Anthony Wilson passed this on to me as a possible feature on our site, and after reading it, I think this is one of the best and most unique pieces we've ever posted on Bad Left Hook. I can't think Mr. Solis enough for his research, and Anthony for sending it our way. It's unique and looks at something much-discussed in a different light that I found very interesting. Give this a serious read if you're interested in the science of the sweet science, because it is tremendous. -- Scott Christ, Managing Editor, Bad Left Hook

Back when I was writing at The Rumble, there emerged in the comments section this diehard boxing fan with a unique background. As it turned out, the dude, Leandro Solis (Rumble username leo_sol) was a scientist. Yes, an actual scientist - one who happened to possess a deep affiniy for the sweet science. And occasionally, he would apply the knowledge of his field to discussions about boxing, providing a unique angle and enlightening us with some pertinent and fascinating information we otherwise wouldn't have been exposed to.

He's basically done the same here, only over the course of 2,000+ words. I won't say too much about it, except that it's plenty interesting and insightful. In particular, I think his findings about Manny Pacquiao will reverberate.

Leo's words begin with the next paragraph. -- Anthony Wilson

* * * * *

The first goal of this little study was to look at some physical characteristics of fighters - specifically height, weight, and wrist size - and check if these three characteristics could indicate how likely it would be for a fighter to have a good chin and stamina. My interest in this is that in most pre-fight writings, fighters are usually given some type of score or grade on these two attributes in addition to others like punching power, experience, etc. In all cases these ratings are given based on the writer's perception of such attributes in previous fights, so I wanted to check if there was a more objective way to assign some of these ratings. Now why did I decide to focus on the combined attribute of chin + stamina, and why am I using height, weight, and wrist as my predictors? Well, the answer lies in the available data (which as it is, unfortunately, is limited), and more importantly, in some aspects of human physiology which I will describe shortly.

The second goal is related to my first goal in the sense that it looks at the same physical characteristics, however, here I was interested in figuring out how big or small Manny Pacquiao really is compared to other fighters, and whether or not there is anything in particular about his physical characteristics that would allow him to move up in weight in such an explosive manner. The reason for this second goal is that in boxing it is pretty much mandatory before every fight to read about which fighter has the size advantage prior to each fight. People usually look at things like which fighter is taller, who has a longer reach, who is the "naturally bigger man," which, at least from what I have seen, to most people means who has fought at a heavier weight for longer and simply looks bigger at the photo-ops. These types of comparisons are particularly prevalent before every Manny Pacquiao fight, who for the past three years has made a habit of not just beating but completely destroying opponents that appear to be too big for a man of his size. In addition to the comparisons already mentioned, to a lesser degree, other measurements like size of biceps, chest, thighs, or neck, among others, are also used to highlight the physical differences between two fighters. The wrist size is at times found on this extended list, but even when it does, most of the time it goes without much fanfare, at least to my impression.

Having stated the goals I had in mind when I started looking into these measurements, I think it is now time to explain why my interest in wrist size. In bone literature it has been shown that in males the wrist size is positively correlated with skeletal frame, as well as bone density and mineral content, which in short means, bigger wrists equals bigger bones. For fighters fighting at a given weight class what this means is that if both fighters weigh say 160lbs, the percentage of that weight that is made up of bone in proportion to soft tissue (skin, muscle, fat, blood, organs, etc) will be more for the guy with bigger bones.

So what does having bigger bones mean to a fighter and how does this relate to my goals? Well, I can think of three basic advantages: 1) Bigger bones in theory should give a fighter a better chance to take a punch, in the same manner a house with strong foundations is harder to bring down than one with weaker ones. 2) An athlete's stamina is highly dependent on the content of red blood cells in the blood since these cells are responsible for transporting oxygen from the lungs to every other organ/tissue in the body. Red blood cells are made in the bone marrow, so bigger and denser bones should mean more available red blood cells, and more red blood cells, better stamina. 3) The bigger the skeleton, the more weight a fighter can put on such skeleton, which should allow him to move up in weight more easily. The caveat for this third point, is that higher muscle content means higher demand for red blood cells, which will decrease your stamina, so it is a bit of a balancing act. If a fighter grows too big his stamina will probably be affected even if he has a really big skeleton; this is somewhat evident in the heavyweights, who generally tend to fight at a less intense pace than smaller fighters.

I collected data available online from fighter's tales of the tape and recorded a fighter's height and wrist size. For weight it is a bit more complicated since most fighters have campaigned in more than one division, so I used the weight from the weight class were said fighter was perceived to be at his peak; for example, in Pacquiao's case I used 147. For fighters in the heavy weight class where there is no standard weight, I used the average weight of several fights. The first figure in the power point slide shows each individual fighter based on their height (x-axis), wrist size (y-axis), and weight class (color and marker). The second figure shows the average height and wrist size for each weight class. Notice the near linear pattern (you can also see this with the individual data points although not as clear). Here are the avg results for each group:

Class Height Wrist Heavyweight 75.31 7.69 Super Middle/Light Heavy 72.38 7.31 Jr/Welterweight 68.81 7.09 Super/Featherweight 66.1 6.35



Ok so the biggest problem so far is how accurate are the measurements, since who knows how they are taken for the tales of the tape. I did find some inconsistencies (if I recall correctly about 4 fighters out of all checked), but they were always for the height. Since luckily for me the height is always reported I looked at several of them and took the one most reported (in general only about 1 or 2 of the pre-fight reports had an odd measurement compared to the rest).

