Probability in Sports

In sport, some events, occurrences, and outcomes are more probable than others, and the potential exists  to  use  information  about  probabilities  to aid  performance.  This  entry  discusses  two  levels on  which  probabilities  are  relevant  to  sport  performance.  The  first  is  the  individual,  immediate performance level. On this level, probabilities are used  implicitly  during  performance;  performers may not even be aware that they are using probabilities,  having  built  up  this  feature  of  anticipation  and  decision  making  (DM)  over  time  as they acquired skill. The second level is a broader, game-analysis and planning level, on which information on probabilities is actively sought to drive strategic  decisions.  This  second  level  seeks  to explicitly  exploit  probabilities  for  planning  and competitive  advantage.  It  uses  a  more  comprehensive  approach,  often  accessing  large  pools  of data to identify meaningful patterns that exist on the  individual,  implicit  level.  Thus  a  strong  link exists  between  the  two  levels  of  probabilities, with one influencing the other, as researchers use probability information to drive interventions and strategy. The sections that follow discuss the individual  and  the  tactical  planning  levels  of  probabilities  by  presenting  examples  that  illustrate how  probabilities  are  used  in  sport  and  exercise psychology (SEP) research.

Individual Level

Though there is relatively little direct exploration of the explicit use of probabilities in DM for individual  action  choices,  it  is  well  known  that  performers  make  informal  “calculations”  and  use probabilities  based  on  the  situation.  In  competition, athletes implicitly assign weightings, or probabilities,  to  the  likelihood  of  an  event  occurring and use this information to guide their decisions. These  implicit,  subjective  probabilities  influence the ability to respond. For instance, a tennis player’s  position  on  the  court  can  influence  the  type of  shot  he  or  she  is  able  to  play.  Knowing  this, a  defender  can  assign  probabilities  to  each  possible shot to anticipate the opponent’s actions. If a defender thinks the probability of a particular shot is high, the defender will show better anticipation of this shot. A shot the defender thinks is less probable will not be as well anticipated if the opponent makes this choice. The attacking player can exploit this information by playing a low-probability shot when another outcome is highly probable and thus catch the defender ill-prepared or off guard.

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The  effective  use  of  probabilities  can  also increase  performance  based  on  availability  of specific  situational  information.  This  has  been explored  by  manipulating  the  situational  information  accompanying  video  clips  when  performers  are  asked  to  decide  on  their  next  action.  For example,  a  baseball  pitcher  is  more  likely  to  try to throw a strike pitch rather than a pitch outside the strike zone when the pitch count contains three balls than when it contains none. This situational information allows a batter to make an informed decision  regarding  the  pitch  location  and,  by reducing  uncertainty,  make  a  quicker  decision about whether or not to swing.

The   use   of   probabilities   also   distinguishes between  more  and  less  skilled  performers.  The use  of  verbal  reports,  in  which  athletes  report their  thoughts  during  play,  have  shown  that  elite athletes,  compared  with  less  skilled  athletes,  are able  to  create  more  detailed  and  sophisticated event  profiles  using  past  and  current  information to  “diagnose”  what  is  currently  taking  place,  as well  as  predict  and  anticipate  future  play.  This probabilistic information can be used to effectively manage  energy  expenditure  during  the  course  of an  event.  In  squash,  for  instance,  the  probability of winning a game is based on the probability of winning  a  rally  and  the  relative  importance  of each rally. Athletes naturally use this information to regulate energy expended on a particular point and energy trade-offs in the context of competition as a whole and its likely outcome.

Relying  on  probabilities  is  not  always  beneficial,  however;  athletes  who  believe  in  the  “hot hand” in basketball, for instance, think there is a greater  probability  of  a  player  making  a  successful shot after they have made one or two previous shots. Teammates are thus more likely to allocate or pass the ball to a “hot” player even though the evidence to support the hot-hand belief is equivocal.  Sports  officials  are  also  prone  to  using  situational probabilities when making decisions; they are more likely to penalize teams in an alternating fashion rather than penalizing the same team twice in a row. Cognitive biases and decision errors such as these provide a place for the use of probabilities in sport on a more tactical level.

Tactical Planning Level

Coaches and athletes often use intuitive methods to derive tactics. Work in the area of calculation, statistics, and machine learning methods are used to support these intuitive processes and avoid errors. Using archived or accumulated performance data, data analytical methods focus on maximizing performance  by  more  fully  exploiting  information for  tactical  planning  and  are  especially  useful  in sports, such as rowing and cycling, where pacing is  critical.  For  example,  historical  performance data can be used to both create race profiles that typify competitors from one team or country and to  determine  optimal  race  patterns  in  sports  like rowing,  which  have  different  race  portions  (e.g., 500-m splits of a 2,000-m race). This information is  used  to  improve  planning  and  the  chances  of achieving success.

The  tactical,  planning  level  of  probabilities  is also  useful  in  multievent  sports,  where  the  final standings  are  determined  after  more  than  one event  (e.g.,  triathlon,  decathlon).  In  some  multievent  sports,  such  as  the  cycling  omnium,  pacing is  considered  between  events  over  more  than  1 day. The omnium is comprised of six track cycling events that take place over 2 days. The introduction of a new event (the elimination race) to create a six-event omnium, before the 2012 Olympics, is a  case  where  the  tactical,  planning  level  of  probabilities is useful to investigate the best strategy to secure  a  medal.  Machine  learning  analyses  have been used to identify the minimum result required in each event that will lead to the highest probability  of  success,  as  well  as  whether  the  addition  of the new elimination race event benefits endurance riders or sprinters. Not only does this use of probabilities help planning before and during the event (i.e., between events, between days) but it can also be useful information for athlete selection.

In  general,  SEP  seeks  to  increase  overall  probabilities of successful performance. Individual DM “in the moment” and structured methodical planning  based  on  the  likelihoods  of  different  events are influential in reaching this goal.


  1. Paull, G., & Glencross, D. (1997). Expert perception and decision making in baseball. International Journal of Sport Psychology, 28, 35–56.
  2. Alain, C., & Proteau, L. (1980). Decision making in sport. In C. H. Nadeau, W. R. Halliwell, K. M. Newell, & G. C. Roberts (Eds.), Psychology of motor behavior and sport—1979 (pp. 465–477). Champaign, IL: Human Kinetics.
  3. Ofoghi, B., Zeleznikow, J., & MacMahon, C. (2011). Probabilistic modelling to give advice about rowing split measures to support strategy and pacing in race planning. International Journal of Performance Analysis in Sport, 11(2), 239–253.
  4. Ofoghi, B., Zeleznikow, J., MacMahon, C., & Dwyer, D. (2011). Has the addition of the elimination race to the track cycling omnium benefitted sprinters or endurance riders? Proceedings of the International Symposium on Computer Science in Sport 2011, Shanghai, China, pp. 34–37.

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