# The Knicks and the 3-ball: What really matters?

On Tuesday, Ian Begley wrote a post on ESPN NY entitled “Opening Tip: Too many 3s?”, in which he questions the wisdom of the Knicks’ approach that led them to setting the record for 3 pointers attempted and made last year. His argument is as follows:

None of the four conference finalists in 2012 were in the top 10 in 3-point attempts per game; one conference finalist finished in the top 10 in 3-point attempts per game in 2011; in 2010, three of the four conference finalists were in the top 10 and two of the four conference finalists in 2009 finished in the top 10.

So, in total, eight of the last 20 conference finalists have finished in the top 10 in 3-point attempts per game in the regular season.

He ends the article with the question, “Do you think the Knicks should shoot as many 3s this year as they did last season? Or is that not conducive to winning a title?”. Let’s examine this further.

To start, let me rephrase the question a bit. Let’s try to determine if shooting more 3s in a season is helpful or harmful to winning games, never mind winning a title. I have compiled team statistics from the last 5 regular seasons, and present to you several plots. First up, let’s just look at how 3PA per game affect winning.

There isn’t great correlation there, even with this being a complex model with multiple variables affecting wins. The line fit having a positive slope does slightly suggest that shooting more 3s in a game has a positive affect on winning games, although there is a lot of noise. At worst we can say that there is no obvious negative effect on wins for a team shooting more 3s in a game. While gathering the data and seeing there is little correlation doesn’t supply as sexy of an answer as drawing conclusions from small sample sizes, it’s still an important exercise. It allows us to avoid the red herrings and focus on factors that really matter. While we can’t really determine if a team would be better or worse if they simply shot more threes, we can see that shooting 3s at a higher percentage does have a much stronger correlation to winning:

An R2 of 0.24 in a case such as this, where we have multiple independent variables affecting wins, is absolutely a significant statistical correlation. Shooting your 3s at higher percentages will statistically improve your chances of winning games. That’s not exactly a revolutionary statement, but it is important to see with real life data.

So what can we say to Mr. Begley’s question? Should the Knicks shoot as many 3s this year as they did last year? I say that the number doesn’t matter — it’s 3P% that has a much stronger correlation with winning. The real question should be, will the Knicks shoot 3s at least as efficiently as they did last year?

## 23 thoughts to “The Knicks and the 3-ball: What really matters?”

1. Hubert says:

Good article, Kevin. Frankly I don’t think the original article even merited a response of this quality.

2. Unreason says:

Another interesting way to look at this would be to do a logistic regression with wins as the outcome and plot the probability of winning as the % of a teams’ points that comes from 3s increases.

3. Kevin Udwary says:

Unreason:
Another interesting way to look at this would be to do a logistic regression with wins as the outcome and plot the probability of winning as the % of a teams’ points that comes from 3s increases.

Slightly better correlation, but still not great: link

I started to play around with doing a linear regression model of team wins with respect to team box score variables (fgs, rebs, tov, ect…) with not too bad predictive results. It could be better though. I do pick up strange hobbies…

4. Unreason says:

Kevin Udwary: Slightly better correlation, but still not great: link

Nice. And by “great” I assume we’re talking “large” not “confirming what we might hope is true about 3s”. There’s no point in trying different approaches to see which maximizes the correlation right?

Kevin Udwary: I started to play around with doing a linear regression model of team wins with respect to team box score variables (fgs, rebs, tov, ect…) with not too bad predictive results. It could be better though.

Cool. If you had game-level data, a logistic regression would take advantage of all the information in all 2460 reg season games + x post-season games per year. Collapsing it into seasonal % wins might hide a lot of meaningful covariation. Plotting the probability of the outcome (wins) as it changes across a realistic range of the predictor (reliance on the 3) is especially informative and easier to interpret than overall model estimates – log of the odds of winning on average. You’d have to transform the logits into probabilities by hand, but that’s a snap. In this case it would show how the probability of winning changes (y axis) as the % of points from 3s goes from 10% to 35% (x axis).

