This week's mailbag features your questions on bad defense from playoff teams, poor free throw shooting and more.

You can tweet your questions using the hashtag #peltonmailbag or email them to peltonmailbag@gmail.com.

"Listening to the most recent Lowe Post, and while discussing the Cleveland Cavaliers, Zach said that since the merger just eight teams with a bottom-two defensive rating have made the playoffs. Not sure how you quantify it, but does that actually seem higher than you'd suspect? Once every five years, a team that's basically terrible at half of the sport makes the playoffs!"

-- Ben

There's an important bit of context to that research from ESPN Stats & Information: Going back to the ABA-NBA merger introduces periods when it was much easier to make the playoffs than it is today. Between the move to 16-team playoffs in 1984 and the NBA's first round of expansion in 1988-89, there was a five-year span in which more than two-thirds of the league's teams made the playoffs.

The playoff teams with awful defenses include the 30-52 1985-86 Chicago Bulls (from Michael Jordan's second season, when he was limited to 18 games by a navicular fracture) and the 31-51 1987-88 San Antonio Spurs, teams that would be unlikely to sniff the playoffs today. No team has made the playoffs with a bottom-two defense since the 2002-03 Milwaukee Bucks, and they're the only ones to do so in the past 26 postseasons. So the Cavaliers would be bucking a lot of recent history.

That said, some of these teams were actually pretty good. The Houston Rockets won 47 games with the league's worst defense in 1978-79 two years after winning 49 games with the second-worst defensive rating. The 1981-82 Denver Nuggets and 1988-89 Philadelphia 7ers also won 46 games apiece despite the league's worst defensive ratings.

Those results point to the fact that offense does tend to be a little more important in the regular season because there's a greater spread between teams in offensive rating than in defensive rating. And such is the case with this year's Cavaliers. Through Friday's games, their offensive and defensive ratings were precisely the same: 109.8 points per 100 possessions.

While that rating was worst in the NBA on defense, being the same amount better than league average on offense was only good for the fourth-best offensive rating. In most cases, we'd expect a team that is simultaneously the NBA's best on offense and worst on defense to perform a little better than .500 and therefore often make the playoffs.

"I've been curious about this for a while and the Lakers' recent 2-for-14 free throw shooting game brought it to my mind again: are NBA players worse free throw shooters now than they were 5-10 years ago? And are there more poor FT shooters (<70%, or some other criteria you'd use to qualify poor shooting) and fewer good shooters (>80%) than there used to be?"

-- Zach

You might be surprised to learn that just last season the NBA set an all-time record for foul shooting by making 77.2 percent of attempts league-wide. That ever so narrowly surpassed the 77.1 percent the NBA shot in both 1973-74 and 2008-09. While free throw shooting is down slightly this year to 76.6 percent through Friday's games, that would still rank fifth in NBA history, according to Basketball-Reference.com.

That noted, I do think you're right to hone in on different measures than league-wide free throw percentage for the same reason that mark jumped 1.5 percent last season: Not all players shoot free throws at equal rates, so taking the league average weights various players differently. The reason the NBA shot free throws better last season is pretty simple when you think about it: The reduction in intentional fouls after rule changes meant fewer attempts for the league's worst foul shooters.

So here's how the distribution of free throw percentages among players with at least 100 attempts has changed over time:

Kevin Pelton

The vast majority of NBA players have always shot between 70 and 90 percent from the line. And while there aren't necessarily fewer poor free throw shooters in the league -- there might even be a little more tolerance for the extremely poor shooters who are targeted for intentional fouls -- this middle group has tilted more toward 80 percent-plus shooting in recent years.

The past two seasons, 44 percent of players with at least 100 free throw attempts have made better than 80 percent of them. It probably shouldn't come as a surprise that the increasing value of 3-point shooting has also brought more good free throw shooters into rotations.

.@kpelton is there a metric that measures cumulative injury impact for a team in a given season, like expected Win Shares Added multiplied by games missed? I'm trying to figure how relatively depressed I should be as a Jazz fan. #PeltonMailbag — Layn (@layns5) January 26, 2018

I track this as part of my injury database using my wins above replacement player (WARP) metric. Because of the use of replacement level, this often yields very different measurements than games lost to injury -- which treats an MVP candidate and a 15th man the same -- or even multiplying games lost by average minutes per game. Through Friday, here are the teams that have lost the most WARP to injury:

Most WARP lost to injury Team Games Minutes WARP San Antonio 143 (24) 3005 (24) 9.3 Golden State 114 (15) 2146 (15) 7.6 Houston 111 (14) 2025 (13) 6.7 Milwaukee 117 (16) 2891 (22) 5.7 LA Clippers 150 (26) 4457 (30) 5.6

To reinforce that, the top four includes three teams in the middle of the pack as far as games lost because of the quality of the players who were injured: Stephen Curry for the Golden State Warriors, James Harden and Chris Paul for the Houston Rockets, and in the Milwaukee Bucks' case, primarily Jabari Parker missing the entire season so far after a torn ACL suffered last year. (Because he has yet to play, Parker's WARP is based on his preseason projection.)

The Utah Jazz rank ninth by this measure, having lost 4.0 WARP to injury, mostly from Rudy Gobert's 26 games missed. (Gobert's absence alone has cost Utah 3.0 WARP by my estimate.) The bulk of the team's other games missed have come from Dante Exum, who was not projected to rate better than replacement level, and Joe Johnson, who was expected to do so this season but hasn't. So the Jazz don't come off as especially hard-hit by injury in this calculation.

One key note to add here: It's not really accurate to say Utah has lost four wins to injury because, naturally, every team has injuries. The appropriate benchmark here is the average WARP lost to injury, which is about 3.3 games so far this season.

"I was just looking at NBA.com stats and noticed that only around a dozen players are averaging 36 or more minutes per game. That got me thinking about why 36 minutes was chosen to be the number of minutes to have a stat that compares players on a level-playing field. Wouldn't per-33 minutes (or something like that) be more appropriate? When this stat was created were there a higher number of players averaging over 36 mpg? Does nobody care because, either way, players are being compared evenly with this stat?"

-- Mike

Your first assumption is correct. When statistical analysts started looking at performance on a per-minute basis, they originally scaled most numbers to a full 48-minute game. My recollection is that John Hollinger made the change to instead use stats per 40 minutes, since that was the typical maximum for starters, and Basketball-Reference.com later went to per 36 minutes because that was a common average for starters. I'm not exactly sure when that was, but it looks like it was somewhere around 2011. Many more players did in fact average 36 minutes per game then:

Players averaging at least 36 MPG Season # 2008-09 42 2009-10 35 2010-11 25 2011-12 17 2012-13 24 2013-14 17 2014-15 6 2015-16 7 2016-17 9 2017-18 12 Minimum 20 games

If we were truly looking at the average minutes for a starter, we'd probably want to use about 30 minutes, which is averaged on the typical team by three players. That number has been a bit more stable.

However, I don't think it really matters much. First off, the point is not so much to show what this player would do if made a starter as to put players on a level playing field and put their numbers in a context that's easier to understand than per-minute stats, for which we have little intuitive understanding of what's good and what's bad.

Moreover, I'd rather not look at per-minute stats that much at all. They can be misleading when comparing across teams that play at different paces, and particularly now when comparing to seasons from the recent past with lower pace of play. Instead, I favor using stats per 100 team plays, which put players on equal footing both for playing time and for pace.