of variability in a one and done tournament. In the regular season it may be frustrating to lose a game here or there because of a cold night shooting from three, but in a single tournament it's devastating - one bad night and you're gone. In addition, the competition is usually tougher in the tournament so your "floor" for acceptable three point shooting goes up.

So, I do believe it's possible that a strategy with a higher probability of success but a greater variance could be dangerous in the tournament, as you have a greater chance that an off night happens. However, if you extrapolate that across multiple tournaments, you might see an effect where you win more frequently than other teams, while getting eliminated early somewhat frequently as well. I think some might say we actually fit that pattern.

Anyway, it's an interesting argument. Personally I like our strategy.

[gus]

One thing I think this argument is missing is the effect of variability in a one and done tournament. In the regular season it may be frustrating to lose a game here or there because of a cold night shooting from three, but in a single tournament it's devastating - one bad night and you're gone. In addition, the competition is usually tougher in the tournament so your "floor" for acceptable three point shooting goes up.

So, I do believe it's possible that a strategy with a higher probability of success but a greater variance could be dangerous in the tournament, as you have a greater chance that an off night happens. However, if you extrapolate that across multiple tournaments, you might see an effect where you win more frequently than other teams, while getting eliminated early somewhat frequently as well. I think some might say we actually fit that pattern.

Anyway, it's an interesting argument. Personally I like our strategy.

I think this is an interesting point, and one I've thought about a bit without any real resolution. I think of march madness pools: you can bet safe on every game, or you can go for some outlandish upsets. With the former, in the long run, it'll give you better results, but you're probably never going to win it, because some is going to have Butler/Duke. But is this truly analogous to the teams and the actual game? I don't know. I guess that's the thesis of the "it's a lottery argument," and I just don't think it applies to actual basketball games.

I think ultimately they way to view it is on an individual game basis: whatever strategy maximizes our winning odds in any individual game is the right one, and gives us the best chance of winning it outright. In that context, a Kansas style, low std deviation strategy probably produces fewer LSU/MSU kind of blow outs, but also ultimately have a lower chance of winning it all. But that's an opinion, and I have no idea if I'm actually right.

[Matches]

One thing I think this argument is missing is the effect of variability in a one and done tournament. In the regular season it may be frustrating to lose a game here or there because of a cold night shooting from three, but in a single tournament it's devastating - one bad night and you're gone. In addition, the competition is usually tougher in the tournament so your "floor" for acceptable three point shooting goes up.

I think you've hit on it nicely. As fans we get nervous about strategies that we perceive as high-risk, high-reward, because we know the NCAAT is a small sample size. The consequences of a bad game are huge.

But there are lots of other crazy things that can happen in any one game, too. There's a significant random component to the NCAAT, and there's just no way to eliminate it.

So the question must be asked: which strategy gives us the best chance to win most of the time? Given our strength from distance, our lack of consistent post scoring, and the inability of anyone other than AR to drive and score with much consistency - it looks like an offense that prominently features 3P shooting is the way to go.