5. Kevin Udwary says:

Why would you use logistic regression as opposed to a linear regression? It’s not something I have too much experience with, but I suppose it makes sense in that you are examining a 2 state variable (win or loss), while I’ve been looking at it as determining number of wins in a season, thus a linear regression. Not sure which is more appropriate here, or if they’ll really vary from each other anyways.

6. er says:

Felton, Prig, Melo, Barg, Tyson starting tonight in RI

7. Kevin Udwary says:

Unreason: Nice. And by “great” I assume we’re talking “large” not “confirming what we might hope is true about 3s”. There’s no point in trying different approaches to see which maximizes the correlation right?

Cool. If you had game-level data, a logistic regression would take advantage of all the information in all 2460 reg season games + x post-season games per year. Collapsing it into seasonal % wins might hide a lot of meaningful covariation. Plotting the probability of the outcome (wins) as it changes across a realistic range of the predictor (reliance on the 3) is especially informative and easier to interpret than overall model estimates – log of the odds of winning on average. You’d have to transform the logits into probabilities by hand, but that’s a snap. In this case it would show how the probability of winning changes (y axis) as the % of points from 3s goes from 10% to 35% (x axis).

Ah, just reread and looked into it and now I see what you mean. I only have season data gathered right now, not game data, though. That would seem to be ideal though…

8. Unreason says:

The advantage would be in using the information about how strongly the reliance on 3s is associated with wins in each game. That could be important. Averages often mask or mischaracterize the individual data points they are supposed to summarize. The average of a bunch of curves, for example, often looks nothing like any of the individual curves that were used to calculate it. If about half take off right away and the other half after a long delay, the average will look like a steady gradual increase. If your interested in the shape of the curve as a predictor or an outcome, e.g. growth curves, loss functions etc., representing them by an average curve might give a very different and potentially misleading picture of the situation your interested in than building a model that uses the individual data points that went into the average.

That said, I’m not implying any criticism of what you did. It’s cool that you plotted these descriptive data and shared them. Thanks.

9. ruruland says:

Nice job, Kevin.

Anyone think Amar’e/K-Mart, MWP, Shump, JR, Beno is a good second unit?

I do. On its face, a very strange way to balance a deep team. When you start to examine it though, it’s quite synergistic.

I think other permutations will work really well, too. But the starting lineup should be exquisite in the pick and roll and one of the most efficient 5 man units in the game.

10. Kevin Udwary says:

Unreason:
The advantage would be in using the information about how strongly the reliance on 3s is associated with wins in each game. That could be important. Averages often mask or mischaracterize the individual data points they are supposed to summarize. The average of a bunch of curves, for example, often looks nothing like any of the individual curves that were used to calculate it. If about half take off right away and the other half after a long delay, the average will look like a steady gradual increase. If your interested in the shape of the curve as a predictor or an outcome, e.g. growth curves, loss functions etc., representing them by an average curve might give a very different and potentially misleading picture of the situation your interested in than building a model that uses the individual data points that went into the average.

That said, I’m not implying any criticism of what you did. It’s cool that you plotted these descriptive data and shared them. Thanks.

No, I very much appreciate it! I do have a statistical background, but a lot of this is new to me and I’m playing it by ear a bit. Any bits of advice or suggestions are great.

11. Frank says:

I think the general talking point against taking lots of 3’s is that at some point they’ll stop going in — which is true. While they can absolutely bury a team, overall they are low-percentage shots (not low-efficiency, low percentage). So perhaps a good thing to know would be a team’s (or specific player’s) variance with 3 point shooting. Are some teams really streaky? Are some players really streaky? For example, JR seems to be a guy who’s either hitting 12 out of 20 or missing 16 out of 20. Actually – his monthly splits were 47.7, 30, 25.4, 42, 34.5, and 40% from 3 point range.

Similarly, Carmelo shot very well from 3 last year, but his monthly splits on 3P% were 44, 42.6, 38.9, 30, 25.5, and 46.7. Huge variance.

In comparison, Stephen Curry was a machine – basically between 42.5 and 48.4% every month of the season.

So if you have a team of guys that are very consistently good 3 point shooters then yes, of course it’s a great idea to keep shooting a million 3’s. But if you have guys that have a high variance, then you could easily shoot yourself out of a series.

12. ruruland says:

Efficient offensively. Obviously won’t be great defensively.

