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The Coin Toss

By : Ethan Allavarpu and Kyle Boal

Reading: The Coin Toss

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A coin toss is just a flip of the coin, but in late years-especially during the NFL playoffs-it has apparently gained heightened importance. A prime exercise of this is the coin discard of the Super Bowl : in the early years, entirely the blue-ribbon few captains and a individual referee met at midfield in a very quick exchange. today, however, things are drastically different, as a little greenwich village of television camera crews and crucial individuals accompany the captains to film the leave of the coin flip. furthermore, mantras about which choice to choose ( “ tails never fails ” ) have emerged, the mint is specially engraved for the occasion, and Las Vegas sportsbooks create a airplane propeller stake on whether the solution of the coin toss will be heads or tails, indicating the grandiosity of what should be an insignificant event.

These decisions, in turn, have led to an increase in the talk about “ coin convulse scheme, ” if such a thing even exists. We wanted to see if there is any robustness to this spill, or if people were fair blowing fume. The mint chuck does n’t seem like the type of consequence to make or break a game, so we were wondering why people pay then much care to its result and their team ‘s decision. For the purpose of this article, we have limited the games we will be investigating to the playoff games between the 2002 and 2019 NFL seasons to impose slightly of an peer play field ( i.e. there are no 0-15 teams facing a 13-2 team ). part of the rationality we chose to compare the 2002-2006 earned run average to 2015-2019 was because coin flip data was not easy to find before this era. In summation, deferring seems to have become the prevailing choice in recent years, but was this the case 18 years ago ?

NFL Playoff Coin Tosses

As shown by the graph above, when comparing the results of the mint chuck decision ( defer vs. welcome ) between two different eras ( 2002-2006 and 2015-2019 ) for the NFL Playoffs, the percentage of decisions resulting in a deferral drastically increased, from around 5 % to around 85 %. In fact, when performing a test for difference of proportions with a null hypothesis of no difference and an alternate that there is a difference ( either positive or negative ), we obtained a p-value of, indicating that we would reject the null hypothesis. It appears that the percentage of mint tosses that resulted in a deferral decision has statistically importantly increased from the era of 2002 – 2006 to 2015 – 2019, as we expected.

Going back to 2002 playoff games, we calculated the overall deferral share in the playoffs for that year and compared it to the win rate of the teams that deferred to understand if there was a correlation between deferring the coin flip and winning the game. On the x-axis we plotted the year up to the 2019 season and on the y-axis the win rate as a symmetry . In terms of postponement share, the data plotted clearly suggest an up tendency in holocene years. In fact, to our storm whereas up until 2006 no team deferred more than three times, in recent years no team has received more than three times. possibly deceptively, the gain share for those years is either at 1.0 or 0.0 as there was not a large sample size of defers to choose from, therefore polarizing the figures. interestingly, as the deferral share among team rises, the winnings share caps at roughly 0.5. In the early years of the postponement revolution ( 2010-2012 ), winning percentages see a significant increase — possibly suggesting that deferring contributed to a team ‘s overall success in the game. however, as the drift takes off from 2015 forth, closely every team defers if they win the discard. consequently, the gain share tumbles, before leveling off around 0.5. This is because teams today nobelium long have an advantage when every single team is doing the lapp thing.

To confirm this impression we took to plotting the opposite swerve : going back to 2002 playoff games, we calculated the overall receive percentage in the playoffs for that class and compared it to the gain rate of the teams that received. While the receive share is just the inverse of the postponement share plot ( blue ), the receive gain share draws on a whole modern sample size.

Assuming the previous hypothesis is correct, it is expected that from 2002-2006 while the experience share is at a league high, the win share should be stagnant around 0.5. however, from 2010-2012, the share should be lower, as team transition into a fresh meta of deferring before last jumping between the two extremes of 0.0 and 1.0 with a little sample size of teams receiving from 2015 forth.

Supporting the hypothesis, the 2002-2006 sector corroborates the idea that when all teams are doing the like thing, in this case receive, the winnings percentage is roughly even. The year 2010 illuminates apparently a major turn charge for the league. Recall that in 2010 60 % of teams deferred and of those teams they won 40 % of their games. however, of the teams that received ( the remaining 40 % ), they won 0 % of the games for the alone fourth dimension in the 18 year window. additionally, skipping to 2015 when all the teams begin to defer, this leaves a small group going against the grain by receiving. Just as in the submit group from 2002-2006, this group of those who receive from 2015 forth have an average 0.8 succeed rate.

