Really enjoyed this one Neil. The one aspect that I suspect might come close to evening things out is that I would guess you are much more likely to turn it over going for a 2-pointer than a 3-pointer. That would be difficult to study without access to the tracking data though.
Thanks Nate! That's an excellent point -- 3PA, especially catch and shoots, would carry far less turnover risk than the typical 2PA, especially at the rim. That's where you'd sort of need to classify the precursor plays to each shot type and predict (or weight) for how likely it would become a 2PA/3PA to account for the turnovers that prevent the shot from ever actually getting off.
Wow, Paine coming out firing after the break! A terrific analysis and a topic that has troubled me for a few years now. In particular, the simplistic "three is more than two" tiresome analysis of the sports media. I’ll freely admit up front that I am not sure my concerns here are valid – and likely could be off base. Still, what follows are some ungrounded observations plus a few crude proxies that are nowhere near as elegant as your solution here but intended to possibly advance the conversation.
I’ll start with an observational proxy using box score data that I made a few years back. What I did was remove the points from three-point shots from the final score, then run all the three point shot attempts using the two-point shot percentage for the entire game and add those points back into the zeroed out three-point shot points to obtain a revised final score for the team using only two-point shots.
What I saw – frequently – was that a team taking zero three points shots would have scored more points presuming the two-shot percentage held. This was true, even where the three-point shot percentage wasn’t terrible – above 33-1/3%. Now, it’s admittedly an imperfect analysis but it reflected to me at a high level that something was amiss with the orthodoxy that more three-point shots always equates to more points and more winning – so fire away.
It then struck me that the “three is more than two” heuristic focuses entirely on the conversion of made shots into points. It’s a simplistic and purely positive forward calculation where 33-1/3% for three-point shots equals 50% for two-point shots. Simple enough, but you are not shooting baskets by yourself in an empty gym and keeping score – you are playing an opponent where the outcome is relativistic and heavily dependent on what strategy you are pursuing.
What about the unspoken negatives from using an overweight three-point strategy…what I call the “taxes?” Your piece calls one of these taxes out brilliantly…the reduction in FT attempts. On the other hand, your readers have called out that some elements could be incrementally improved by shooting more threes e.g., rebounds and turnover rate. True, but right or wrong, while these strike me as worthy adjustments, they feel relatively small in effect.
What seems much larger to me is possessions. At a fundamental level, possessions reflect the opportunities to convert shots to points and prevent your opponent from doing that as much. Thus, possessions alone can be seen as statistically yielding points, i.e., “Value of Ball Possession (VBP).” While the formulae and numbers can vary to some degree, I recall that a possession is usually equal to slightly more than one point over time – say, 1.1 points.
From a possession perspective, the problem with an overweight strategic approach to the three-point shot starts to come into focus. Three-point shots are far less successful than their two-point counterparts, resulting in additional incremental possessions and points. That feels important, because a heavy three point shot strategy will create more possessions for your opponent versus a two-point strategy. As you wade more heavily into three-point shots, the possession tax gets larger given the time bound nature of the game and the upper constraint on the number of possessions during a game.
One important caveat. Any possession arbitrage can only be captured where a team is willing to be two-point shot heavy in their counter strategy…to take those extra possessions and convert them into two points, or lock in 1.1 points over time. If both teams are pursuing the same strategy of shooting high numbers of threes, the arbitrage is still available but never leveraged. Everyone is paying the same tax.
But what if a team adopted a decidedly different shooting strategy and tried to lock in added points from the incremental possessions it was given from more missed threes? Would the added points from made three-point shots still outrun this counter strategy regardless of number of missed shots, or is there some optimal number/levels for three-point shots based on shooting percentage?
There would seem to be other secondary efficiency benefits as well to a two-point strategy later in games. Near the end of games, teams in the lead tend to do three things: (1) they over defend the perimeter to make three-point shot attempts more difficult but leaving the basket under-defended; (2) they try and wind the shot clock down before taking their own shot - resulting in increasingly poor shot selection and more missed shots; and (3) they become reticent to physically challenge teams taking the ball down low for two-point attempts for fear of a whistle and free throws or a foul out at a critical juncture. Thus, inside shots become progressively easier and more efficient near the end of games when they matter most.
Now, I’m not suggesting that a team should never take a three-point shot or we should return to rates that were prevalent 30 years ago. What I am saying is that it seems to me that there exists a more complex balance between the two strategies to optimize performance versus blindly espousing that “three is more than two.” Things like segmenting three point shots attempts by areas on the floor where the three-point shooting percentage is lower and thus a less optimal spot to attempt shots – those sorts of things.
Your work here strikes me as a significant effort toward clearing the smoke on this topic. Thanks as always for the stimulating work.
