It’s the first post here on HumbleBola about the UAAP since last season and the first Let’s Talk Basketball post since we moved to the new servers so I wanted it to be good. And boy, is it good. Or, at least I think it is.

The difference between reality and fiction? Fiction has to make sense. – Tom Clancy

Today we take a look at new “old” statistics (since most of these have been used before by NBA writers but have barely been used in the Philippine setting) that study shot distributions. Why is this so important?

Process over Result

One of my favorite quotes/ideals/beliefs, especially when talking about basketball, is that process matters more than result. In basketball (and sometimes, in life),  nobody cares about the process so long as you get the results. As they say, the end justifies the mean. Of course, that quote brings along with it some discussion of evil for good but I’m here to focus on how everybody focuses on the end. Time and time again, athletes from different teams, sports and eras have been subjected to this results-based judgement.

Oh, LeBron passed to Donyell Marshall and Marshall missed it?? Lebron choked. 

Oh, Kobe makes a contested, falling away 22-ft 2PT jumper to win the game? Kobe is clutch.

Yes, results matter. But in the overall scheme of things, following a certain process yields better results than aiming only to gain results (with of course no regard for how to get there). There are a lot of reasons why but chief among them is the fact that unguided results are unsustainable; results stemming from the right philosophy, ideology or process are sustainable. And that’s something that people seem to miss out on — sustainability.  The goal is to not only get results (wins) but to sustain them and sustaining them requires some sort of understanding of the process that got you those wins. The end argument of all analyses is to make sure that a team can replicate what allowed them to excel in the first place. So in order to get to the bottom of the question: what allowed my team to excel? We need to know “what gives teams the best chance at excelling” and “how do we go about doing this” and of course “why do this?”

Expectation vs Reality

There’s a certain dichotomy that comes with comparing expectation and reality. Google defines expectation as “a strong belief that something will happen or be the case in the future.” Notice how expectation brings along with it the idea of a future and the uncertainty that comes along with it? A belief that’s grounded on something – history, statistics, your own prejudiced expectation, something.


You think you look cool when you play ball, but you don’t (Photo Credit: Google Images)

Reality, on the other hand, is actuality. Reality is what is happening as opposed to what is supposed to happen. More often than not, if your expectation is grounded on probability theory, expectation becomes reality. This is especially true in a long basketball season.

Unconditional vs Conditional

A few months ago, I posted an article on the Blue Eagles’ win over the UST Growling Tigers in Game 1 of the Finals and titled it “Dendritic Connectivity and Game One: A tale of two halves.” The basic premise of the article was that a game is a series of dependent events, not of independent ones. It’s not a series of photos but rather a film strip where images are connected, not individual and placed on top of each other. In analyzing what shots are efficient, we need to consider the things that are born out of the shot other than the shot itself. We cannot merely discuss about the percentage of shots that go in. We must also discuss a lot of different things such as the gravity it has on the player, the possible succeeding action during and after the shot. My writers, in our first ever meeting, pointed out some really good reasons.

  • Layups and dunks are the most efficient shots in the game because they are closer to the rim
  • Layups and dunks are the most efficient shots in the game because you draw more contact when you’re inside the paint and therefore, there’s a higher probability of getting a foul. 
  • Layups and dunks are the most efficient shots in the game because when the shots are closer to the rim, then the ball won’t bounce too high and too far from the player resulting in more offensive rebounding opportunities. This also results in fewer fastbreak opportunities. 

All very valid concerns and probably reasons why layups, dunks and tip-ins are widely accepted as the most efficient shots in the game. From then on, people will think that the farther you move out from the rim, applying similar reasons as above, the less efficient the shot becomes. And to a degree, they are right — the farther you are from the rim, the harder the shot gets, the probability of an offensive rebound gets lower and the probability of a fast break goes higher. But there comes a point when this is no longer true. There comes a point when shots are worth 1 more point than they usually are, and these are called… three-point shots! I’ve talked about this in detail (shooting efficiency) but the gist of it is to use effective field goal percentage as a way to adjust for the added value of a 3 point shot.

Points Per Shot, Expected Points Per Shot and Scoring Index

The UAAP stat keepers have done a marvelous job of keeping track of shot locations. Because of this, we can add another wrinkle into our analysis. Here, I’ll introduce three things: Points per Shot (PPS), Expected Points per Shot (XPPS) and Scoring Efficiency Index (SE).

Points per Shot is very straightforward – we look at how many points you scored in each shot. If you scored 20 points and took 20 shots, that’s a PPS of 1. If you scored 10 points and took 7 shots, that’s a PPS of 1.4. It’s a quick way of analyzing a player’s scoring efficiency. It’s closely tied to effective field goal percentage (if you scored all of your points from field goals, then dividing PPS by 2 would get you your effective field goal percentage).

Expected Points Per Shot (XPPS) takes into account the shot distribution and the league average. I’ll just give an example. The Ateneo Blue Eagles had a shot distribution of 54/26.5/19.5 [At-the-Rim/Mid-Range/3 PT shots]. If we assume 100 shots, that means they take 54 at-the-rim shots, 26.5 mid range shots and 19.5 3PT shots. The league average FG% are 49.5/30.1/26.9. This means Ateneo has an XPPS of 0.85 from field goals (again we remove free throws into the equation since we are studying shot distributions). This means that if Ateneo maintained their shot distribution and were average, they’d score around 0.85 points per shot. In reality, Ateneo scored 0.93 points per shot because they shot way better than average in all three locations.

