Introduction

I am a huge MMA fan, and the UFC is the largest MMA promotion, I saw this dataset on Kaggle and had to play with it. The following is an attempt to model what elements of fights and fighters are most important to winning fights. At the end, I compare the statistics with some real life intuition, to see how the numbers stack up against popular wisdom, add some caveats to the results, and potential next steps.

The fight-level dataset contains super granular data on every fight from 1993 to 2019. Our goal is to build a model that:

gives us an understanding of what factors contribute the most, and in what ways, towards one fighter winning over another. In other words, this is an exercise in understanding how fighters compare across a variety of attributes, and evaluating to what extent each comparison matters.
is able to predict which fighter will win

Before we start building models on top of it, we have to wrangle the data to make it make sense for modeling:

Removing uninformative dimensions: Some dimensions in our fight-level dataset, such as the referee or state, do not help us understand the fighters and how they compare. To that end, we start by removing these details from our training datset Even though they might marginally improve our model’s evaluation metrics, they do not contribute to our understanding of each fighter, and are therefore unlikely to meaningfully explain why one fighter wins over another. We’re also removing rows that have NAs - these fighters tend to not be representative of your typical UFC fighter, and unfortunately it poses too many data concerns. We’re left with over 3,000 fights to work with. (A quick comparison of the two datasets shows us that the majority of fights excluded are between 1993-1997, likely when some of these metrics were not recorded).
Factorizing Intuitively, it makes sense that different attributes will matter differently according to the weight class. We’ll reframe this column into a factor to make it easier to work with.
Probability of red winning This prediction problem is a binary classification - we’re looking at whether the blue of red corner wins. If we’re using an OLS regression technique (like with logistic regression) we’ll have to reframe the problem as “what is the probability that __ corner wins?”. Given that for most fights, the UFC gives the fighter with this most name recognition the red corner, we’ll assess the probability that the red corner wins.
Difference between fighters Finally, at its core, our analysis seeks to understand how fighters compare against each other. To this end, it is useful to have a datsaet that explicitly the differences in fighters for each stat. We’re going to be looking at the \(\frac{Red Fighter - Blue Fighter} {Red Fighter}\) difference.

The Data

The two datasets we’re working with are the following:

