The “Wisconsin Stat”

As a kid growing up in the Los Angeles area, playing in AAU, the Nike leagues, and the Marmonte; we had a team that was a little ahead of its time: take three’s, switch everything, run teams into the ground by scoring before the defense was set, and force every opponent shot in the short corner. It usually worked. We averaged roughly 80 points a game, won division titles, and had big shooters who were shooting 40+% with 10 attempts a game. Our program developed several Division 1 and Division 2 NCAA players (we had six on our teams). UCLA style of play was key: could you run the court like Tyus Edney or shoot like Ed O’Bannon…

My basketball world was rocked when I moved to Wisconsin and played out the remainder of my high school career in Madison, Wisconsin. In Wisconsin, the Badgers were the team of interest to the casual fan; but the team of the state was University Wisconsin – Platteville, headed by then head-coach Bo Ryan; the originator of the most famous Wisconsin high school offense: the Platteville Swing. There in Wisconsin, most teams did not rely on shooting or athleticism. Instead, they focused on ball control and grinding games to a halt. Possessions were no longer 10-15 seconds as in California; but rather 45-70 seconds as no shot clock was in existence. Scoring 60 was viewed as a “high octane offense.” For example, my senior year, we averaged 64 points a game; which was considered blasphemously high. Most teams in our conference averaged 44 points a game. We even had one conference game result in a 9-6 final.

The 30-Point Game

With downtrodden possessions, came the need for defensive discipline. In practices, we played the 30-point game, which focused on scoring a point for every pass of “reasonable” distance. Shots, worth five points, could only be taken as lay-ups or dunks. Teams turnover possessions whenever a turnover is made or a team dribbles the ball; a turnover being worth -5 points. First team to 30 wins, loser gets a “down-back” for every point they lost by. Losing by 15 was always terrible. More importantly, a defensive foul was worth three points to the offense.

What this taught a defense was to reinforce ball denial, teach how to use hands on defense, and how to force turnovers. The ultimate discriminator of team points came down to fouls. Due to this, we had to learn how to reach without reaching, and block without bodying, and take charges without blocking. Try learning how to slide into a charge during a break and no dribbles are being taken. After about forty collisions, you start to become an expert.

Need to reach for a steal? You learn at the swipe is almost always called for the foul. Absorbing contact and using the upward-and-inward, two-hand motion results in jump-balls or outright steals.

The ultimate goal was to eliminate an opponents possession through the use of disciplined defense; specifically to disrupt opponent’s offensive flow at the passing, cutting, and driving level.

Need specific examples? Feel free to watch the 2014-15 Wisconsin Men’s basketball team play almost any game. Of read any of these articles here, here, or here.

Possession Killing

When we got to game time scenarios, we would keep tracking of possession ending events and measure them against the fouls a player had. It’s great if a player had three steals in a game, but if it came at the price of four fouls; the defender put the offense in a better position later in the game due to the bonus and removed them from being as aggressive as necessary in higher stress situations (aka Crunch Time). A prime example has been Dwane Casey trying to handle Andre Drummond in foul trouble.

On-ball defensive fouls are commonly obtained through one of three actions: reaching/hacking for steals, bodying/hacking for attempting to block, and blocking for attempting to draw a charge. There is a fourth foul, the hand-check, but this is a pre-cursor to the above three, as its aim is to re-position an offensive player. The three main defensive statistics used to measure the impact of a player directly on action are then the steal, the block, and the charge. These measures do not directly measure the impact of all players on the court, but they do encapsulate the position of the player relative to the ball and is performing the potential possession killing action.

For a steal and a charge, the offense is credited with a turnover; an immediate possession killing event. For a block, however, a possession is not necessarily terminated. We have seen extensive discussion about this in the past. Therefore, we must look at blocks that lead to change of possession; known as kills in volleyball.

Therefore, we aggregate these statistics to form what we call the Wisconsin Stat.

The “Wisconsin Stat”

The Wisconsin stat is a measurement of the number of possessions terminated directly by a player divided by the number of fouls that that defender has achieved. What this value gives us is an identification of players that are “disciplined” when they get into the middle of the action. This means the defender is either a low-fouling possession-killing block specialist, or a thief who can make clean getaways, or they are an expert at drawing the charges.