Really enjoyed this one Neil. The one aspect that I suspect might come close to evening things out is that I would guess you are much more likely to turn it over going for a 2-pointer than a 3-pointer. That would be difficult to study without access to the tracking data though.
Thanks Nate! That's an excellent point -- 3PA, especially catch and shoots, would carry far less turnover risk than the typical 2PA, especially at the rim. That's where you'd sort of need to classify the precursor plays to each shot type and predict (or weight) for how likely it would become a 2PA/3PA to account for the turnovers that prevent the shot from ever actually getting off.
Wow, Paine coming out firing after the break! A terrific analysis and a topic that has troubled me for a few years now. In particular, the simplistic "three is more than two" tiresome analysis of the sports media. I’ll freely admit up front that I am not sure my concerns here are valid – and likely could be off base. Still, what follows are some ungrounded observations plus a few crude proxies that are nowhere near as elegant as your solution here but intended to possibly advance the conversation.
I’ll start with an observational proxy using box score data that I made a few years back. What I did was remove the points from three-point shots from the final score, then run all the three point shot attempts using the two-point shot percentage for the entire game and add those points back into the zeroed out three-point shot points to obtain a revised final score for the team using only two-point shots.
What I saw – frequently – was that a team taking zero three points shots would have scored more points presuming the two-shot percentage held. This was true, even where the three-point shot percentage wasn’t terrible – above 33-1/3%. Now, it’s admittedly an imperfect analysis but it reflected to me at a high level that something was amiss with the orthodoxy that more three-point shots always equates to more points and more winning – so fire away.
It then struck me that the “three is more than two” heuristic focuses entirely on the conversion of made shots into points. It’s a simplistic and purely positive forward calculation where 33-1/3% for three-point shots equals 50% for two-point shots. Simple enough, but you are not shooting baskets by yourself in an empty gym and keeping score – you are playing an opponent where the outcome is relativistic and heavily dependent on what strategy you are pursuing.
What about the unspoken negatives from using an overweight three-point strategy…what I call the “taxes?” Your piece calls one of these taxes out brilliantly…the reduction in FT attempts. On the other hand, your readers have called out that some elements could be incrementally improved by shooting more threes e.g., rebounds and turnover rate. True, but right or wrong, while these strike me as worthy adjustments, they feel relatively small in effect.
What seems much larger to me is possessions. At a fundamental level, possessions reflect the opportunities to convert shots to points and prevent your opponent from doing that as much. Thus, possessions alone can be seen as statistically yielding points, i.e., “Value of Ball Possession (VBP).” While the formulae and numbers can vary to some degree, I recall that a possession is usually equal to slightly more than one point over time – say, 1.1 points.
From a possession perspective, the problem with an overweight strategic approach to the three-point shot starts to come into focus. Three-point shots are far less successful than their two-point counterparts, resulting in additional incremental possessions and points. That feels important, because a heavy three point shot strategy will create more possessions for your opponent versus a two-point strategy. As you wade more heavily into three-point shots, the possession tax gets larger given the time bound nature of the game and the upper constraint on the number of possessions during a game.
One important caveat. Any possession arbitrage can only be captured where a team is willing to be two-point shot heavy in their counter strategy…to take those extra possessions and convert them into two points, or lock in 1.1 points over time. If both teams are pursuing the same strategy of shooting high numbers of threes, the arbitrage is still available but never leveraged. Everyone is paying the same tax.
But what if a team adopted a decidedly different shooting strategy and tried to lock in added points from the incremental possessions it was given from more missed threes? Would the added points from made three-point shots still outrun this counter strategy regardless of number of missed shots, or is there some optimal number/levels for three-point shots based on shooting percentage?
There would seem to be other secondary efficiency benefits as well to a two-point strategy later in games. Near the end of games, teams in the lead tend to do three things: (1) they over defend the perimeter to make three-point shot attempts more difficult but leaving the basket under-defended; (2) they try and wind the shot clock down before taking their own shot - resulting in increasingly poor shot selection and more missed shots; and (3) they become reticent to physically challenge teams taking the ball down low for two-point attempts for fear of a whistle and free throws or a foul out at a critical juncture. Thus, inside shots become progressively easier and more efficient near the end of games when they matter most.
Now, I’m not suggesting that a team should never take a three-point shot or we should return to rates that were prevalent 30 years ago. What I am saying is that it seems to me that there exists a more complex balance between the two strategies to optimize performance versus blindly espousing that “three is more than two.” Things like segmenting three point shots attempts by areas on the floor where the three-point shooting percentage is lower and thus a less optimal spot to attempt shots – those sorts of things.
Your work here strikes me as a significant effort toward clearing the smoke on this topic. Thanks as always for the stimulating work.
Brilliant answers to important questions.