A Few Variables & Their Correlation with Republican Winner
fighter	current_lose_streak	current_win_streak	draw	avg_BODY_att	avg_BODY_landed	avg_CLINCH_att	avg_CLINCH_landed	avg_DISTANCE_att	avg_DISTANCE_landed	avg_GROUND_att	avg_GROUND_landed	avg_HEAD_att	avg_HEAD_landed	avg_KD	avg_LEG_att	avg_LEG_landed	avg_PASS	avg_REV	avg_SIG_STR_att	avg_SIG_STR_landed	avg_SIG_STR_pct	avg_SUB_ATT	avg_TD_att	avg_TD_landed	avg_TD_pct	avg_TOTAL_STR_att	avg_TOTAL_STR_landed	longest_win_streak	losses	avg_opp_BODY_att	avg_opp_BODY_landed	avg_opp_CLINCH_att	avg_opp_CLINCH_landed	avg_opp_DISTANCE_att	avg_opp_DISTANCE_landed	avg_opp_GROUND_att	avg_opp_GROUND_landed	avg_opp_HEAD_att	avg_opp_HEAD_landed	avg_opp_KD	avg_opp_LEG_att	avg_opp_LEG_landed	avg_opp_PASS	avg_opp_REV	avg_opp_SIG_STR_att	avg_opp_SIG_STR_landed	avg_opp_SIG_STR_pct	avg_opp_SUB_ATT	avg_opp_TD_att	avg_opp_TD_landed	avg_opp_TD_pct	avg_opp_TOTAL_STR_att	avg_opp_TOTAL_STR_landed	total_rounds_fought	total_time_fought	total_title_bouts	win_by_Decision_Majority	win_by_Decision_Split	win_by_Decision_Unanimous	win_by_KO/TKO	win_by_Submission	win_by_TKO_Doctor_Stoppage	wins	Height_cms	Reach_cms	Weight_lbs	age	stance
Aaron Phillips	1.0000000	0.000000	0	14.000000	12.000000	6.000000	3.000000	26.00000	9.00000	8.000000	6.000000	23.00000	5.00000	0.000000	3.000000	1.000000	1.0000000	1.0000000	40.00000	18.00000	0.4500000	1.0000000	0.000000	0.0000000	0.0000000	137.00000	109.00000	0.0000000	1.000000	13.000000	8.000000	6.000000	4.00000	31.00000	12.00000	31.000000	21.000000	53.00000	28.00000	0.0000000	2.000000	1.000000	7.0000000	1.0000000	68.00000	37.00000	0.5400000	1.0000000	8.000000	5.0000000	0.6200000	129.00000	95.00000	3.000000	900.0000	0	0	0.0000000	0.000000	0.000000	0.00	0	0.000000	175.26	177.80	135	25.00000	Southpaw
Aaron Riley	0.7916667	0.375000	0	14.886905	12.436905	26.699405	15.647024	71.04464	24.41488	2.977381	2.159524	70.40595	18.85536	0.000000	15.428571	10.929167	0.8041667	0.0000000	100.72143	42.22143	0.4049583	0.3553571	2.839881	0.8511905	0.3019940	133.25357	72.51012	0.7083333	2.916667	13.207143	10.910714	24.312500	13.35714	83.91071	28.59226	6.923214	3.514286	97.66131	32.18810	0.4607143	4.277976	2.364881	0.0000000	0.0000000	115.14643	45.46369	0.3908869	0.0000000	3.826786	2.3178571	0.3226190	132.08155	62.15536	9.458333	646.6417	0	0	0.0000000	1.416667	0.000000	0.00	0	1.416667	172.72	175.26	155	28.37500	Southpaw
Aaron Rosa	0.0000000	1.000000	0	23.500000	21.000000	31.500000	26.000000	107.50000	40.00000	0.000000	0.000000	110.50000	40.50000	0.000000	5.000000	4.500000	0.0000000	0.0000000	139.00000	66.00000	0.4950000	0.0000000	0.500000	0.0000000	0.0000000	284.50000	195.50000	1.0000000	1.000000	9.500000	8.000000	15.500000	13.00000	94.00000	36.50000	4.000000	4.000000	92.50000	36.00000	0.0000000	11.500000	9.500000	1.0000000	0.0000000	113.50000	53.50000	0.4700000	0.0000000	7.000000	1.0000000	0.1750000	189.50000	116.50000	6.000000	793.0000	0	1	0.0000000	0.000000	0.000000	0.00	0	1.000000	193.04	198.12	205	28.00000	Orthodox
Aaron Simpson	0.4761905	1.309524	0	10.122449	7.128685	17.370975	11.932341	35.32381	11.43931	15.311111	8.886990	51.50334	19.08965	0.543424	6.380102	6.040306	0.8887755	0.0000000	68.00590	32.25865	0.5123336	0.1816043	6.382313	2.6608560	0.6325468	95.37177	56.16344	2.7857143	1.452381	4.392942	3.372931	22.182171	12.92883	37.15958	11.10768	1.512840	1.233702	51.35788	17.92857	0.0000000	5.103770	3.968707	0.0150794	0.0953231	60.85459	25.27021	0.3638418	0.3374717	1.787869	0.3284297	0.0643577	73.02200	36.78424	12.166667	521.2818	0	0	0.8571429	1.023810	1.928571	0.00	0	3.809524	182.88	185.42	170	36.04762	Orthodox
Abdul Razak Alhassan	0.2500000	1.000000	0	1.708333	1.104167	5.416667	4.104167	41.72917	16.97917	2.083333	1.562500	45.12500	20.16667	1.770833	2.395833	1.375000	0.0000000	0.2708333	49.22917	22.64583	0.4862500	0.0000000	0.437500	0.1458333	0.0481250	51.91667	24.37500	1.2500000	0.750000	4.854167	3.687500	5.395833	3.93750	46.95833	13.39583	6.687500	3.979167	52.52083	15.95833	0.0000000	1.666667	1.666667	0.8125000	0.0000000	59.04167	21.31250	0.2770833	0.0000000	2.854167	1.6875000	0.2100000	76.16667	34.39583	4.000000	323.6042	0	0	0.0000000	0.000000	1.750000	0.00	0	1.750000	177.80	185.42	170	32.00000	Orthodox
Abel Trujillo	0.5833333	1.000000	0	12.142130	10.475066	15.108532	11.621958	37.90476	10.65483	14.117527	11.861243	51.90794	20.58221	0.428373	3.080754	3.080754	0.5609788	0.0000000	67.13082	34.13803	0.4720298	0.5920635	1.994114	1.3677249	0.7785245	84.07176	49.26739	1.8333333	2.333333	3.482077	2.533664	7.300926	4.11541	32.79987	11.86587	6.188823	4.033664	37.66369	13.90536	0.0000000	5.143849	3.575926	0.9390873	0.0000000	46.28962	20.01495	0.4701184	1.1196429	9.544511	5.6351190	0.4725694	58.51455	29.74497	11.583333	578.2272	0	0	0.0000000	0.250000	2.250000	0.25	0	3.166667	172.72	177.80	155	31.25000	Orthodox

