Examining momentum in 5-set tennis matches

Since 2001, no player has won more often from two sets down in Grand Slam matches than Roger Federer

For the first time, 5 Added Minutes takes on a non-football analysis.

The concept in question, however, is universal to sport: momentum. It’s a term often used by pundits to rationalise sequences of events – but to what extent does it actually exist?

Five-set tennis matches provide a test case to look at momentum. Often lasting longer than three and a half hours and with hundreds of individual points contested, there’s plenty of scope for the match to swing both ways.

Since the start of the 2001 season, 1128 of 6096 Grand Slam matches (18.5%) have gone to five sets. This ratio is fairly consistent across all rounds.

The order of set wins in 5-set matches is less consistent. In fact, the data suggests momentum very much exists in matches that go the distance.

Five-set matches where no player wins back-to-back sets – an order of ABABA – are significantly less likely than any other combination of set wins.

Equally, five-set matches where both players win their sets in uninterrupted ‘chunks’ – an order of BBAAA – are significantly more likely than any other combination of set wins. Over 1-in-5 five-set victories are wins from two sets down.

This immediately points to evidence of momentum. Matches where players constantly exchange blows are relatively rare; we’re much more likely to see players take control of matches for more sustained periods.

This is further highlighted when we isolate two combinations from the chart above; matches where one player led 2-0 in sets (AABBA and BBAAA).

At 2 sets all, the player who won the third and fourth set is significantly more likely to win the final set than the player who won the first two sets.

In other words, in matches where one player won the opening two sets, the outcome of the final set is not equivalent to the flip of a coin. It’s equivalent to the flip of a coin heavily weighted in favour of the man who won the third and fourth set.

This is true even after controlling for the rank of players involved; there is a negligible difference in ability between players who go two sets up and two sets down. Therefore the rate of victories from 2-0 down is not attributable to the fact that better players tend to lose the first two sets in five-set contests.

But is this momentum?

Is this a case of the player who was two sets up feeling deflated having handed over control of the match to his opponent?

It’s a difficult question to answer. The effect is likely to be as much caused by fatigue as psychology. Players at two sets up are likely to have exerted themselves at a rate unsustainable over a five sets. This is somewhat supported by the fact that the five players with five or more wins from two sets down since 2001 – Federer, Davydenko, Murray, Hewitt and Wawrinka – generally have reputations as supremely fit and dogged performers.

To what extent do these findings apply to sports outside of tennis?

The hot hand phenomenon in basketball and other often-cited examples of momentum were largely discredited in Scorecasting. An application to football is tenuous, too. Individual goals and results in football are much more likely to be influenced by random, uncontrollable events whereas the weight of points in tennis means that the better, less tired and psychologically in control player is more likely to turn these factors into victories.

So, a player with the ‘momentum’ going into the final set is more likely to win – but whether this momentum is explained by physical or psychological factors is still up for debate.

All data from tennis-data.co.uk.