# Measuring Momentum in Game Margins

The topic of momentum is one I've explored before: in terms of game-to-game results for different teams, from the perspective of quarter-to-quarter outcomes, and even by examining scoring shot to scoring shot progressions within a game.

For today's blog I'm going to measure the effects of momentum, if any, on home teams' victory margins from one game to the next, and assess whether these effects vary from season to season.

DATA AND METHODOLOGY

I'll be using a simple statistical model today - so simple it's got "ordinary" right there in the name - in the shape of Ordinary Least Squares regression, with the target variable the home team's victory margin. I'll fit this model to the data for every game from R1 of 2000 to R19 of 2013, including Finals.

Now a team's victory margin in any game is, obviously, a function of its own and its opponent's abilities and, as we've seen before, of whether or not the team is playing at home or away and whether the clash is an Interstate clash or not. In order to isolate the effects of momentum I need to control for these known determinants.

Controlling for Interstate status is fairly straightforward, and home team effects can be accommodated by defining the game margin from the home team's perspective and by including separate coefficients for the team abilities.

I've two options for measuring for these team abilities: TAB Bookmaker prices and MAFL's MARS Ratings.The problem with using the former is that Bookmaker prices reflect more than just the teams' relative abilities; most problematic, if there is a momentum effect, it will include that too. We want to separately measure the effects of momentum, however, so the TAB Bookmaker prices are out. That leaves MARS Ratings as the means by which we'll control for differences in team abilities. These Ratings don't explicitly incorporate a momentum component, except to the extent that teams that have been winning recently will tend to have higher Ratings than those that have not been winning.

Lastly, I need to include variables to reflect team momentum, measured over different durations. For this purpose I created a range of variables equal to the home team's winning rate in its last X games, using values of X from 1 to 6. So, for example, for X=4 I'm creating a variable that takes on a value of 0 if the home team has lost its last 4 games, 0.25 if it's won only 1 of its last 4 games, 0.5 if it's won 2 and lost 2, 0.75 if it's won 3 and lost only 1, and 1 if it's won all 4.

In calculating these variables I've ignored the fact that some of the last X games for a particular team might have been in Finals and some home-and-away, and I've also ignored the fact that they might span byes or even seasons. So, for example, the variable reflecting the results for the last 5 games for a particular team might include Round 1 from one season, and the Finals and a few home-and-away games from the previous season. Momentum, as I'm defining it here then, can have a long memory.

Now it's probably not surprising that the variable reflecting teams' performances over the past X games is highly correlated with the variable reflecting their performances over the past X+1 and X-1 games, so including all the momentum variables in the same statistical model leads to significant problems of multicollinearity. To avoid this I fitted separate models, including only a single momentum variable in each.

THE RESULTS

The following table provides the regression results for the models including the momentum variables for X = 1 through 4. I've excluded those for X = 5 and X = 6 for reasons that I'll come to in a minute. First though, the results.

The model on the left is for X=1 and tells us that the home team's victory margin, ignoring momentum effects, can be estimated as 76.98 + 0.72 x Home Team MARS Rating - 0.79 x Away Team MARS Rating + 10.35 x Interstate Status.

The remaining coefficients provide estimates of the one-game momentum effects in each season. For Season 2000 the effect is a modest 1.89 points, meaning that a home team that had won its previous game could be expected to score a bit less than 2 points more than if it had lost its previous game. This effect is small and not statistically significant. Other coefficients are interpreted similarly.

In general for this model we see that the effect sizes are small, sometimes even negative, and often not statistically significant. A reasonable conclusion would therefore seem to be that momentum measured with a one-week window, has only a small, if any, effect.

When we stretch back just one game further, however, the story changes dramatically. Now we see much larger effect sizes, as large as 20 points in some seasons, many more of which are statistically significant. In interpreting the coefficients on the momentum variables in this model recognise that these variables can now take on one of three values (ignoring draws): 1 if the home team has won its two previous encounters, 0.5 if it won one and lost one, and 0 if it lost both. Note also the increase in R-squared as we move from the leftmost model to this one (although these are not strictly comparable as we lose a couple of observations in expanding the momentum window by an extra week). This model has much to recommend it.

Moving next to the model with momentum measured over the previous three games we see some more, modest increases in effect sizes but also find more of the momentum variable coefficients to be statistically significant. We also see a very small decline in R-squared, but not one that I'd assess as decisive.

Finally, if we use a four-game window for measuring momentum, we see reductions in effect sizes and in the number of momentum coefficients that are statistically significant. We also see a further reduction in R-squared. The results shown here are similar to those we get if we further expand the momentum window to five and to six weeks, which is why I've excluded those results here.

Forced to choose my preferred model I'd probably go with the model using a three-game window for measuring momentum, though the version with a two-game window is almost equally compelling and, in any case tells much the same story about momentum.

CONCLUSION

This modelling makes a fairly compelling case, I'd suggest, for the existence of momentum at the team level, relatively short-term in nature, in team's week-to-week game margins. So, if you wanted to predict the margin of an upcoming game - assuming that you didn't have or didn't trust bookmaker prices for that game - you'd do well to include some measure of momentum.

That said, if you were making that projection this season, you'd need to worry far less about including momentum effects. The only seasons for which the momentum variable was not statistically significant across the period modelled were 2001 and the current season, 2013 and, even if we ignore issues of statistical significance, our best estimate of the effect size of momentum for 2013 is just 4.91 points, and that's for a home team with a 3 and 0 recent record in comparison to one with an 0 and 3 record. A home team with a 2 and 1 record would have a momentum effect only two-thirds as large (ie about 3.2 points).

In summary then:

• empirically, momentum has been seen to exist in most if not all seasons
• using a three-game window to measure it, historically it's been worth about 2 to 4 goals for a home team with a perfect record compared to a home team with three strikes
• this year it's been worth substantially less than 1 goal
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