A Few Variables & Their Correlation with Republican Winner
fight_id	diff_wins	diff_Weight_lbs	diff_total_time_fought	diff_total_rounds_fought	diff_Reach_cms	diff_losses	diff_longest_win_streak	diff_Height_cms	diff_current_win_streak	diff_avg_TOTAL_STR_landed	diff_avg_TOTAL_STR_att	diff_avg_TD_pct	diff_avg_TD_landed	diff_avg_TD_att	diff_avg_SU_ATT	diff_avg_SIG_STR_pct	diff_avg_SIG_STR_landed	diff_avg_SIG_STR_att	diff_avg_REV	diff_avg_PASS	diff_avg_opp_TOTAL_STR_landed	diff_avg_opp_TOTAL_STR_att	diff_avg_opp_TD_pct	diff_avg_opp_TD_landed	diff_avg_opp_TD_att	diff_avg_opp_SU_ATT	diff_avg_opp_SIG_STR_pct	diff_avg_opp_SIG_STR_landed	diff_avg_opp_SIG_STR_att	diff_avg_opp_REV	diff_avg_opp_PASS	diff_avg_opp_LEG_landed	diff_avg_opp_LEG_att	diff_avg_opp_KD	diff_avg_opp_HEAD_landed	diff_avg_opp_HEAD_att	diff_avg_opp_GROUND_landed	diff_avg_opp_GROUND_att	diff_avg_opp_DISTANCE_landed	diff_avg_opp_DISTANCE_att	diff_avg_opp_CLINCH_landed	diff_avg_opp_CLINCH_att	diff_avg_opp_ODY_landed	diff_avg_opp_ODY_att	diff_avg_LEG_landed	diff_avg_LEG_att	diff_avg_KD	diff_avg_HEAD_landed	diff_avg_HEAD_att	diff_avg_GROUND_landed	diff_avg_GROUND_att	diff_avg_DISTANCE_landed	diff_avg_DISTANCE_att	diff_avg_CLINCH_landed	diff_avg_CLINCH_att	diff_avg_ODY_landed	diff_avg_ODY_att	diff_age	red_win
1	0.5000000	0.0000000	0.4352276	0.6666667	-0.0468750	0.5000000	0.0000000	-0.0312500	0.0000000	0.6584660	0.4888376	0.7816594	0.8947368	0.8490566	-3.0000000	0.0000000	0.4863636	0.3550296	0.0000000	0.6666667	0.5565820	0.5131222	-1.0000000	-3.0000000	-0.1111111	0.0000000	0.2976190	0.4347826	0.4655870	0.0000000	0.0000000	0.2131148	0.2765957	-1.0000000	0.4566474	0.4796321	0.3333333	0.2500000	0.3507463	0.4342541	0.8823529	0.8666667	0.5454545	0.5187970	-0.4594595	-0.4339623	-1.0000000	0.5313808	0.3450135	0.6923077	0.7234043	0.2226415	0.1653333	1.0000000	0.9882353	0.6341463	0.5799087	0.0312500	1
2	0.2000000	0.0000000	0.2005650	-0.1600000	0.0000000	-2.0000000	-0.5000000	-0.0153846	-0.5000000	0.3233333	0.0177719	0.6258907	0.7941176	0.8055556	-0.6333333	0.3069479	0.1367788	-0.1988903	1.0000000	0.5333333	0.0836806	0.0420054	-0.5699029	-0.0500000	0.3000000	-1.4500000	0.0666667	-0.0846645	-0.0608158	0.0000000	-0.2250000	0.5370079	0.5916667	0.0000000	-1.4781609	-0.5794457	-0.6100000	-0.2600000	0.0175439	-0.0317391	-0.2218182	-0.2108108	0.3424242	0.4709302	0.3067961	0.3622222	0.0000000	0.1351351	-0.3243243	0.8843478	0.8697674	-0.1648221	-0.4147488	-0.0645833	-0.2707692	-0.1796296	-0.2166667	-0.0322581	1