Scoring Efficiency Index (SE) tries to find out which shot distributions are optimal. It’s a very simple index, really. You just add the percentage of at-the-rims and percentage of 3PT shots and divide them by the percentage of mid-range shots you take. We’ll take the UST Growling Tigers as an example. UST takes 47.5% of their field goal attempts at the rim, 22.4% of their field goal attempts from mid-range and 30.1% of their field goal attempts from three. Their SE, therefore, is (47.5+30.1)/22.4 = 3.47. The higher this is, the more optimal the team’s shot distribution is. Take note, we’ll also use this on the defensive side – which team forced the most optimal shot distribution.

The Numbers


Team PPS Rank XPPS Rank SE Rank
ADMU 0.937 1st 0.852 4th 2.772 7th
ADU 0.848 5th 0.848 6th 3.759 4th
DLSU 0.807 6th 0.867 1st 3.865 2nd
FEU 0.912 2nd 0.841 7th 3.093 6th
NU 0.858 3rd 0.859 2nd 4.557 1st
UE 0.786 8th 0.855 3rd 3.800 3rd
UP 0.787 7th 0.825 8th 2.293 8th
UST 0.858 4th 0.848 5th 3.465 5th


Team PPS Rank XPPS Rank SE Rank
ADMU 0.786 2nd 0.831 1st 2.624 1st
ADU 0.940 8th 0.854 7th 3.793 7th
DLSU 0.754 1st 0.836 2nd 2.943 2nd
FEU 0.828 3rd 0.851 5th 3.610 6th
NU 0.837 4th 0.853 6th 3.359 3rd
UE 0.919 7th 0.849 4th 3.394 5th
UP 0.863 5th 0.874 8th 4.090 8th
UST 0.864 6th 0.846 3rd 3.361 4th

(Note: This is an inverse ranking, since it’s defense. The lower the PPS, the better. Same with XPPS and SE.)

Notes and Comments

  1. It was not surprising to see that Ateneo had a less than optimal offense (7th SE) since Ateneo takes more than 26.5% of their shots from mid-range. A big reason for that is because Salva, Chua and Kiefer loved taking mid-range jumpers. The good news? They made mid-range jumpers at an above average clip (league average is 30.1%, Ateneo made them at 33%). The bad news? 33% is still 33%.
  2. FEU is another team that has a good PPS (their ORTG was actually 2nd best in the league) and then suffer from XPPS and SE analysis. Why is this? Similar to Ateneo, FEU eschews some of the more efficient shots (at the rim or 3PT shots) in favor of mid-range shots. The difference is that while Ateneo chooses to minimize their 3PT shots, FEU chooses to limit their attacks at the rim. With no interior presence and heavily reliant on perimeter isolation and, hmm, chucking from Romeo and Garcia, it was reasonable to expect fewer at the rim attempts (FEU attempted 45.7% of their attempts at the rim. League Average is 48%) and more mid-range (and also, 3PT shots).
  3. UE has among the most optimal shot selection based on XPPS (3rd) and SE (3rd). Problem is they had a really hard time finishing shots especially at the rim (44%, league average is 49.5%). Maybe we’re seeing the fruits of these optimal shot selection when they won the recently concluded FilOil tournament?
  4. Defensively, there was no doubt who the top two teams were – Ateneo and La Salle. They were the only teams to allow an above average percentage of shots from mid-range (the least efficient among the three). In fact they are 1 and 2 in all categories with Ateneo being the team with the highest XPPS Defense and SE Defense and La Salle with the highest PPS.
  5. Like their offense, FEU has quite a steep decline when comparing their Defensive PPS and Defensive XPPS/SE. Their Defensive PPS ranks 3rd in the entire league, when they allowed 0.828 points per possession. However, their Defensive XPPS is 0.851 ranking 5th and their Defensive SE clocking in at 3.610, ranking 6th.
  6. Coach Ricky Dandan has a lot of work to do. The UP Fighting Maroons, I think have high aspirations and new recruits. Well, nothing better than throwing this kids into the fire with expectations to improve on the worst offense (7th in PPS, 8th in XPPS and SE) but also on the least optimal defense (8th in XPPS and  SE). This season, Kyles Lao and Andre Paras better be good on D or else UP’s fortunes are not closer to turning around than it was a year ago.
  7. The National University Bulldogs had quite possibly the optimal shot distribution of them all, and it’s not even close. Only 18% of their shots came from mid-range. That means 82% of their shots came from the efficient shots, i.e. 3PT shots and at-the-rim shots. Their conversion was below average from 3 (23.9%, league average is 26.9%) but shooting 23.9% from downtown is better than shooting 30.1% from mid-range. If you converted both to eFG, 23.9% would become 35.8% while 30.1% will still be 30.1%. Ahh, I love math.
  8. Adamson was a surprising revelation. They had the 4th most optimal shot selection. They did shoot way below league average. The league average percentage of at-the-rim shots is 48%, Adamson takes 45.8% of their shots near the rim. That’s a bad thing. The good thing? All of those shots that they didn’t take at the rim were made into 3PT shots. They took 33.2% of their shots from downtown. They made a good number of them too (eFG of 47.2%). That’s probably a good reason why their ORTG ranked 5th best, behind ADMU, FEU, UST and NU. The question now is – how will they survive without Eric Camson? We’ll have to wait and see.
  9. UST was just about where they were supposed to be on offense. Their defense however didn’t perform as well as it should. Their Defensive XPPS ranks 3rd and their Defensive SE ranks 4th on defense but they were only 6th in terms of Defensive PPS. They allowed fewer shots at the rim (47% of their opponent’s shots were at the rim shots). The bad thing? Those shots were converted into 3PT shots. What made it even worse? They allowed a higher FG% than average near the rim and especially from the 3PT line. That’s not a recipe for success.