# To Win A Grand Final You Must First Lead

/History suggests that, as the higher-Rated "Home" team, Hawthorn must lead early and lead well if it is to be confident of success in Saturday's Grand Final, and not assume that its superior Rating will allow it to come back from any substantial deficit.

The broad empirical evidence supporting this contention is that of the last 16 GFs, ignoring the drawn result in 2010, the higher-Rated team has won only half of them, and of the last 30 only 60%. In recent times, as I'll demonstrate in a moment, what's mattered in Grand Finals far more than the difference in the team's pre-game Ratings has been the ability of one team to establish a lead, however slight.

**PREDICTING THE RESULT OF GRAND FINALS IN-RUNNING**

As data for today's blog I'll be using the scores at the end of every quarter in all the Grand Finals since 1898 (there was no GF in the first season), as well as the participating teams' pre-game all-time MARS Ratings, which were estimated using the more-recent assumption that, for Finals, the higher-Rated team is the home team.

For modelling I'll be using a variant of a technique I've used previously (for example in this blog from 2010), which was inspired by Brownian motion and which allows me to estimate in-running game probabilities.

The model is a binary logit and for today's blog is of the form:

*Prob(Home team wins) = logistic(a + b*L/(sqrt(1-T)) + c/(sqrt(1-T)) + d*MARS_Diff)*

where L is the Home team lead at a particular point in a game,

T is the fraction of the game completed at the time L is measured, so 0 <= T <= 1, and

MARS_Diff is the difference in the pre-game MARS Ratings of the stronger team less that of the weaker team.

Each game contributes three data points to this model, these being the Home team's lead at the end of Q1, Q2 and Q3.

I've split the data into four Eras, the first running from 1897 to 1919, the next from 1920 to 1949, the third from 1950 to 1979, and the last from 1980 to 2012, and estimated the model separately for each Era.

The coefficients of these fitted models are shown in the table at left. Coefficients on the Lead term - those in the next-to-last column - reflect the value of a lead, in terms of victory probability, to the Home team at any point in the game. Higher values mean that a given sized lead is more likely to result in a Home team victory.

Values in the rightmost column reflect the contribution that Rating superiority makes to the Home team's victory chances. The tiny value shown here for the latest era reflects the significantly diminished importance of pre-game favouritism during that period.

In fact, so diminished is it that even a 30 Ratings Point (RP) stronger team - such as Hawthorn this weekend - starts a Grand Final in the modern era as a narrow underdog according to the model, as shown in the following table.

The rightmost block of percentages provides the fitted estimates of the GF victory probability of a Home team with a 30 RP superiority. It's the 46% figure under the column headed Start of Game that tells us the Home team starts as a narrow underdog in that scenario.

Moving across the rows we see that, for example, a lead of 5 points at Quarter time would make that 30 RP superior Home team now only a narrow favourite (53%), but a similar lead at Three Quarter time would make them only even money chances.

Trailing, however, is devastating for the Home team's prospects. Even a trail as small as 5 points at Three Quarter time renders them 3/1 outsiders.

The relative unimportance of RP superiority can be seen by comparing the same game state across the three blocks, each reflecting a different level of RP advantage. So, for example, a 10 point trail at Three Quarter time implies a Home team victory probability of 15% if the Home team has a 10 RP pre-game advantage, and a probability of 17% if, instead, that superiority is 30 RPs.

In the previous Era, which I've defined as spanning 1950 to 1979, Home (ie Stronger) teams had a much better time of it in Grand Finals, as depicted in the following table, which shows the same information as above but using the fitted coefficients for this Era instead.

The first thing to note here is the much higher presumption of victory. Even a 10 RP superiority is sufficient to warrant 2/1 on favouritism at the first bounce.

This apparently generous estimate derives from the empirical reality that, during this Era, Home teams won 70% of the time.

There's also no real hurry for the Home team to establish a lead. Should that 10 RP more highly Rated team dawdle its way to Three Quarter time and find itself still tied with its opponent, its chances of victory will actually have increased to 71%. Only when the trail is relatively substantial at Three Quarter time - say 20 points or more - does the Home team find itself with seriously reduced prospects.

If, instead, it came into the GF with a 30 RP advantage it can afford to spot the underdogs 20 points start at Three Quarter time and still rate itself about a 60% chance of victory. If it's established any sort of a lead at all, it can consider itself a near certainty.

Oh how Hawthorn must wish it were playing Saturday's game back in the 1970s.