3	-0.6428571	0.0000000	0.0372750	-1.0606061	0.0394737	-7.0000000	0.2727273	-0.0281690	0.7272727	0.1711611	0.2202280	-0.0654467	-0.6935484	-1.3156682	0.6451613	-0.1537884	0.1567153	0.2198391	0.2741935	-1.8064516	-0.2894869	0.0170976	0.5161290	0.6612903	0.2685671	-0.4516129	-0.3330171	-0.2548146	0.0407528	0.7580645	0.9032258	-0.7008798	-0.5268817	0.1532258	-0.0984427	0.1357092	0.6658986	0.6420681	-0.1821278	0.0715770	-6.9618768	-2.0069124	-0.4595452	-0.2375502	-0.0887097	-0.0194175	-2.2258065	0.3466836	0.3007047	0.1078629	-0.0342742	0.2200678	0.2703048	-1.5310174	-1.3518380	-0.3064516	-0.1073201	-0.0285714	1
4	0.3333333	0.0000000	0.0554147	0.5500000	0.0147059	1.0000000	0.2000000	-0.0468750	0.0000000	-0.7093596	-0.3184239	-1.7710843	-1.0000000	-0.1111111	0.0000000	-0.5017065	-0.5355191	-0.2192394	0.0000000	-3.0000000	0.2992327	0.0901194	0.0000000	0.0000000	-0.8947368	0.0000000	0.2436975	0.2924791	0.0800451	0.0000000	0.0000000	0.6179775	0.4528302	-1.0000000	-0.0552147	-0.0662359	-0.6666667	-1.0000000	0.3051948	0.0860606	0.3333333	0.1272727	0.5514019	0.3950617	0.7826087	0.7692308	-0.3333333	-1.2395833	-0.4440994	-15.8000000	-12.0000000	-0.1890244	-0.0441001	-1.6666667	-1.3404255	-0.3658537	0.0684932	0.1034483	0
5	0.6666667	0.0530303	-1.7226319	-0.1428571	0.0266667	0.0000000	0.6666667	0.0405405	0.0000000	-0.8931298	-2.2125984	0.0000000	0.0000000	1.0000000	0.0000000	0.4311927	-0.8923077	-2.2690763	0.0000000	1.0000000	-2.2432432	-2.3966942	0.0000000	0.0000000	0.5000000	0.0000000	-0.0817610	-3.0000000	-2.7363636	0.0000000	1.0000000	-1.6666667	-0.9090909	1.0000000	-3.0357143	-2.5260116	1.0000000	1.0000000	-4.5076923	-3.7953216	0.8571429	0.8888889	-3.9473684	-5.8000000	0.3333333	0.4666667	1.0000000	-0.9780220	-2.6354680	1.0000000	1.0000000	-1.4040404	-2.9605911	0.7241379	0.7727273	-1.1481481	-1.1935484	-0.2307692	0
6	0.1111111	0.0000000	0.3402531	0.2812500	0.0845070	-0.3333333	0.0000000	0.0149254	0.0000000	0.4460641	0.2578313	0.4411178	0.6666667	0.4843750	0.1111111	-0.0187075	0.2057416	0.0641234	0.0000000	0.6111111	-0.2290749	-0.3691830	0.2284768	0.5384615	0.0370370	1.0000000	-0.3160763	-1.4423963	-0.8349929	1.0000000	0.9000000	-0.0185185	0.1200000	1.0000000	-2.6261682	-1.0460653	0.0000000	0.0909091	-2.2258065	-1.0228758	0.6666667	0.5362319	-0.5535714	-0.4766355	0.0546875	0.0000000	0.0000000	-0.0285714	-0.0568783	0.7092199	0.6839378	-0.1784703	-0.1699196	0.6917293	0.5654762	0.5936073	0.4039735	-0.1034483	1