In all three categories, we can think of current NBA leaders. For blocks, we usually think of Hassan Whiteside, Rudy Gobert, DeAndre Jordan, or Andre Drummond. For steals, we think of Stephen Curry, Paul George, Robert Covington, or John Wall. For charged drawn, we think of Kyle Lowry, Ersan Illyasova, DeMarcus Cousins, and Kemba Walker. These guys always tend to hover around the tops of each of these lists. However, are they all as efficient at terminating an offensive possession?

To measure this, we simply add the three key defensive stat categories and divide by the total number of fouls drawn. Using the introduction above, we can see why we would call this the “Wisconsin Stat.” Ideally, it would be the “Ryan Score if we were Nylon Calculus or Liberty Ballers; but you know my despise for naming any stat after someone’s last name.

If a player scores a one, this means they are equally likely to cause a foul as they are in terminating a possession. Think about that for a moment. These are players that can eliminate five possessions a game without fouling out. These players inherently grant you more than five points of defense without having to rely on a synthesized measurement such as defensive RAPM, RPM, or PIPM.

Granted, we would not want to use this measurement on its own. Instead, we’d rather focus on using the value a transformed variable in a bigger model. For instance, what does the impact of such a statistic really play on defensive efficiency. Sure, we gain five points over the course of the game; but that requires the player to play at a level of fouling fives time a game; which is almost unheard of.

Therefore, we use this statistic with care; and look into what the statistic is telling us. Which, we will do here.

Players That Would (Sorta) Make Bo Ryan Proud

If we construct the Wisconsin Stat for all players in the league and then limit the list of players to those that have created at least ten defensive actions: Kills + Steals + Charges Drawn; we obtain a list of 165 players across the league for the 2018-19 NBA season.

Who tops that list? Tyus Jones of the Minnesota Timberwolves. Let’s call this a coincidence:  Tyus Jones was on the 2015 NCAA National Championship Duke Blue Devils that vanquished the Wisconsin Badgers. Jones is a bench player with curiously high up-side; but has been relatively moderate at the start of this season. In fact, Minnesota actually projects well on this statistic; something we will look deeper into in a moment. Therefore, we look into the “true number one” of this list: former teammate…

Jimmy Butler – 1.3333 “Stops” per Foul

Butler has only garnered 13 blocks and zero charges over the course of the season; but his 33 steals plants him fourth in the league. Combine this with his 30 fouls drawn, and Butler is sitting at 1.3333 possessions terminated per foul. Over the span of 15 games, that’s 2 fouls per game. Meaning, Butler salvages an average of 2.66 points per game for his teams. Second on this list is no slouch either…

Kawhi Leonard – 1.3158 “Stops” per Foul

Leonard has been known for his defensive prowess for a few years now. This stat backs that up. Leonard is tied for 29th in the league for steals with 23 and has similar statistics as Butler. However, Leonard has only played in 13 games this season and has registered a mere 19 fouls. This indicates that Leonard only produces approximately 1.92 points per game for his teams.

Game Theory: Comparing Jimmy and Kawhi

We immediately see that Butler actually improves defenses from an individual point of view. However, teammates matter and a team may not be able to afford the extra 0.54 fouls per game. Note that if we had a team of eight Jimmy Butlers playing a standard eight-man rotation; we’d have roughly 16 fouls expected over the course of the game. If we were so lucky to have pure uniformity, we’d have no bonus attempts. Otherwise, every fifth foul results in two free throws; effectively 1.5 points yielded. This means that Butler’s 2.66 points per game isn’t necessarily so. It could potentially be a mere 1.16; worth less than Kawhi’s 1.92 points!

Therefor we’d have to look at the impact of fouling as well.

Before we do that, we unveil the entire list of Wisconsin Stat guys for the 2018-19 NBA season (through Thanksgiving):

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We will even let you scroll through all the teams:

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Impact of Fouling

To understand the impact of fouling, let’s quickly trot through the scoring rules associated with fouling. First, if a shooter is fouled, then they are awarded the number of free throws equal to the value of the field goal attempt (if missed) or one free throw (if the field goal is converted). Second, two free throws are awarded for every team foul, starting with the fifth team foul in a period of play. A team foul occurs only during a defensive possession or a loose ball event. Tertiary, the NBA implemented a “two-minutes” fouling system that awards free throws, regardless of count of team fouls, on the second team foul within the final two minutes of a period.

