# Introducing foul drawn percentage

There are a ton of available NBA statistics outside of a regular box score. You can check out Nylon Calculus’ here, but several sites offer new ways to look at scoring, rebounding, and passing.

Statistics for fouling and drawing fouls have lagged behind, though. A standard box score doesn’t even have fouls drawn, even though for every foul committed there should be a player who draws the foul. In play-by-play logs, different foul types exist like different shot types, but no description of where the foul was committed like we see with shot attempts. Free throw attempts after a foul help, but only to separate shot fouls from two and three-point attempts. Fouls drawn per 36 minutes and per 100 possessions are available on NBA.com, but unlike other box score stats you have to venture outside of the basic pages to find it, and measuring by possessions can be confusing when loose ball fouls happen on both sides of the floor. Everything is terrible (but not really).

A common way to measure foul-drawing has been by free throw attempts per 36 minutes or per 100 possessions, much like minutes and possessions have been used to look at scoring, rebounding, and passing, but those aspects of the game have been expanded upon with statistics like usage rate, rebounding percentage, and assist percentage. In this post, the formulas for those metrics were used to add a few offerings related to foul-drawing. Personal foul and team foul drawn percentage are estimates of an opposing team’s fouls drawn by a player when he’s on the floor. The latter statistic filters out offensive fouls.

Calculations for each, like for rebounding and assist percentages, were fairly simple:

(Personal or Team Fouls Drawn by Player/Personal or Team Fouls Drawn by Team) / (Player Minutes/Team Minutes).

Both statistics correlate strongly with free throw rate and attempts per 36 minutes, the former with an R^2 of .48 and the latter in the mid-.80s. Depending on the site, dividing team minutes by five might be necessary. That would have to be done if using Basketball-Reference’s team minutes here.

## More from FanSided

One example of calculating this would be looking at Anthony Davis in a game against the Sacramento Kings. He drew 10 of the 25 opposing team’s fouls while playing 38 of a possible 48 minutes, for a personal foul drawn percentage of 50.5. Had he played all 48 minutes, the percentage would’ve been 40, or if he played 24 minutes it would’ve been 80 percent. Small samples like one game can produce wonky results, though. In a game against the Houston Rockets, Andre Drummond drew 25 of the team’s 41 drawn personal fouls while playing 23 minutes, for a personal foul drawn percentage of 127. Drummond drew a record number of fouls that night dating back to 2006, when drawn fouls started showing up in play-by-play data. Before then, drawn fouls could only be pieced together when they led to free throws.

So who showed up well or struggled in these two statistics over the last decade? Check out the table below:

The very top and bottom since 2006 matched positional and age averages, physical bigs in their mid-20s taking up the top while the bottom had spot-up shooters with their most versatile days behind them. Using Basketball-Reference’s designated positions, there’s been a shift over the last decade in foul-drawing that matches what we see today on offense. Centers drew the largest portion of their team’s drawn fouls last season, in a tier of their own partly because of intentional fouling, but it’s also increasingly hard to play low-usage guys like Joel Anthony or Kendrick Perkins. Power forwards and point guards were in a second tier while wings were at the bottom:

As we see, though, 2006’s averages were much different than last season. A decade ago, things were quite balanced in both fouls (and minutes) and at one time may have been the opposite from last season, had all drawn fouls been available in play-by-play data from the late-90s and early-2000s. That would’ve caught the peaks of wings with a lot of free throws like Tracy McGrady, Jerry Stackhouse, Grant Hill, and even Richard Hamilton, but also the best of Shaquille O’Neal, so maybe nevermind. It’s a shame prime Shaq wasn’t able to be calculated here.

As for age-related averages (ages also via Basketball-Reference), check out the graphs below. I excluded players 18 years old or over 39 because of the small samples.

This probably also matches when the prime of a player’s career is expected to happen, except that bump at 36 years old. Some of the players to blame for this might be obvious: 2009 Shaquille O’Neal and 2013 Tim Duncan, but also 2013 Vince Carter, 2014 Manu Ginobili, and a few other Hall of Fame candidates who turned back the clock.

If only we could look at prime Shaquille O’Neal with what DeMarcus Cousins and Dwight Howard have done since then, but while comparing players at the top and bottom like that can be fun, sometimes it isn’t the best way to use these statistics. Personal and team foul drawn percentages are team and game-based. League-average without accounting for positions is always 20 percent. It hurts players on teams who draw a ton of fouls and bumps up those on teams with below-average amounts, as we can see when including fouls drawn per 36 minutes. The decline in fouls per game since 2006 matters, too, 22.8 fouls a decade ago but 20.3 last season and as low as 19.6 in 2012. It doesn’t mean it’s wrong to compare players from different teams and seasons, but it’s worth noting, similar to rebound rates thanks to the decline in offensive rebounding.