By this bespeak we ‘ve proven that from the years 2002-2006, NFL teams were probable to receive should they win the convulse. furthermore, from 2015 ahead, the reverse is dependable : NFL teams are more probably to defer than to receive. We decided to plot the postponement rate as a symmetry on the timeline by round. We expected that as the games got “ bigger, ” the teams would become more likely to either receive or postpone — subject on what was in style at the time. In early words, from 2015 ahead, it ‘s assumed that the deferral rate should increase from the barbarian menu to the ace bowl — not only because the games are more important but besides due to the sample size. On the x-axis we plotted the year and on the y-axis the postponement proportion . As expected, in those two major prison term periods, the course is true : for all ten of those years in the league championship and superintendent bowl, teams picked the popular drift at the prison term ( meaning 30/30 times the team picked the popular choice ). additionally, for the last decade the team that has won the flip at the super bowling ball has chosen to defer.

ultimately, we wanted to see why teams switched from receiving the football to deferring to the second one-half upon winning the coin convulse. Was it because that strategy was “ better ” ? Bill Belichick is renowned for deferring to the moment half, as it provides his team with the opportunity to “ double up ” just ahead and just after half prison term : if his team can score at the end of the foremost half, then, by receiving the ball to start the second half, they have the prospect to score again ; this provides the team with the chance at a large momentum swing of up to two possessions ( i.e. sixteen points ). By considering this scheme, it would appear that deferring is the better decisiveness and that the teams which defer would be expected to have a higher acquire percentage than the teams which receive after winning the mint toss . The above bar graph displays the winnings percentages for teams that won the mint toss separated by their decisions to ( 1 ) postpone and ( 2 ) pick up for all years in the data sic ( 2002 – 2019 ). As portray, there was no significant remainder in win percentage between teams that deferred versus teams that received on the whole, indicating that the sole decision of deferring versus pick up does not help a team in the playoffs. however, as some of the graphics displayed earlier in the article bring, this percentage could vary depending on the year and whether deferring was considered “ popular ”. When further looking at the datum, it is interesting to note that the gain percentages hover around 0.45 for teams that won the coin toss regardless of decision, leading us to wonder whether teams that won the mint pass in the playoffs had a statistically lower win share than teams that lost the coin flip . When comparing the gain percentages for teams that won the coin toss against teams that lost it, we performed a guess screen for difference of proportions to see whether the respect dispute was statistically significant. Since the p-value for this bilateral test was 0.0562, at the meaning level, we fail to reject the nothing hypothesis that the percentages are different. What this means is that the likelihood of observing this deviation of winnings share in a sample given that there truly is no deviation in the population is 5.62 % ; since our shortcut for that premise being improper is 5 %, we say that we can not reject the affirmation that the win share is different for these two categories. however, this p-value is still reasonably moo ( about significant ), so we may want to investigate this issue far. While winning or losing the coin pass will not directly determine whether or not a team wins the plot, there could be confounding variables implicit in to the data and to playoff games that could impact the relationship between the coin toss result and succeed percentage. One such model would be overthinking, as the team which won the mint toss would overcomplicate the decisiveness and ultimately make a poor one. Another potential confuse variable star would be the queer of herd mentality : as more and more teams are opting to defer, they may be opting to defer for the lone cause that other teams are making the lapp choice.


Teams have increasingly analyzed the mint toss and its impression on the game, in change by reversal flipping the script from about every team receiving the ball to about every team choosing to get the ball in the second half. This change has become thus prevailing that many football fans are outraged when their team does n’t defer after winning the coin flip. however, blindly choosing to defer has its own pitfalls : teams are not thinking about their decision at all but merely going with the flow, which could have veto consequences if they are not train. Just like football, making a decision from the coin toss is moral force and adaptive : each adversary is different, each team is unlike, and each game is different. Making the decision fair because everyone else does it has perils of its own, and when looking at the datum, the teams that by and large saw an increase in their success were the ones that began this postponement drift and deferred when all anyone considered was receiving the ball and having the inaugural possession. possibly with an increasing number of teams choosing to defer, the properly decision is to go against the grain and choose to receive.

But then again, it ‘s all just the flip of a coin.

Sources : ESPN, Pro Football Reference

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Category : Economy

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