# Quantifying Comebacks and Excitement With Win Probability

As promised the other day, there’s a lot we can do with point-by-point and win probability stats for over 600 grand slam matches.

I’ve beefed up those pages a bit by borrowing some ideas from Brian Burke at Advanced NFL Stats.  He invented a couple of simple metrics using win probability stats to compare degrees of comebacks and the excitement level of (American) football games.

The concepts transfer to tennis quite nicely.  Comeback Factor identifies the odds against the winner at his lowest point.  I’ve defined it the same way Burke does for football: CF is the inverse of the winning player’s lowest win probability.  In the US Open Federer/Djokovic semifinal, Djokovic’s win probability was as low as 1.3%, or 0.013.  Thus, his comeback factor is 1/.013, or about 79.  That’s about as high a comeback factor as you’ll ever see.

On the other end, comeback factor cannot go below 2.0 — that’s the factor if the winning player’s WP never fell below 50%.  Matches in which the winner dominated are often very close to 2.0, as in the Murray/Nadal semifinal.  In that match, Nadal’s low point was facing a single break point at 2-3 in the first set; the comeback factor is 2.3.

A good way to think about comeback factor is this: “At his lowest point, the winning player faced odds of 1 in [CF].”

Excitement Index is a measure of volatility, or the average importance of each point in a match.  “Volatility” measures the importance of each individual point; EI is the average volatility over the course of a match.

(Burke sums the volatilities, reasoning that in football, a fast-paced game with many plays is itself exciting.  Since there is no clock in tennis [not exactly, anyway], it seems appropriate to average the volatilities.  Win probability already considers the excitement and importance of a deciding final set.)

At the moment, I’m calculating EI by multiplying the average volatility by 1000.  The Murray/Nadal match is 35 (not very exciting, though Murray fought back), the Djokovic/Federer match is 47 (more on that in a minute), while the 2nd rounder between Donald Young and Stanislas Wawrinka is 64.  I haven’t looked at all the matches yet, but EI should generally fall between 10 and 100, possibly exceeding 100 in rare instances like the Isner/Mahut marathon.

It seems like Djok/Fed should be higher, perhaps because we remember the excitement of the final set.  (And it may be that the final set should be weighted accordingly.)  But looking at the match log, there were an awful lot of quick games, which translate to relatively low volatility.  By contrast, Donald/Stan was more topsy-turvy throughout, as the players traded sets, then send volatility through the roof with a pair of breaks midway through the final set.

Both EI’s scaling and its exact definition are works in progress.  When I get a chance, I’ll do a survey of matches for which I have point-by-point data to further investigate both of these new (to tennis) metrics.