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@IngaVovchanchyn
A few days ago, I created this thread to analyze a fighter's win probability as a function of his age advantage over his opponent.
In general, I created this probability function:
Viewers observed that the inclusion of other input variables besides age would make the model more accurate.
Specifically, @MMAart asked for me to construct a model based on reach advantage too.
Ever wish you could determine probability based on multiple variables with one model?
1. The Multi-Variable Probability Function
Now generalized to allow for the input of several variables:
Again note the absolute value operator for A indicating that this model only calculates the probability of the more likely outcome.
2. Is Reach an Advantage?
Analyzing the data, I made a startling discovery.
Having a reach advantage over your opponent is statistically irrelevant.
This is because having a reach advantage, in and of itself, indicates only that you're taller and therefore skinnier (height indicates skinniness due to weight restrictions) than your opponent. Being taller and skinnier is not an advantage.
However, having disproportionately long arms for your height is an advantage.
So the real advantage is reach/height.
This explains why fighters like Anderson Silva, Jon Jones, Conor McGregor, and Michael Venom Page are so dominant, where fighters like Stefan Struve, Alexander Gustafsson, and Charles Oliveira are eminently hittable.
Reach/height then became my second input variable.
Note that reach and height by themselves are statistically irrelevant (their sensitivity constants were both estimated to be zero!).
3. Calibrating the Parameters
After analyzing historical bout data and mathing around, I calculated these parameters.
See my original thread for details concerning the definition of the age advantage and the derivation of sensitivity constants, represented by k.
4. Win Probability Based on Age Advantage and Reach/Height
Here's the probability function applied to fighter win probability for the two input variables.
Note that Big K, the sensitivity constant of the net advantage, was estimated to be about .8937.
5. Daniel Cormier vs. Jon Jones (example)
Daniel's weighted age advantage is
Note that the prime fighting age is 27.99 years old.
Daniel's weighted reach/height advantage is
Daniel's weighted net advantage is
Since this is negative, we now switch to the favorite's perspective.
Jon's chance of victory is
Conclusion and Key Take-Aways
1. Neither reach nor height are advantages in fighting. However, having disproportionately long arms for your height (reach/height) is an advantage!
2. The average win probability of a fighter with a reach/height advantage was only 53%, indicating that it is still a weak determinant of bout outcomes
However, the average win probability of a fighter with an age advantage was 70%! So age is a very strong determinant of bout outcomes.
3. After expanding my sample size, I determined that the prime fighting age is actually 27.9921875 years old.
Hat tip to @fermaPY .
4. This model can be improved by expanding the sample size and inputting more variables. So far I've only entered two, age and reach/height.
A few days ago, I created this thread to analyze a fighter's win probability as a function of his age advantage over his opponent.
In general, I created this probability function:
Viewers observed that the inclusion of other input variables besides age would make the model more accurate.
Specifically, @MMAart asked for me to construct a model based on reach advantage too.
Ever wish you could determine probability based on multiple variables with one model?
1. The Multi-Variable Probability Function
Now generalized to allow for the input of several variables:
Again note the absolute value operator for A indicating that this model only calculates the probability of the more likely outcome.
2. Is Reach an Advantage?
Analyzing the data, I made a startling discovery.
Having a reach advantage over your opponent is statistically irrelevant.
This is because having a reach advantage, in and of itself, indicates only that you're taller and therefore skinnier (height indicates skinniness due to weight restrictions) than your opponent. Being taller and skinnier is not an advantage.
However, having disproportionately long arms for your height is an advantage.
So the real advantage is reach/height.
This explains why fighters like Anderson Silva, Jon Jones, Conor McGregor, and Michael Venom Page are so dominant, where fighters like Stefan Struve, Alexander Gustafsson, and Charles Oliveira are eminently hittable.
Reach/height then became my second input variable.
Note that reach and height by themselves are statistically irrelevant (their sensitivity constants were both estimated to be zero!).
3. Calibrating the Parameters
After analyzing historical bout data and mathing around, I calculated these parameters.
See my original thread for details concerning the definition of the age advantage and the derivation of sensitivity constants, represented by k.
4. Win Probability Based on Age Advantage and Reach/Height
Here's the probability function applied to fighter win probability for the two input variables.
Note that Big K, the sensitivity constant of the net advantage, was estimated to be about .8937.
5. Daniel Cormier vs. Jon Jones (example)
Daniel's weighted age advantage is
Note that the prime fighting age is 27.99 years old.
Daniel's weighted reach/height advantage is
Daniel's weighted net advantage is
Since this is negative, we now switch to the favorite's perspective.
Jon's chance of victory is
Conclusion and Key Take-Aways
1. Neither reach nor height are advantages in fighting. However, having disproportionately long arms for your height (reach/height) is an advantage!
2. The average win probability of a fighter with a reach/height advantage was only 53%, indicating that it is still a weak determinant of bout outcomes
However, the average win probability of a fighter with an age advantage was 70%! So age is a very strong determinant of bout outcomes.
3. After expanding my sample size, I determined that the prime fighting age is actually 27.9921875 years old.
Hat tip to @fermaPY .
4. This model can be improved by expanding the sample size and inputting more variables. So far I've only entered two, age and reach/height.
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