This question has been addressed in the paper by Lionel Page and Katie Page (2007) 'The second leg home advantage: Evidence from European football cup competitions', Journal of Sports Sciences, 25: 14, 1547 — 1556.
The researchers statistically analyzed 12,364 individual matches from the following competitions:
- UEFA Champions League (1955 - 2006)
- UEFA Cup (previously InterCities Fairs Cup, now Europa League, 1955 - 2006)
- Cup Winners Cup (1955 - 1971)
In order to reduce the effects of the UEFA seeding system allocating the "better" teams as the second leg home team, the UEFA club coefficients were taken into account in calculations of the probability of the second leg home team winning the tie. The results were as follows:
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| Tie-breaker | Prob. of SLHT* winning the tie | Number of ties |
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| None | 53.77% | 5750 |
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| Extra time | 66.42% | 186 |
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| Penalties | 57.33% | 148 |
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| Overall | 54.33% | 6084 |
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*SLHT - Second leg home team
The probabilities above show us that SLHTs have slightly better chances for winning the tie, but the following chart illustrates how these probabilities (considering only the ties without tie-breakers) decreased over time since the beginning of the aforementioned competitions.
Source
What this paper shows us is that there is a very small second leg home advantage in the ties decided without tie-breakers and a significant advantage in the ties where tie-breakers were used.
There was also another research by Manuel J.A. Eugster, Jan Gertheiss & Sebastian Kaiser (2010) LMU Munich 'Having the Second Leg At Home – Advantage in the UEFA Champions League Knockout Phase?', where they analyzed only 304 individual matches from the UEFA Champions League (1994 - 2010) also using UEFA club coefficients for removing seeding system disturbance and they concluded that:
There is no statistical evidence for the
common belief that the chance of winning is higher if a team is
playing away in the first leg and having the second leg at home.
Moreover, they have proposed:
to change UEFA regulations in the sense that in the round of 16 group
winners do not automatically play at home in the second leg, but may
choose depending on their individual preferences.
But, why people do believe in this phenomenon despite poor statistical evidences?
Well, perhaps, because when the tied teams are equal they choose "defend away, win at home" strategy, and mainly because of the away goals rule. Probably, the general reasoning, as Patrick Kluivert stated, is that:
Sometimes people make mistakes and it is better to make your mistakes
in the first leg away from home because there is still time to put
things right in the second match.