To determine who is better between Lionel Messi and Cristiano Ronaldo using z-scores, we need to compare their performance statistics. Here are some key stats for both players12:
| Statistic | Lionel Messi | Cristiano Ronaldo |
|---|---|---|
| Goals | 841 | 903 |
| Assists | 375 | 254 |
| Appearances | 1,073 | 1,240 |
| Minutes Played | 88,128 | 101,157 |
| Goals Per Game | 0.78 | 0.73 |
| Minutes Per Goal | 104.8 | 112.0 |
| Successful Dribbles | 3,819 | 1,871 |
| Key Passes | 1,861 | 1,191 |
| Big Chances Created | 514 | 222 |
| Man of the Match Awards | 406 | 214 |
| Average Match Rating | 8.42 | 7.78 |
To calculate the z-score for each player, we need to standardize these statistics. The z-score formula is:
z = \frac{(X – \mu)}{\sigma}z=σ(X−μ)
Where:
- ( X ) is the value of the statistic for the player.
- ( \mu ) is the mean value of the statistic for both players.
- ( \sigma ) is the standard deviation of the statistic for both players.
Let’s take an example with “Goals Per Game”:
- Calculate the mean (( \mu )):\mu = \frac{0.78 + 0.73}{2} = 0.755μ=20.78+0.73=0.755
- Calculate the standard deviation (( \sigma )):\sigma = \sqrt{\frac{(0.78 – 0.755)^2 + (0.73 – 0.755)^2}{2}} = 0.0354σ=2(0.78−0.755)2+(0.73−0.755)2=0.0354
- Calculate the z-scores:
- For Messi:z_{Messi} = \frac{(0.78 – 0.755)}{0.0354} = 0.707zMessi=0.0354(0.78−0.755)=0.707
- For Ronaldo:z_{Ronaldo} = \frac{(0.73 – 0.755)}{0.0354} = -0.707zRonaldo=0.0354(0.73−0.755)=−0.707
In this example, Messi has a higher z-score, indicating he performs better in “Goals Per Game” compared to Ronaldo. You can apply the same method to other statistics to get a comprehensive comparison.
Would you like to see the z-scores for more statistics or need help with anything else?
by Annual_Expression790
5 Comments
this is not a statistical comparison. even though Messi does trump Ronaldo on nearly every stat there is, it is just clear to anyone with eyes and a fully-developed brain that Messi is by far the greatest to ever do it
Messi is better. But Ronaldo not too far behind.
When a goal is scored also matters.
Theres less impact scoring 2 in the league during the start or end of a season compared to 1 in a quarter or semi final of a CL game.
1 semi final goal in a CL would also matter more than a 1 semi final goal in the Copa Del Rey.
Point is, context matters to paint a picture. Stats itself is not enough.
“It’s not the statistics, it’s not the statistics, you don’t measure that by statistics, it’s immeasurable. When you see this run again Phil Shane with your statistics, you tell me how do you measure somebody that could balance a balloon in a wind tunnel on a needle because Messi is capable of that. Astonishing.” – Ray hudson
so brave of you to cover a topic that no one else ever has before