13. EB says:

ruruland:
Nice job, Kevin.

Anyone think Amar’e/K-Mart, MWP, Shump, JR, Beno is a good second unit?

I do. On its face, a very strange way to balance a deep team. When you start to examine it though, it’s quite synergistic.

I think other permutations will work really well, too. But the starting lineup should be exquisite in the pick and roll and one of the most efficient 5 man units in the game.

According to Posting and Toasting, JR is in the running for the starting unit and Woodson is looking to have a more traditional 2. Also the lineup is only guaranteed for tonight.

14. ruruland says:

Yep, the assumption is that JR and Shump are competing for the starting guard.

I’m not so sure though. Why would it make sense to have JR compete for that job when he’s not going to start playing for another couple of weeks?

This, to me, is about seeing if the two point guard lineup can work as well as it did last year with the inclusion of AB.

Woody is probably more of a numbers guy than people give him credit for, and has no problem sticking with unconventional lineups when they work over a long period of time.

I think his loyalty issues conflict with that at times.

15. EB says:

I’m excited to see what Beno can do. I always thought he was being underutilized in other places.

Question though… Why does he shoot so few 3’s? He makes a good percentage.

16. BigBlueAL says:

ESPN.com is using SCHOENE projections in their Insider conference previews. Today the Nets were unveiled as the 3rd seed in the East winning 50 games. It was mentioned in the article that they are projected to win a dozen more games than the Knicks.

So looks like the Knicks will be projected to win 37 games and finish 7th in the East since their preview article is slated to come out on Oct 15th which is when the 7th seed in the East is revealed. Amazing.

17. Unreason says:

Frank:
I think the general talking point against taking lots of 3?s is that at some point they’ll stop going in — which is true. While they can absolutely bury a team, overall they are low-percentage shots (not low-efficiency, low percentage).So perhaps a good thing to know would be a team’s (or specific player’s) variance with 3 point shooting. Are some teams really streaky? Are some players really streaky?For example, JR seems to be a guy who’s either hitting 12 out of 20 or missing 16 out of 20. Actually – his monthly splits were 47.7, 30, 25.4, 42, 34.5, and 40% from 3 point range.

Similarly, Carmelo shot very well from 3 last year, but his monthly splits on 3P% were 44, 42.6, 38.9, 30, 25.5, and 46.7.Huge variance.

In comparison, Stephen Curry was a machine – basically between 42.5 and 48.4% every month of the season.

So if you have a team of guys that are very consistently good 3 point shooters then yes, of course it’s a great idea to keep shooting a million 3?s.But if you have guys that have a high variance, then you could easily shoot yourself out of a series.

To some extent, but the impact of an individual’s streakiness on winning will be dampened because the 3s come from multiple guys. The chances that say four guys all have a poor shooting night simultaneously are going to be a lot lower than for just one guy.

I agree though that variance as an indicator of streakyness is relevant to interesting issues like how many 3s a team takes when they’re not falling. I think that measure might be needed to ask questions about team’s versatility/exclusive dependence on 3s and test ideas like:

Teams that shoot a higher % of 2s when 3s aren’t falling are more successful than those that keep shooting the 3s regardless.

18. EB says:

Unreason: To some extent, but the impact of an individual’s streakiness on winning will be dampened because the 3s come from multiple guys. The chances that say four guys all have a poor shooting night simultaneously are going to be a lot lower than for just one guy.

I agree though that variance as an indicator of streakyness is relevant to interesting issues like how many 3s a team takes when they’re not falling. I think that measure might be needed to ask questions about team’s versatility/exclusive dependence on 3s and test ideas like:

Teams that shoot a higher % of 2s when 3s aren’t falling are more successful than those that keep shooting the 3s regardless.

Yes but doesn’t it become a problem that we don’t know who will have a hot night and who won’t? Or if after hitting a number of 3s the player will go cold or a cold player will get hot? It seems problematic to assume the hot player shoots while the cold ones pass up open shots.

Of course I also have to think that shooting threes is correlated to bad teams who fall behind by a lot explaining why no team first in 3p wins a championship

19. BigBlueAL:
ESPN.com is using SCHOENE projections in their Insider conference previews.Today the Nets were unveiled as the 3rd seed in the East winning 50 games.It was mentioned in the article that they are projected to win a dozen more games than the Knicks.