Having all my data the first thing I did was do a regression analysis using only the height and wrist size, in which the height was used as a predictor for the wrist size. This test showed a statistical significant result, meaning that as height increases so does the wrist size (which I must say is not surprising). The actual equation for this was wrist = 0.935 + height * 0.088. What this means is that someone who is, for example, say 68in (5ft 8in) should have a 6.9in wrist. To check for accuracy, I looked at the data reported in a study from a bone journal, in this study the participants had a reported avg wrist size of 7.17in, with an avg height of 70.6 in. Using the equation I just mentioned above, the expected wrist size of someone who is 70.6in should be 7.15in. What this suggests to me is that the reported heights and wrist dimensions from fighters are actually accurate enough, and that the actual dimensions of the fighters do fall within the average dimensions of a regular population. Now lets look at some fighters: for example, Mayweather is right on target (5ft 8in, 7in wrist), Wlad Klitschko has a wrist a bit smaller than what his height would suggest (should be 7.8in instead of 7.5in), while Hatton is a bit higher (should be 6.8in instead of 7in). Variation is a certainty in everything, so again, it is no big surprise that some fighters are above average while some are below average. Where things get interesting is in the extreme cases, and among these fighters there is no bigger extreme than Pacquiao. The man has 8in wrists, which is higher than the wrist average for heavyweights. When you consider he is only 66.5in tall (just over the superfeatherweight avg height) it feels even more impressive. While I was not thinking of this at the start of this little project, something caught my eye as I looked at the data. One of the things that has characterized Pacquiao during the past two or three years is his ability to punch extremely hard for someone his size against seemingly bigger foes. Well, two fighters among those I checked who also were recognized for their power and who also have 8in wrists with much smaller height than their wrist size would suggest are Joe Louis, 74in height, 8in wrists (should be 7.45in) and Mike Tyson, 71.5in height, 8in wrists (should be 7.23in). I'm assuming it is not necessary to highlight that both Louis and Tyson fought at the heavyweight class.

So far I've only looked at height and wrist together. Now we all know weight is a crucial element in boxing, it is the way to ensure that fighters fight against someone their own size and don't get unfair advantages. What I did next was I used both height and wrist size as my input variables, and the weight of each fighter as the outcome variable and again did a regression analysis. Again the result was statistically significant, meaning that indeed height and wrist can predict the weight of a fighter. The equation this time was weight = -469.47+(7.523*height)+(14.874*wrist). I again compared this outcome to the one reported in the bone study I mentioned before. So again using a height of 70.6in and wrist of 7.15in, the expected weight should be 168lbs. The actual average weight for the participants in that study was 178lbs, so my estimate is off by 10lbs, but if we take into account that most fighters typically fight lighter than their actual walking weight then I'd say the result is probably not to far off since the equation was built using official fighting weights. Using the same approach I did before, again I found that some fighters fight at around their expected weight, some fight lighter than they should (meaning they probably really kill themselves to make weight), while some actually fight heavier than what you'd expect given their height and wrist size (this was the case for almost every heavyweight). Something to take note of, is that if you add 10lbs to the expected weight of a heavyweight then most of the heavyweights included here fight right around their target. This makes sense if one assumes a heavyweight doesn't need to drain himself to make weight and fights at a weight closer to walking weight (assuming they stay in shape between fights).

Having this information in hand I looked at some particular cases. The two men that sit at the top of every p4p list right now are Mayweather and Pacquiao.

Floyd has always looked nearly unbeatable at 147lbs and Pacquiao certainly does as well since he moved into the division. So what are their expected weights: 146lbs for Floyd, 150lbs for Pac. Some other interesting cases:

Marquez has always looked in top form and at his best except when he fought Floyd as a welterweight. Even at lightweight many think he is already pushing his limit, well, according to my calculations his fighting weight should be 131lbs, just around the weight where he gave Pacquiao hell in their second fight and defeated Barrera. Pacquiao is ½ inch shorter than Marquez yet he was able to move up in weight while Marquez could not. Many people have used this argument to suggest something improper on the part of Pacquiao; what they miss is that Pacquiao's wrists are 8in while Marquez's are only 6.5in, giving Pacquiao an overall much bigger skeleton. This highlights why a great fighter like Pacquiao can easily adapt to a much higher weight without losing any speed, power, or chin, while another great fighter like Marquez can't, event though both have very similar heights.

Another interesting fighter is Margarito, he always seemed huge for a welterweight, and prior to his defeat against Mosley there were reports that he looked awful in camp and struggled to make weight (Margarito claims that was the reason he looked so bad in that fight). Since then he's moved up in weight, and against Manny, even though he made the catchweight of 150lbs, come fight night he was close to the super middleweight limit. Well, his estimated weight is 176lbs, since he has decent height (71in, and bigger than avg wrists 7.5in). Margarito is someone who certainly benefited from having really big bones in a division that should be too small for his frame size, which might explain why his iron chin took so damn long to get cracked. Another place where this advantage would show itself, assuming he made weight in a safe manner (meaning he did not just drain himself like he did for the Mosely fight), is in the stamina department, with proportionally more bone (+red blood cells) than muscles (less demand for red blood cells) compared to every other fighter in the division.

Cotto cemented his name in the 147lbs division, but since then has moved to the 154lbs division claiming the title there, which he successfully defended this past weekend. His estimated weight: 154lbs.

Roy Jones Jr., one of the best fighters of the last 20yrs, campaigned and had success at several divisions. Many have claimed he is the best 168lbs fighter ever. His optimal weight: 169lbs.

The point I hope is becoming evident is that "how big" a fighter is should not be based solely on height (which in many occasions is what happens). Referring specifically to the case of Pacquiao, Nazeem Richardson said it best: "The best trick Pacquiao has pulled is making you believe he is smaller than you are" (I'm paraphrasing). Sure the man is short compared to most if not all top fighters in the 147lb division, but if you were to look at x-rays of every fighter in the division, I'd put money down that he has the biggest skeleton in the division (in overall bone volume) with the exception of Margarito if he were to go back to 147lbs.