# Showing my work: More on "It's the defense, stupid"

In today's column, a follow-up on my last column making the statistical case that Duke''s performance declines over the course of the ACC's schedule, I tried to determine whether that decline in performance is due to fatigue. I made four separate, but related, points:

1. Neither high-minute players (guards averaging greater than 34 minutes per game or forwards averaging greater than 32 minutes per game) nor low-minute players demonstrate decline in offensive performance over the course of the season over the last nine years.
2. From 2004-2009, almost the entirety of Duke's decline over the course of the ACC scheulde can actually be attributed to a drop-off in defensive performance.
3. Of the factors influencing defensive performance that can be logically tied to fatigue, only steal percentage (the percentage of opponent's possessions in which a defense stole the ball), declined over the course of the ACC season. Defensive rebound percentage (the percentage of opponent's shots rebounded by the defense), block percentage (the percentage of opponents shots blocked by the defense) and free throw rate (free throw attempts divided by field goal attempts) remained constant over the course of the season.
4. Over the course of the ACC season, opponents tend to shoot a higher percentage against the Blue Devils, while their assist rate (percentage of baskets that were assisted) remained constant

The combination of these statistical facts painted (for me, at least) a picture of a team that did tire over the course of the season. The team's fatigue manifest as an inability to contest passes and shots as aggressively later in the conference season, leading to fewer steals and a higher shooting percentage for opponents.

I thought I'd show some of the graphs that didn't make it into the paper here, along with some explanation, where necessary.

The first two graphs correspond to point one above, that neither high-minute nor low minute players decline on offense over the course of the season. I graphed offensive rating -- a stat that measures the number of points a player produces per 100 possessions "used" -- against ACC game (where game one is the first game of the season, and game 19 is the ACC championship game). A player "uses" a possession when he attempts a field goal or free throw or turns the ball over. In offensive rating, a player produces points when he makes a field goal, makes a free throw, or grabs an offensive rebound; when a player misses a shot or turns the ball over, he uses the possession without producing points.

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Next, I looked at team defensive performance and offensive performance in seasons from 2004-2009, graphing points scored or allowed per possession as the ACC season progressed. As it turned out, offensive performance remained stable while defensive performance declined. In fact, it appears as though the entirety of the decline in Duke's performance can be attributed to worse defensive performance. Duke's defense worsened by 0.01 points per possession per game; over the course of a 19-game ACC season, that difference adds up to the Blue Devil defense being 13 points worse in the final game of the season then they were in the opener.

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At the beginning of the season, the Blue Devils were better than their opponents by approximately 0.1 points per possession; however, by the end of the season, the gap had been erased.

Honestly, this finding shouldn't have surprised me much. From personal experience, fatigue seems more likely to show up on defense than on offense. I postulated that fatigue, if it existed would show up in four areas -- steal percentage, block percentage, defensive rebound percentage and opponent free throw rate.

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Only steal percentage showed a significant decline; however, I worried I was missing something. Wouldn't opponents tend to shoot better against a tired defense that didn't do a good job contesting shots? But drawing conclusions from shooting percentage (or the more-accurate effective field goal percentage, which counts three-pointers as 1.5 made shots) seemed tricky. How could I tease out good offense by Duke's opponents from bad defense by the Blue Devils? Both were possibilities, and both had implications for my conclusions. Bad contesting of shots would point toward fatigue, while improved opposition offense would point toward other teams improving more over the course of the season than did Duke (lending credence to the "Coach K gets more out of his players all season long, but when everyone plays harder at the end of the season, talent wins out" theory).

I settled on assist rate, a statistic that measures the percentage of baskets scored by a team that were assisted. As a measure of "good offense," its not perfect, but I think it's helpful. A good, crisp offense tends to pass the ball better and score more easy baskets, and easy baskets are often assisted. A bad defense would enable opponents to make shots without crisp passing. When I ran the numbers, I found that opponents shot the ball better against Duke over the course of the season, but their assist rate remained constant.

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The combination of improved opponent shooting percentage along with a stagnant assist rate over the course of the season, points toward worsening defense, rather than improving offense as the reason for Duke's defensive slide. Worsening contesting of shots combined with fewer steals indicates, to me, a tired team.

I said in the original column that I didn't know why Duke has historically tired down the stretch. But given that defense is such a team-centric concept, it is almost certainly related to fatiguing of the entire team, not just high-minute players, which would indicate that intensity of practices (where everyone fatigues the same amount) is the culprit.

To my eye, it seems as though Mike Krzyzewski is not driving his players as hard this season, which means that maybe he caught on to this fatigue thing well before I did (and he should, since he can talk to his players and find out if they're fatigued, instead of relying on statistics). Either way, this year's team defensive performance has, so far, been improving. Here's hoping that it keeps trending in the right direction.

I've included the spreadsheets that I used in my calculations below.

[Click here for a spreadsheet showing opponent FTR, DR%, Steal%, Block%, opponent EFG and opponent assist rate]

[Click here for a spreadsheet showing individual per game offensive rating for high-minute and low-minute players, 2001-2009]

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