One extreme-ish example when looking at percentages in a single season was Dwight Howard with the Houston Rockets, a team that finished last season leading in drawn personal fouls. Howard had a similar personal foul drawn percentage as Paul Millsap, Brook Lopez, and Damian Lillard, who all drew about one less foul per 36 minutes, but played on teams in the bottom 10 in that part of the game:

Another example with Howard was when he went from the Orlando Magic, a team that routinely placed near the bottom in fouls drawn while he was there, to the Los Angeles Lakers, which led that statistic in 2013. This can also serve as an example of how foul drawn percentages look when viewing players on the same team:

Dwight’s fouls drawn per 36 minutes in 2012 and 2013 were about the same, but along with his usage rate, his foul drawn percentages dropped. The same thing happened to Kobe Bryant and Pau Gasol. A possibly confusing one was with Metta World Peace and Robert Sacre, similar percentages on the same team but World Peace with a slightly higher drawn fouls per 36. This seems to be from playing in different games and/or Sacre’s small sample of minutes.

Looking at a whole team, the top five players in minutes will typically add up to over 100 percent and reserves will post smaller percentages, but there are exceptions like high-usage players off the bench and defensive specialists starting. After his trade to Boston, Isaiah Thomas became the only player since 2006 to start less than half his games, clear a 500-minute filter, and post a foul drawn percentage over 45 or average seven drawn personal fouls per 36 minutes. Not even Corey Maggette could do that. Tayshaun Prince last season was the opposite, the lowest foul drawn percentage (4.3) of any player to start over half their games and second only to 2012 Andris Biedrins in lowest personal fouls drawn per 36 minutes, with a rate of 0.69.

Those examples included personal fouls drawn, but team fouls drawn filters out offensive fouls since no matter what NBA.com’s play-by-play says, they don’t count as team fouls and don’t have the benefit of leading to free throws if a team is in the bonus. Often, the results between personal and team fouls drawn were similar, but adjusting for offensive fouls hurt “energy” or “hustle” guys. In the example I posted below, Jon Brockman in 2011 holds the highest offensive fouls drawn per 36 minutes at 2.07, and Anderson Varejao drew 97 offensive fouls back in 2007, a total that hasn’t been touched since. Both show up a bit worse while guys like Dwight Howard and Isaiah Thomas in 2015 had two of the most positive bumps in their percentages:

As a reminder, it wouldn’t be wrong to compare players from different teams and seasons (I did it for looking at foul-drawing reserves and contact-avoiding starters), but free throws and fouling have changed a bit over the last decade. Assist and rebounding percentages run into similar situations, sort of. John Wall and Ricky Rubio averaged 10.2 assists per 36 minutes last season with Rubio having an edge by .5 assists when adjusting for pace, but the percentage of field goals Wall assisted on when on the floor was five percent higher and he finished with a higher playmaking usage. When it comes to total rebounding percentage and rebounds per 100 possessions, league-average offensive and defensive rebounding have changed quite a bit over the last decade.

Foul-drawing percentages (or drawn fouls per 36 minutes) aren’t meant to be perfect, but hopefully they add to the discussion of that part of the game rather than looking only at free throw attempts or dividing free throw attempts by field goal attempts.

## Some other notes on foul drawn percentage:

I also included drawn team foul rates, dividing player totals by their field goal and free throw attempts. League-average for each since 2006 was 23 and 78.5 percent, respectively, but last year they were 22 and 79.6 percent. Eyeballing this with penalty-related stats and watching guys like Kevin Martin, it looks like players who had low team foul to free throw ratios, but high free throw attempts per 36 minutes either fed off the penalty with late-game fouling or cheap fouls like rip-throughs.

Louis Williams showed up sometimes as Louis, other times as Lou, and sometimes as both. When merging different documents, his numbers got mixed up so I scrapped his name for most seasons. It’s too bad since he’s quite the foul-drawer, especially on jump shots. Remember this when looking at teams he’s played for, but was missing. The foul percentages for the 2012 Sixers, for example, do not make a ton of sense without his stats because I did not erase his fouls drawn from the team totals. Had I done that, everyone’s percentages from his squads would be juiced up and incorrect.

Minor discrepancies from NBA.com and Basketball-Reference may exist for a couple of reasons. From 2006 to 2012 there were a handful of missing games in NBA.com’s play-by-play data each season. This was adjusted for, but some (not all!) minutes will not match official totals. There were also blank play descriptions in some fouls, events that don’t make a ton of sense when looking at film, that I left out but may have counted in NBA.com’s total drawn fouls.

As a reminder, personal and team foul drawn percentages were compiled from NBA.com play-by-play data.

More from NC: Who was better: Tim Duncan or Kobe Bryant?