So looks like the Knicks will be projected to win 37 games and finish 7th in the East since their preview article is slated to come out on Oct 15th which is when the 7th seed in the East is revealed.Amazing.

I think the projections assume Bargs is going to get a lot of PT. The advanced metrics are all very down on Bargs, especially if it assumes the last two years are a baseline. Hence, the big drop in wins. Will be interesting to read though.

20. Z-man says:

I have a problem with this way of looking at basketball success. To me, playing winning basketball comes down to a very simple concept: scoring more points than the other team. On a given night, you can win by shooting no 3’s or shooting only 3’s.

The best sports teams are those who can win in multiple ways, depending on the circumstances. At some point, it is likely that a contending playoff team is going to run into a team or coach that takes away what they are most comfortable doing. If going to plan B is too far outside a team’s comfort zone, they are going to lose in a 7-game series, unless they are able to do the same thing to the opponent.

The Knicks had grown dependent on the 3 because they had virtually no low-post presence or penetrating finishers beyond Melo, and were a poor rebounding team. When that was exposed (mainly by Hibbert) there was nothing else to go to when the 3’s stopped falling. In fact, perimeter defenders were freed up to press up rather than double down.

So, it’s OK to win lots of games with lots of 3’s, but you have to have a plan B when that strategy is neutralized. Same is true with the P&R, or the low-post iso, or the triangle.

Certainly, in today’s game you better be able to drain 3’s if you want to contend. But, as Riley put it back in the day, depending too much on 3’s is fool’s gold. Do the Knicks shoot too much 3’s to get to the Finals? Probably, but only because it is indicative of deeper problems that limit their choices against excellent defensive teams.

21. thenamestsam says:

ruruland:
Nice job, Kevin.

Anyone think Amar’e/K-Mart, MWP, Shump, JR, Beno is a good second unit?

I do. On its face, a very strange way to balance a deep team. When you start to examine it though, it’s quite synergistic.

I think other permutations will work really well, too. But the starting lineup should be exquisite in the pick and roll and one of the most efficient 5 man units in the game.

I think the whole concept of “second units” gets way too much play. The amount of time that teams play 5 bench guys together at a time is relatively low, and that relatively low amount goes to zero in big/playoff games. Having good synergy among big minutes lineups is obviously important but there just really aren’t a lot of high minutes all-bench lineups. The highest one from last year was the Clippers 282 minutes for the Barnes-Crawford-Bledsoe-Turiaf-Odom group. As a point of comparison the most used unit in the league was the Thunder starters who played 1307 minutes together.

22. Unreason says:

EB: Yes but doesn’t it become a problem that we don’t know who will have a hot night and who won’t? Or if after hitting a number of 3s the player will go cold or a cold player will get hot? It seems problematic to assume the hot player shoots while the cold ones pass up open shots.

Of course I also have to think that shooting threes is correlated to bad teams who fall behind by a lot explaining why no team first in 3p wins a championship

If you’re refining the idea by thinking about it’s implicit assumptions, I like that. I was only bringing the up as one that could be tested a bit if Franks notion using variance to measure streakyness were valid. I don’t have a good hunch about whether teams that keep shooting 3s in general are more successful than those who switch to other shots when the 3s stop falling. I just think it’s interesting and would be cool if it could be validly analyzed. I’m not sure I followed all of what you wrote, but I agree that there’s a lot that this kind of measure wouldn’t take into account. And some of those things might be very import to examining questions about dependence on the 3.

23. ruruland says:

thenamestsam: I think the whole concept of “second units” gets way too much play. The amount of time that teams play 5 bench guys together at a time is relatively low, and that relatively low amount goes to zero in big/playoff games. Having good synergy among big minutes lineups is obviously important but there just really aren’t a lot of high minutes all-bench lineups. The highest one from last year was the Clippers 282 minutes for the Barnes-Crawford-Bledsoe-Turiaf-Odom group. As a point of comparison the most used unit in the league was the Thunder starters who played 1307 minutes together.

Agreed.