A week or two ago, I watched the Pitt-Stanford game that ultimately determined the winner of the ACC. It was a 5th set thriller, which is always cool, but what really stood out to me was the fact that Stanford came back to win the very first set 26-24 after being down 14-20, 17-22, and 20-24. Stanford then went on to win the next set and then lose the next two. This meant that Stanford was in jeopardy of being reverse swept. They almost were reverse swept: Stanford was down 11-14 in the 5th set, and went on a 5-point run to close out the match 16-14.
These amazing comebacks reminded me of a tool I built this past summer to calculate win probabilities. So, after this game, I decided to graph Stanford’s win probabilities across the match. Take a look at this:
Crazy, right? Super competitive, wild comebacks (and of course great volleyball).
Looking at match win probability gives an interesting take on comebacks and the importance of scoring runs. Stanford’s five-point run from being down 11-14 to winning 16-14 in the fifth set was a swing from a 4% match win probability to 100%–an extraordinary 96% swing to end the match. The five-point run from being down 21-24 to winning 26-24 in the first set was a swing of just shy of 40% in terms of overall match win probability (32% to 69%). But a five-point run at a place in the match where the score isn’t close–like Pitt going from being up 19-15 to 24-15 in the fourth set–only moved the match win probability by 6% (56% to 50%). This data shows that, while all points may be technically equal, some points have much greater implications on match win probability.
When you think about it, this makes perfect sense. Getting an ace when the score is 5-6 is always great–I mean, who doesn’t love aces? But when you think about the course of a match, that ace probably won’t be the consequential point that turns the tide of the entire game. Getting an ace when the score 25-26, however, could easily be one of the key determining factors in a match. It’s still just one ace, but the momentum shift and the timing of the point in relation to where you are in the match makes all the difference in win probability.
Here’s another, even larger comeback from last week: Kentucky vs. Texas
Kentucky had lost the first two sets to Texas, and were down 19-23 and 22-24 in the 3rd set, which brought their win probability down to 1%. They were able to fight off two match points and then win the set 26-24, and then won the 4th and 5th set to complete the reverse sweep. The score was tied 9-9 in the 5th set, and Kentucky had a 50% win probability, which makes sense. They then went on a 6-point run to close out the match 15-9, which we can see in that final upwards surge at the end of the graph.
Now that we’ve looked at two exciting matches, I wanted to figure out how we can summarize the differences between a boring match and an exciting match. Well, there are actually two very interesting things that differentiate the Pitt-Stanford or Kentucky-Texas match and blowout matches.
The first is the presence of the amazing comebacks–something easily visible in the chart above. The second is how close the match stays–the competitiveness. It is possible to have an exciting, competitive match without many big comebacks (imagine the score being close all the way from the beginning to the end), just like there can be big comebacks in matches but there could be long stretches in which the set or match isn’t particularly competitive.
Can we summarize the competitiveness and comebacks for a match using win probabilities? Absolutely.
The simplest version of a “Comeback Rating” is also the most compelling–it’s the difference between the ultimate win (100%) and the winning probability that the winning team had at its lowest point on the graph. If we start with both teams equally likely to win (by assumption), a team that is in the lead wire to wire never falls below 50%–so a 50% Comeback Rating means there was no ‘comeback’. A team that wins after losing the first set will have a Comeback Rating of at least 70%. Coming back from a 4% win probability, like Stanford did, would be a 96% Comeback Rating.
A “Competitiveness Rating” can be created by adding up all the (absolute) changes in match win probability point by point over the set. In a boring, one-sided match, the match win probability for the winner marches inexorably from 50% to 100%, with long stretches in uncompetitive sets where the match win probability doesn’t move much. In competitive, close sets, every point has an effect on the win probability. Mathematically, we can summarize this as the total length of the line being graphed. The more ups and downs in the line, and the more points that actually affect the win probability, the longer the total line.
The Pitt-Stanford match had a Competitiveness Rating of 8.0, whereas a lopsided match will typically have a score of 2.0 or less (mathematically, the lowest possible Competitiveness Rating is 0.5). Because there’s no upper limit to the score of a match, there’s no maximum value of the Competitiveness Rating. If Pitt and Stanford had traded side outs several times after 14-14 in the 5th set, the score would have continued to increase beyond 8.0.
The selection show this past weekend marks the start of the NCAA tournament for Division 1 volleyball, but I have already been watching some great games from the DIII tournament! The first three rounds of the DIII tournament were played across three consecutive days, so 56 games across 8 regional locations. The graph below is a scatterplot showing the Competitiveness Ratings and Comeback Ratings for every match in the first three rounds of the DIII tournament.
The first few rounds of the DIII tournament had some uncompetitive matches, which can be seen in the lower left of the scatterplot, but there were some matches that were were even more competitive than the Pitt-Stanford game. One of them had an even larger comeback (96.7% Rating!!!) than the 96% for the Pitt-Stanford match.
I’ll write up a bit more on comebacks and competitiveness in the first three rounds of the DIII tournament in my next post, and will use data from the DI regular season to do a little DI tournament preview later this week!
Notes:
- Photocredit: Drake University Athletics
- The win probabilities calculated for the graphs and Comeback and Competitiveness Ratings above all start from an assumption of equally matched teams with average side out percentages. The tool I developed allows for win probability calculations with other assumptions, but for generating these ratings and graphs, I thought it would be nice to develop measures of comebacks and competitiveness for which mathematically each team has an equal chance of winning when starting the match.
- After piloting automating these calculations on the DIII tournament matches (more on that in my next post), this past weekend I scraped, parsed, and began the analysis of the play by play data for EVERY regular season DI match. Play by play is available for just over 5000 DI matches this season. I’ll be sharing more analysis of this data soon, but I’ll just say right now that while the Pitt-Stanford and Louisville-Texas matches were amazing, they are NOT the matches that are the most competitive or with the biggest comebacks, at least not according to the measures I developed. I look forward to sharing more soon!