Up Three, Time Running Out, Do We Foul? The First Comprehensive CBB Analysis

By John Ezekowitz

Back in March, Maryland and Michigan State played one of the best final minutes of an NCAA Tournament game in recent memory. Down two points with a timeout left after a Greivis Vasquez layup, the Spartans pushed the ball up the floor, leading to this:

If you look closely, you can see Tom Izzo on the sidelines, about to signal for a timeout when he thinks better of it. This led the excellent John Gasaway of Basketball Prospectus to wonder “if teams actually do better in these situations [at the very end of games] without a timeout?”

Like the naive college student I am, I took on Gasaway’s challenge and decided to find out empirically. After many hours of work, I have compiled a database of every play from the 2009-2010 college basketball season in which a team had the chance to tie or win the game (ie down 3 points or less to tied), 1546 plays in all. In future posts, I will use this dataset to analyze the effectiveness of timeouts in various end-of-game situations, but would first like to present an appetizer on fouling when up three points.

To foul or not to foul? The debate about the efficacy of intentionally fouling has raged on in basketball circles for years. Recently, Luke Winn looked at the issue through the lens of the classic Kansas St-Xavier Sweet Sixteen game, and Henry Abbott at TrueHoop looked at the issue from an NBA point of view. Abbott cited hoops statistician Wayne Winston’s study of NBA games that found no significant advantage to fouling when up three points. My dataset presents, to my knowledge, the first comprehensive empirical study of the issue for college basketball.

In the 2009-2010 season, I found 443 instances where a team held the ball down three points during their last possession of a period (either the end of the 2nd half or an overtime period). In 391 of those cases, the team leading did not foul. In 52 cases, the team chose to foul. While the unequal sample sizes aren’t ideal, the 52 cases of fouling are significantly more than found in Winston’s NBA study (27).

Of the 52 teams that committed a foul, six lost the game for a winning percentage of 88.46%. Of the 391 teams that did not foul, 33 lost the game for a winning percentage of 91.56%. Both a two sample t-test of proportion and a Chi-squared test fail to reject the null hypothesis that there is a difference in winning percentage between the two strategies. In this sample, teams that did not foul won slightly more often. For the less statistically inclined, this means that there is no significant difference between the two strategies.

Another way to analyze the effectiveness of fouling is to look at how often the team that trailed scores at least three points (I say at least because of this epic case which I have highlighted previously). Because of the way my sample is constructed, the possessions in which a team trails by three points really are at the end of the game. A team that fails to score three points in my sample cannot win.

(Edit: In response to some issues raised by readers, I went back and re-ran the numbers. The conclusions did not change. The explanation follows below)

Here, too, the two strategies are almost identical. Interestingly, in eight cases, the leading team fouled the shooter in the act of shooting a 3-point shot (six of those times, the shooter made all three free throws) .Some of these cases, like the Kansas State, are players who are instructed to foul simply fouling too late. In others, the coach probably did not want an intentional foul while up three. I went back using game stories and video (where I could find it) for these eight cases and determined to the best of my ability that four of these cases were intentional, three were not, and one was unclear. To be conservative, I called the unclear case “not-intentional.”

Teams that intentionally foul allowed the opponent to score three seven times out of 48. Teams that did not allowed the opponent to score three points 93 out of 395 times.  While teams that did intentionally foul gave up three points a smaller proportion of the time than teams that did, the difference was not statistically significant (p values of .067 and .113 for a two sample t-test and a Chi-squared test). That means that in 2009-2010, teams that were down three points at the end of the game scored the necessary points at rates that did not differ based on which strategy the leading team pursued.

(Edit: I just wanted to make this clear: in only 3 of 52 cases did a team miss the 2nd free throw, successfully get the offensive rebound, and score. In this data set, the reason that the intentional foul strategy is not significantly different from not fouling are the cases in which the team fouls a player in the act of shooting a three.)

While these results are certainly interesting and convincing, clearly there is further study to be done. While my study does not have a “time remaining” component, it does largely deal with Winston’s criticism of early studies, which did not account for the uncertain number of further possessions in the game. This is because the possessions analyzed here are the last ones where the team has a chance to tie the game.

I would love any thoughts or comments you might have on this work. Please stay tuned for the bulk of the research on the efficacy of timeouts.

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  • Very interesting study, I think this kind of statistical analysis could open a lot of eyes.

    Did you happen to look at the variable of time remaining, or was it simply the last possession of the game, always assuming the trailing team milked the clock to get the last possible shot off?

    I’m curious to see what the data present in those situations when the foul came with less than ten seconds left vs. five, etc. Some are of the perception that fouling with less than five seconds would tilt the scales in the defense’s favor.

    • Brian,

      One of the problems that I ran into was that CBB does not have a unified and standard source of play-by-play data. This prevented me from a) using a computer program to make this much easier and b) using the time component in any meaningful way.

      I agree that a study using the time component would be very interesting. As I said in the post, these possessions are not necessarily the very last possession of the game, but the last possession where the trailing team could tie the game in one possession. It is safe to assume, however, that these possessions came very close to the end of the period (I would say that very few of these came with more than 20 seconds remaining).

      • This is a really interesting article, thanks for doing the legwork. As other people have suggested, I think looking at the time variable could shed more light on this story, though you would probably need more data for it to be meaningful.
        I would think that fouling becomes more effective as the time dwindles. If Team A fouls with 20 seconds left, and Team B hits both free throws, Team B still has time to foul Team A and get a good possession. The same cannot be said if this happens with 5 seconds left.

      • John,

        Where did you cull the play-by-play data from? The best available, if relatively disorganized, I’ve found is through NCAA.com. Is that where you’ve gone?


