# Shooters vs Dunkers: Their Effects on Winning

## 15 April, 1996

Imagine yourself building a team where you have the choice between a good three point shooter and a good inside scorer. Which would you choose? No numbers and no specifics here, just this choice between a generic good outside shooter and a generic good inside scorer.

Would you go for the more consistent inside player, who, if you get him the ball, will probably get you a two point basket? Or would you go for the streaky outside bomber who can get you bunches of points in a hurry or miss a few in a row?

Now that you've thought about it, let's attach some numbers. Say, your inside player shoots 50% from the field and only takes two point shots, whereas your outside player shoots 35% from three point land and takes only three point shots. It's unrealistic, of course, but it helps to make a point. All you math people are now thinking, "Hmm, this is too easy. The outside player gets 3*0.35 = 1.05 points per shot and the inside player gets 2*0.5 = 1. Gotta go with the outside player, right?" All you non-math people are now thinking, "Damn, where's my calculator? Aww, forget it, this guy thinks too much. Time to go to ESPNet." And all you people who got to this site because I put that one little word on my front page are thinking, "First, there are no pictures, now he's testing me!"

Should you really take the three point shooter? He does score more points per shot and other factors like turnovers, free throws, etc. are not being considered. But, even in this hypothetical simple example, where it looks like the answer is obvious -- it's not.

The answer, in this case and in far too many cases in this shade-of-gray-world, is "It depends." What it primarily depends upon is how many shots the two players will take in a game. If they both take the same number of shots, but that number of shots is fairly small, the inside shooter makes the team better. If they both take the same number of shots, but that number is fairly large, the outside shooter makes the team better.

For example, if both players take only five shots per game on average (plus or minus two from game to game) and they play on a team that allows 95 points per 100 possessions, then the inside player wins roughly 59% of the time and the outside player wins roughly 57% of the time. (The method used to determine these numbers is explained below and is approximated in the Individual Winning Percentage Calculator:

which approximately duplicates the calculations used for this article. It doesn't reproduce them perfectly, apparently due to some bug.)

On the other hand, if both players take 20 shots per game on average (plus or minus 10 from game to game), then the outside player wins 61% of the time and the inside player wins 58% of the time.

But, these results apply when the defense allows only 95 points per 100 possessions, making these players generally good. As pointed out in Basketball's Bell Curve, it pays to be inconsistent if you're generally bad, not when you're generally good. For the case of only 5 shots per game, if the defense now allows 105 points per 100 possessions, then the consistent inside scorer wins 42% of the time and the inconsistent outside shooter wins 43% of the time. Because neither player looks good compared to the defense that is backing them up, it pays to be inconsistent like an outside shooter.

This has been a rather extreme example. In basketball, shooting two's or three's is not everything. However, this contrast exemplifies the difference between players like Dell Curry and Shaquille O'Neal, for example. One player's offense consists of streaky three pointers that can bring the team back from big deficits or explode a small lead into an overwhelming one. The other player's offense consists of consistent scoring from the inside, through dunks and free throws, that is a reliable offensive option throughout the game. When commentators refer to a player as hot or cold, they are usually referring to a player like Curry, not O'Neal.

Moving past the extreme example to use numbers more typical of NBA players, I performed several different comparisons of "high variance players", like Curry, to "low variance players", like O'Neal. These comparisons use a simplified method of approximating the contributions of an individual to winning. In short, the method determines how often an individual's offense is better than his team's average defense. So, when I present a player having a winning percentage of 60%, this means that 60% of the time, the number of points that player creates with his possessions will be greater than the points allowed to a player or team using the same number of possessions and always scoring with the given efficiency.

The first example I looked at were one where the high variance player had a floor percentage of 0.500 and an offensive rating of 114.0, whereas the low variance player had the same offensive rating but a floor percentage of 0.600. (These numbers were based on those of Nick Van Exel and Shaquille O'Neal in 1995.) Both players were assumed to use an average of 20 possessions per game, ranging between 10 and 30 uniformly. For each of these players, I put them within the context of different defenses and found the following results:

 Good Player (Floor%) Defensive Rating 100 105 110 115 Low Variance (0.600) 75% 67% 58% 49% High Variance (0.500) 70% 64% 55% 45%

Here, the low variance player outperformed the high variance player in every case, even when the offensive rating is lower than the defensive rating. The general conclusion is that being consistent is better when the overall offensive rating is good.

