A Game of Two Halves ?
by Denis O'Regan.
One of the easiest traps to fall into when trying to predict the likely outcome of a sporting event,is to give far too much importance to the value of recent events.For example if a strong,pre game favourite is only narrowly leading a lower rated opponent at the half or is even trailing,it is tempting to assume that the remaining part of the game will be similarly fought out.
I therefore decided to look at the outcomes of games that had not appeared to have "followed the script" for all or part of their course based on pregame assumptions.
Firstly,I needed a robust model that did a good job of predicting the likely game result.This subject is extensively covered all over the net,so I'll simply give a broad outline of the parameters I used.The four main variables used in most models are the offensive rushing and passing capabilities of both team and the defensive rushing and passing counterparts.These factors are reasonably predictable from game to game and even with little or no adjustments for strength of schedule,they have quite an impressive predictive power for future match ups.I used data gathered from at least the previous four games for each team.
Alternatively,the against the spread quotes of the Vegas line are a reliable indicator of the likely outcome.
Next I needed to ensure that game situation was not unduly influencing the points scored in the remainder of the game.Passing sides inevitably run the ball when they have a large lead and running sides are forced away from their core values if they trail.So it was decided to chose games that were tied at the interval (or within a point either way in some cases to increases sample size).This ensured that we still had a contest where both teams were playing to their strengths and trying to maximize any points they scored.
Lastly,I needed to know how the pregame expected supremacy of the favoured team would decay over the course of the game.In sports such as soccer the scoring rates of each team in a game decays as a factor of initial expected scoring rate and time remaining in such a way as there is slightly more scoring activity in the second half compared to the first.Unfortunately,the scoring in the NFL is much more messy.A score can amount to either 2,3,6,7 or 8 points and time outs and 2 two minute warnings can prolong quarters.I decided against incorporating an extensive study into how teams scoring rates decay and instead used the broadly correct assumption that by half time a favourites pre game expected points supremacy has decayed to half it's initial value.
In short,a team with a win probability at kick off of 0.78 which would expect on average to win such match up by 10 points would expect to win the second half alone by,on average 5 points.
Games tied at halftime.
In order to obtain a reasonably large number of games I was forced to go back into the '80's and I looked at all games from the view point of the team who were favoured to win,be they the home or away side.It wasn't possible to eliminate any games where a team had lost a significant player such as the quarterback during the first two quarters,but these matchups would most likely be small in number.
Almost 450 games over the 20+ year period saw a favoured team tied at half time and the average pre game expected margin of victory for those favourites was around 5.5 points.If the previous 30 minutes of action was a better indicator of the relative strengths of both teams then we would expect that the ultimate game winners would be split almost equally between the pre game favorites and the pre game underdogs.However,if the pregame model,based on at least four previous games was a better predictor we would expect the pre game favourite to win more of the half time stalemated games.
And it's the latter that occurs.
All favourites that are tied at halftime go on to win about 64% of those games and their average margin of victory in these games is around 2.5 points,about half of their predicted pre game supremacy.
If you slice and dice the sample the effect remains.Teams favoured by a field goal or more should win by an average of six points,but if they are tied at the half they still win more than half the games (66%) and the margin of victory is around a field goal.
Strong favourites win 84% of games in which they are held at the break and their margin of victory is 7 points compared to the pre game predicted 13.
However you look at things,judging a game solely on what has happened in the first 30 minutes is flawed,pre game esimates derived from a robust model is much the better indicator of what will happen in the third and fourth quarters.
If tied games after two quarters resulting in the favourite eventually winning the larger share isn't perhaps too surprising,what about overtime games,where teams appear to be equally matched over 4 quarters.Again sample sizes are small so we need to go back 20+ years,but the results are very similar.
We now have a sample size of around 300 and in almost 57% of the games the pregame favourite wins in OT,by an average margin of victory of 0.5 of a point compared to a pre game predicted m.o.v. of 6.The effect is smaller because the game is often decided in just a few drives and any score,as opposed to a maximized score is all that is required (extra points aren't kicked either).The coin toss advantage should even out (unless better teams are also lucky ones).
Again if you group the games from weak favourites to stronger favourites the effect of the better pre game side winning more than a 50% split outright remains in each and every group.For example teams favoured to win by a touchdown or more won over 60% of their games when they were taken to overtime.
Very recent,but low sample size evidence is a poor indicator of future events compared to larger sample size,but older data.
Generally speaking the best indicator of what will occur in the second half of a game is what we would have forecast before the match began, before we had watched the first half.Predictions based on probabilities describe the most likely outcome,but that outcome is not exclusive. Favourites can easily trail at the half (it's just one of the less probable outcomes),but that is not inconsistent with the pre game prediction that they are the superior side.And results suggest that on average in the second half they demonstrate their superiority regardless of what occurred in the first half.
Friday, October 16, 2009
A Game of Two Halves ?