Initial Analysis

We plug our modelling dataset into a random forest of 500 trees, randomly selecting 20 variables at a time, and plot how much splitting on each variable contributed to a decrease in the gini coefficient, averaged across all the trees.

## 
## Call:
##  randomForest(formula = red_win ~ ., data = forest_df, ntree = 500,      mtry = 20) 
##                Type of random forest: classification
##                      Number of trees: 500
## No. of variables tried at each split: 20
## 
##         OOB estimate of  error rate: 36.66%
## Confusion matrix:
##     0    1 class.error
## 0 279  907   0.7647555
## 1 267 1749   0.1324405

It looks like the following variables are the key drivers to determining the outcome of fights:

% Difference in age – by far the most important variable: the importance of this variable is super interesting. Much of the mma media discusses fighters in relation to “their prime” (generally around 28-30). Fighters like Randy Couture, Fedor, Yoel Romero have made legends fighting well past their “primes” and succeeding. That this narrative is backed by some statistical analysis suggests that there is something to this general perception.
Percent of significant strikes landed – the importance of significant strikes is not surprising, significant strikes are called out in the judges scorecards, which contribute how judges score fights that go to a decision. What is surprising, however, is that the % of significant strikes is so important (vs. overall volume). This suggests that fighters with accurate striking are favoured over those with volume.
Number of ground strikes landed – contrasing numbeer of ground strikes vs % of significant strikes presents an interesting nuance. Ground strikes are those landed against a grounded opponent (typically brought to the ground by a takedown or trip). What’s interesting about the number of ground strikes being more important than % of ground strikes landed, is that it suggests that overall ground control time is potentially more important than actual damaage done on the ground. Interstingly, barring actively working for a submission (which referees sometimes don’t catch), ground strikes are the only way to keep your opponent on the ground without the referee standing you both (due to inactivity). I would be curious as to how relatively important ground strikes are compared with overall ground control time
% Difference in reach – this makes intuitive sense, a fighters relative reach over another presents the opportunity to land strikes with less risk of getting hit. Shorter stature fighters like BJ Penn made their names using technique, physicality and a strong chin to overcome this disadvantage. I would be curious to see how this variable becomes more/less important if you subset the data for the more proficient athletes (potentially filtering by only UFC champions)
Number of head strikes landed – headstrikes are some of the most damaging strikes to receive. Most KO/TKO via strikes will be due to at least one head strike. Sports like boxing focus heavily on strikes to the head, so fighters coming in from this background will carry that instinct. In practice, head strikes are set up by shots in longer combinations (shots to the body, elbows in the clinch etc.). It would be great to understand if the importance of head strikes is a function of ones ability to land long combinations (and so potentially a proxy for % significant strikes), or if the damage of a head strike is inherently important.
% Difference in time fought – again, this makes intuitive sense. MMA is a crazy sport, and time in the cage contributes to a fighters “fight IQ” (ability to make adjustments on the fly), endurance to go all 3 (or 5) rounds, ability to handle stress etc… .

Another interesting comparison is how many of the key drivers were physical attributes vs. in-fight strategies. A learning for future fighters would be to look at their age and reach relative to their peers, seriously. Fighters who are particularly young with large reaches would be especially advantaged. The analysis also highlights the importance of conditioning for MMA athletes, particularly when fighting more experienced fighters.

One piece I would love to understand more is the importance of submissions - submissions are a key element of the game, and a great submission game can neutralize threats of reach or size (famously proved by Joyce Gracie in the very first UFC tournament in 1994). I was surprised at how striking-heavy the important variables turned out to be. I would love to see how the important variables shift as we subset for 1) current or ex champions - my hypothesis is that as calibre of fighter goes up, physicality becomes less important and technique-driven variables will emerge (such as % sig strikes, submission attempts etc…).

Neural Network

As a predictive exercise, we’ll feed these variables into a small, 5 layered neural net. Neural nets have the advantage of learning, through each layer, which variables (and/or which combinations of layers) are most important to predicting the outcome. While this makes large neural nets strong algorithms, it is very hard to interpret them and get an intuition for which variables are important and why. Therefore, in this case, we feed the neural net with variables we already know from our random forest (and our intuition) are important. The neural net improves marginally on the random forest, achieving an overall accuracy of 65%. Looking at the confusion matrix, it looks like Recall actually went down to about 73% and Precision went up to 67%. Comparing this to the random forest, it looks like the model loosened its prediction of wins, versus the random forest that overpredicted the red corner winning.

Confusion Matrix

## # weights:  41
## initial  value 2523.180341 
## iter  10 value 2039.947608
## iter  20 value 2021.179624
## iter  30 value 2010.110831
## iter  40 value 2002.729564
## iter  50 value 1998.996950
## iter  60 value 1997.313435
## iter  70 value 1994.292583
## iter  80 value 1989.469108
## iter  90 value 1988.625653
## iter 100 value 1988.417170
## final  value 1988.417170 
## stopped after 100 iterations

##                red_win
## neural_predicts    0    1
##               0  294  216
##               1  892 1800

## [1] 65.39663

##                red_win
## neural_predicts    0    1
##               0  294  216
##               1  892 1800

65% accuracy is decent, although the ability to accurately predict upsets is far less than a predictive model would like to be. MMA is an inherently chaotic and surprising sport (part of why I love it so much), so I am honestly surprised that a model is able to predict with even this level of accuracy. If the community has refinements to my modelling or additional techniques to try, I would be very open.

The Art of War: Understanding key drivers of winning UFC fights (1997-2019)

Sahil

Introduction

The Data

Initial Analysis

Neural Network

Confusion Matrix