Within the NBA, a player cannot secure more than six personal fouls. Therefore, they are limited by the number of fouls they can tally before the Wisconsin stat “times out.” Therefore, deeper analysis into this statistic and its associated impact requires an advanced study into survival analysis. That is, the probabilistic time it takes for a player to foul out of a game.

What this means, at a high level, is that the better the Wisconsin stat, the better defender. There is a diminishing return against the number of fouls a player obtains. Alternatively, there is a initialization cost for teams that are less-aggressive and create almost no fouls; limiting towards a zero-divided-by-zero phenomenon. This cost shows that teams are tentative, non-aggressive as a whole, but assertive when aggressive. These teams must be good at corralling shooters if they are to win ball-games.

Therefore, we need to find low-fouling, but not too low, and high Wisconsin stat players and teams to really identify the power of what the statistic is describing.

Team Level: Minnesota and Indiana

Let’s look at this from a team level:

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We see that the Minnesota Timberwolves and Indiana Pacers top the league in the Wisconsin Stat. But if we take a look at the Defensive Ratings for both teams, we see that the Indiana Pacers are currently fifth in the league with 105.3 while the Minnesota Timberwolves are resting at 112.8 for 26th in the league. We can’t definitely suggest this is a pacing issue as the Timberwolves only run 100 possessions a game to the Pacers’ 97 possessions a game.

The difference comes between the effectiveness in corralling opposing teams. In fact, both teams have played 18 games and are perfect candidates for analysis. With 368 fouls, the Timberwolves are 25th in the league in fouls. Similarly, with 362 fouls, the Pacers are tied for the third lowest number of fouls in the league. Read that as both teams are conservative (or assertive) when it comes to their aggression. Compare this to the Toronto Raptors (435 fouls over 19 games converts to 413 fouls over 18 games) and we see that the Raptors are far more aggressive.

When we take a look at the corralling numbers, we find the following shooting distributions of the Timberwolves and Pacers opponents:

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And we immediately see that the Pacers are “better” at limiting field goals between 3-16 feet to bad looks. These are typically the hooks and floater attempts. Whereas the Timberwolves are a victim of high field goal percentages from 10-16 feet. Combine this with the three percent differential at the rim, and Indiana shows to have a better interior defensive posture. Combine this with Indiana’s abnormally high defensive three-point percentage (could be noise), the near 40% clip at which teams take those attempts (third highest in the league) indicates that either the Pacers are such an intimidating force inside (Myles Turner by chance) that teams take longer range attempts;  or that Indiana will yield the three, knowing they won’t put you on the line as much and bait opponents into their assertive defensive scheme.


Given the above, we can measure the assertiveness of a team on defense; but realize that the story is not completely told through this statistic. What it does is identify the assertiveness and aggressiveness of a particular player and team. Combining this statistic with others, such as the discussion of comparing the Pacers and Timberwolves, we begin to stat seeing the actual values of assertiveness and aggressiveness each player/team exhibits.

More importantly, we can start breaking apart players at the top of the counting stats. For instance, Anthony Davis (5th) appears to be the top post defender as he barely fouls compared to his contemporaries, such as Andre Drummond (154th). And it’s why we see Dwane Casey fretting about convincing Drummond to play through the foul trouble. Ideally, Drummond would identify more optimal methods for picking up his blocks without fouling.

Similarly, it’s part of the notion of why we picked on Steph Curry as a defensive player (during my days in the Western Conference) as his Wisconsin Stat rating is actually fairly low in specific situations. And this is what separates players such as John Wall from Curry as a defensive stopper. It actually gave edge in those games.

At the same time, as a third reminder: Buyer beware. Use this statistic as a talking point to something bigger; and perform rigorous analysis of the entire situation before understand the actual impact of the statistic on the game.

For fun, feel free to search all players through all games played up until Thanksgiving here:


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