The above comparison was repeated, but for relatively poorer offensive players. Specifically, I reduced the offensive rating to 105.0 and varied the floor percentage. For a player who ranges between 7 and 21 possessions in a game, the following results are obtained:

 Mediocre Player (Floor%) Defensive Rating 100 105 110 115 Low Variance (0.550) 59% 50% 42% 34% Normal Variance (0.530) 54% 49% 39% 38% High Variance (0.480) 54% 51% 45% 35%

These results are very strange, ones that I have a difficult time drawing a firm conclusion from. It appears that the variability of a player does not have a straightforward relationship on winning when the player is average or mediocre. These results, however, are subject to scrutiny due to the limitations of the simple method.

I also looked at the effect that the number of possessions used makes on an individual's winning percentage. I again used a high variance (0.500, 114.0) and low variance (0.600, 114.0) player, but I varied their average number of possessions per game (and how much they varied from that average):

 Low Variance Good Player (0.600, 115.0) Avg. Poss/G (Spread) Defensive Rating 100 105 110 115 10 (5) 68% 63% 57% 48% 20 (10) 75% 66% 59% 49% 30 (15) 78% 70% 59% 48%
 High Variance Good Player (0.500, 115.0) Avg. Poss/G (Spread) Defensive Rating 100 105 110 115 10 (5) 65% 59% 56% 44% 20 (10) 70% 64% 55% 46% 30 (15) 74% 67% 57% 47%
This generally shows that good players are better when they use a lot of possessions, something not overly surprising. This is something to investigate further when I finish a model that correlates the performance of individual players to that of their teammates, a consideration not included here (or anywhere).

I did the same thing again with relatively average or mediocre players. As above, I looked at a low variance player with a floor percentage of 0.550 and a high variance player with a floor percentage of 0.480, both having ratings of 105.0. In the context of various defenses, these are their success rates when you vary the number of possessions they use:

 Low Variance Mediocre Player (0.550, 105.0) Avg. Poss/G (Spread) Defensive Rating 100 105 110 115 10 (5) 56% 50% 43% 37% 20 (10) 60% 50% 41% 32% 30 (15) 61% 50% 39% 28%
 High Variance Mediocre Player (0.480, 105.0) Avg. Poss/G (Spread) Defensive Rating 100 105 110 115 10 (5) 54% 52% 40% 39% 20 (10) 58% 49% 39% 34% 30 (15) 60% 49% 37% 31%
These results show that using fewer possessions when you are a bad player means you do not lose as much, a result that follows from The Effect of Controlling Tempo. However, these results are still a bit clouded by the earlier results for mediocre players. Namely, the high variance player generally does better than the low variance player if the defensive rating is 115 (compare the third columns of the two above tables), but the low variance player is slightly better if the defensive rating is 110. Also, why the high variance player apparently does better than the low variance player when he uses only 10 possessions per game and has the same offensive rating as the defense (105) is not known to me. I was simulating 15,000 "games", so artifacts should have died out; plus, I redid it for this odd case and still found this result. Fortunately, the principal result -- that using fewer possessions if you are relatively bad -- still holds.

### Conclusions

I generally found what I expected to find with this study, which was that consistently good offensive players "win" more often than inconsistently good offensive players of the same average quality. This conclusion was a bit more murky for players of mediocre offensivly ability, showing some "nonlinear" relationships between floor percentage and winning percentage, where there are points when it pays to be inconsistent and points when it does not pay. This is something that will be explored more as the models improve to account for player interaction.

A second conclusion that was also previously suspected was that players who use a lot of possessions and are relatively good offensively do better than if they only used a few possessions. For average players, the number of possessions used per game seems to make little difference. For poor players, it makes sense to use fewer possessions per game.

### Winning Percentage Method

The method I chose to evaluate winning percentage for individuals in this case is rather simple, overly simple for some purposes. The method credits a win if the player creates more points (according to methods described in The Fundamentals for Analyzing Basketball) than his team is expected to allow on the three to seven possessions used. Some of the falsehood in this method is that the defense is entirely consistent (which makes players look more extreme than they are, i.e., their winning percentages are farther from 0.500 than they should be), fractions of points are credited when a scoring possession occurs, and we are removing players from the context of a team (which makes players look less extreme than they are). Each of these poor assumptions, however, do not adversely affect the study as I framed it. Since my point was to generally understand the trade-off between two pointers and three pointers and each of the above factors primarily magnify (or lessen) the impact of these effects, I believe the general conclusions that can be drawn are correct.