**TLDR: The outcome of (most) sports is determined not by the**

*actual*

**value of an individual's or team's performance, but by the**

*relative*

**performance.**

**Despite the fact that winners and losers are determined by the point differential, every sport summarises the score as the cumulative total points for each opponent. Athletes, coaches, fans, and pundits alike are then forced to calculate the point differential themselves in order to determine how close the game really is.**

**In the NBA, each team may call a time-out in attempt to alter the momentum of the game, particularly when the momentum is not in their favour or when their team is not in the lead.**

**In the small window of time available to call for a time-out, if a team miscalculated how many points their team was trailing by, would they be more likely to call a time-out?**

**I find that teams are more likely to call a time out when they are down by a score spanning two tens places over a score spanning one tens place, even when the point differential is the**

__exact__same!**For example, if a team is down**

__8__1-__6__9, they are 10% more likely to call a time out than if they were down__8__3-__7__1!The outcome of (most) sports is determined not by the

**value of an individual's or team's performance, but by the**

*actual**performance. It matters not how many points (or goals, etc.) you have, but how many points you have in comparison to your opponent.*

**relative**Despite the fact that winners and losers are determined by the point differential, every non-racing sport summarises the score as the cumulative total points for each opponent (please comment below if you have a counter-example). Athletes, coaches, fans, and pundits alike are then forced to calculate the point differential themselves in order to determine how close the game really is. Due to cognitive biases in the way we perceive numbers, we may then expect to see some interesting patterns in data pertaining to these cumulative vs relative scores.

The National Basketball Association (NBA) is a league where the average combined score of a single game is over 200 points and the average margin of victory is just 10 points. Each game can see multiple lead changes and notable swings in momentum between the two teams. During the course of the game, each team may call a time-out in attempt to alter the momentum of the game, particularly when the momentum is not in their favour or when their team is not in the lead.

But do certain game conditions entice teams to systematically choose when to call a time-out? Does trailing your opponent by certain values induce more time-outs than others? And what sort of mental arithmetic biases might we see when dealing with basketball scores?

To answer all of the above, I first began by collecting all of the play-by-play data for the 2016/2017 NBA regular season, conveniently provided by Reddit. I organise the data to the point where each observation is a single possession (generally, a possession begins every time the shot-clock is reset to 24 seconds). I collected data on the team, the opponent, the amount of time remaining in regulation, the quarter, and the current score. It is from the latter that I calculate the point differential.

Using a computer to calculate point differential, I am all but guaranteed to get the correct answer. However, using mental math, I am likely to make some mistakes. In fact, I first noticed that when the two scores span a difference of two tens places, e.g.

__8__1-

__6__9, I was more likely to overestimate the difference: I erred by incorrectly thinking the losing team was further behind than 12 points. Yet, I often was able to accurately calculate the point differential if the scores span only one tens place, e.g.

__8__3-

__7__1. In the small window of time available to call for a time-out, if one miscalculated how many points their team was trailing by, would they be more likely to call a time-out?

To test if others shared in my blunders, I ran a logit model to predict how many times a time-out is called based on the actual point differential and the tens-place point differential. Here I considered only the instances where the team calling the time out was a) trailing their opponent in score, and; b) the actual point differential was between 11 and 19 points. The latter limits the data to possessions where the team making the time-out decision is down by only scores spanning one or two tens places. I also control for the time remaining in the quarter and game, the team making the time-out call, and the score change since the last time-out/end of last quarter (also known as the 'run').

I find that teams are more likely to call a time out when they are down by a score spanning two tens places over a score spanning one tens place, even when the point differential is the

__exact__same! Below is the graphical depiction this increase in probability of calling a time-out from the score spanning two tens places:

__8__1-

__6__9, they are 10% more likely (taking the overall number) to call a time out than if they were down

__8__3-

__7__1!

I have shown there exists some evidence that certain scores induce more time-outs than others, namely when the point differential spans two tens places. I suggest that may be due to our tendency to systematically miscalculate the difference between two numbers which overstates the difference in certain circumstances. We may also see a similar effect when people are trying to calculate the time between two events, such as a layover at an airport: 7:35 to 10:10 is the same span of time as 5:00 to 7:35 despite that the former may look like a larger interval.

In the end, the same point differential and just a subtle change in the actual the scores can make

*all the difference in the world*in how we perceive the margin of victory.

Nice findings!

ReplyDeleteThis comment has been removed by a blog administrator.

ReplyDeleteThis comment has been removed by a blog administrator.

ReplyDeleteThis comment has been removed by a blog administrator.

ReplyDeleteThis comment has been removed by a blog administrator.

ReplyDeleteThis comment has been removed by a blog administrator.

ReplyDelete