  • Is it a good idea to differentiate between whether a foul was intentional or not if you can’t look at all of the other games to analyze the converse? There are definitely instances, including Kansas-Memphis in ’08, where the team tried to foul at half court, but was unable to do so. I seem to remember Cal claiming that he told his team to foul, but Rose got beat by Collins on a crossover in the back court and chose not to foul from behind. Instances where this happens can leave a defense scrambling and perhaps increase the likelihood of an easier 3-point attempt.

  • The one thing I disagree with this study is that you used statistical data from both the end of the half and the end of the game. Of course a team isn’t going to foul at the end of a half up three. They’re trying to go into the half with a three point lead, not a one point lead.

    Also, in my opinion, the correct strategy is that you foul when the other team is bringing the ball up the court and you’re up by three points with less than 10 seconds remaining. You MUST get the foul around half court, as to not allow the player to get up a shot attempt and be allowed to shoot three free throws. If the opposing team is taking the ball out of bounds around half court, you dig in and try to get a stop.

    • This analysis doesn’t include final possessions of the first half: “In the 2009-2010 season, I found 443 instances where a team held the ball down three points during their last possession of a period (either the end of the 2nd half or an overtime period).”

    • Stile is right on in the second paragraph. It sounds like your data makes it look like the strategies give almost identical results but only because of the situation where fouls were in the act of shooting. The whole point of the strategy is to foul while the opposing team is bring the ball up so that time is wasted, they only get 2 shots on the line.

      • Alex,

        Yes that is the point of the strategy, but what if teams can’t execute that strategy correctly? Luke Winn quotes Frank Martin as saying his guys mess up the foul about 1/8th of the time in practice. Using my data, the number is slightly lower than that, but regardless: you have to take that possibility for the strategy failing into account when you analyze the two strategies.

        • So did you only consider the full-court case? You’re trying to compare two competing theories, but there is only one theory in the half-court case: play D.

          It’s a pity the data collection is so hard. It would be nice to see larger sample sizes by using more seasons.

          My forte is monte carlo so I would probably devise a MC scheme to compute the relevant expectations that would be parameterized by a couple of the relevant quantities.

  • Are you considering the possibility that the coach’s choice of whether or not to tell his team to foul is endogenous? Certainly, coaches aren’t randomly choosing between these two options as your statistical tests would imply.

  • Dick Vitale has been known to say that he never wants the other losing team to shoot at the end of the game with the clock stopped. And, did you figure in if the opposing team was a good or bad free throw shooting team, or even if the player was a good or bad free throw shooting player. And, were you playing at home or on the road. I don’t foul.

  • Well… nice work, but there are just to many varibles in the data that is not available to make these numbers accurate.. Bottom line I will say up by 3 with less then 10 seconds to go and if you smart foul you will win 90% +

  • I say you do not foul when up 3 because if you don’t foul you can’t lose the game w/o gaining possession of the ball.
    If you do foul,you can lose the game w/o ever regaining possession of the ball.(multiple ways)
    1.1st FT made,2nd miss,rebound,& 3pt Fg
    2.1st FT made,2nd miss,rebound,putback,+1 FT
    3.1st & 2nd FT miss,rebound,3pt.FG+1 FT
    4.Ref. calls the foul intentional,2 FT’s made + poss., and FG
    5.Ref. calls the foul intentional,1 of 2 FT’s made,+poss.,and 3pt FG

  • Hi-

    I wrote an article about the up 3 scenario a few years ago with the help of a math Professor here at DePauw University. I think there are too many things missing here for your findings to be accurate. If you’d like to read my findings send me an email and I’ll pass it along.

    Bill Fenlon
    Head Basketball Coach
    DePauw University

    • I would like to see your study. This is a spirited topic of discussion on message boards. Most recently, it came up at the end of Wednesday’s Marquette-USF game in which MU coach Buzz Williams had his players foul intentionally after MU missed a FT with a 3 point lead and 1.1 seconds left. Regardless of the strategy when a team has the ball in the front court, I thought this was a very poor decision because the chances of USF hitting a turnaround 90% heave were next to nothing, while their chances of scoring 3 points (after missing the second FT intentionally) would be slightly higher (albeit still very slim).



  • I believe there needs to be a culture change regarding this “strategy” as a whole. I would eliminate the entire concept of trading two points for three points. It’s complete horsesh*t and nobody seems to think anything of it. Any intentional fouling in the final minute of a game gets two shots and the ball. It just shouldn’t happen. It’s a bush league loophole that has crept its way into modern basketball “strategy”. If your team is good enough to have a 3 or 4 point lead with 30 seconds left, then guess what… you deserve to win. Intentional fouling of any kind, “fouls to give”, etc. Pure bull. It needs to go.

  • Great article. Could you elaborate on how you identified which games in the 2009-2010 season involved the dilemma of whether to foul or not when down by 3?

  • Very nice article, I think up 3, you’ve gotta take the SMART foul. I mean, with like 6 seconds and the other team bringing the ball up the court for example, don’t foul until midcourt, or with an out of bounds play, foul the guy who hands the ball of, things like that. But still it can crush you if you foul or not, either way. At least you’ve gotta hit your own free throws, lol. Personally I’d say don’t foul because there’s always the chance to get 3 FT’s, just contest the shot, don’t let them get a clean look. Only exception; when you’ve got Kobe or LeBron coming at you, foul them immediately, lol.

  • If you foul, it seems like there is some chance that you will lose (small probability). But if you don’t foul, the worst that can happen is go to OT. I wonder how many times the teams that fouled lost in the regulation. Also, i’d look at the cases when the teams went to OT, and compare the winning %’s between the two conditions. You have to make sure the there is no difference there.

    So to me, if you assume that the chance of winning in OT is equivalent, it doesn’t make sense to foul because it leaves the chance of losing the game. I think this is more of a decision analysis.

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