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ANALYSIS OF THE GAME OF BASKETBALL
Why Do "Upsets" Occur?
No team plays its average every night, and there is a normal distribution of performance levels about any mean, especially when we examine human performances. When a team with an lower mean performance level competes against a team with a higher mean performance level, the outcome is not ever guaranteed. When the team of lesser talent plays better than average and the team with superior talent plays at its average or below average, upsets often occur.
The probability of such an upset is determined by the magnitude of the separation between the two teams' average performance levels and the standard deviation between the predicted and actual game margins. When these averages are close, but different by slight amounts, the probability of an "upset" if you insist on calling it that approaches 50%. As this separation increases the probability of an upset declines. It never reaches 0%, but it does approach 0% as the difference becomes larger.
The statistical analysis applies to all games. Some games do end up with upset outcomes because the superior team played enough below its average and the inferior team played enough above its average to overcome the statistical differences that separate them on average.
If you will consider a team's distribution of performance data and you should imagine the classic bell shaped curve defined in classic statistical terms with a Standard Deviation and a Mean. Consider two such curves for the opponents of a game. If both curves have the same mean and same standard deviation, they will overlap perfectly. In this special case, each team has a 50% probability of winning, e.g the total area under their curve divided by the total areas under both curves combined.
As these two bell shaped curves move apart, by either increasing the mean of one or decreasing the mean of the other, these curves no longer overlap perfectly, but they will overlap in smaller proportions. As this shift occurs, the probabilities of winning also shift. The calculation becomes the area of over lap for the underdog divided by the total area of the favorite plus the area of the overlap of the underdog. As the shift continues to become greater, eventually, the amount of the overlap will approach zero, at which time the probability of any upset occurring also approaches zero.
I remember my dad explaining to me once about baseball that the best team in the league will lose 1/3 of its games regardless of how good they are, and the worst team in the league will win 1/3 of its games regardless of how bad they are. The teams that win most of that middle 1/3 of games, those that can be won, but are often lost, are the teams that will succeed over the course of a full season. In baseball, the overlap of these bell shaped curves is greater than in college basketball, from best to worst, but the principle is the same. These relationships are all statistical.
Many fans have observed that recent UK teams are inconsistent and more prone to being upset as a result of their inconsistency. However, an examination of the statistical relationships describe above illustrate why recent UK's team have been more prone to upset over the last few years is not inconsistency, but a decline in the quality of play. The standard deviation about UK's mean performance level has remained within a fairly narrow range. However, the mean value of that performance has fallen.
When a team moves from near the top levels of performance toward lower levels of performance, more and more games become "competitive" because competitiveness increases on the upside and remains constant on the downside as means fall. Therefore, you see a team that does indeed win games that most think it should lose, and losing games that most believe they should win. However, when a team is at the top of the game, the only "upsets" that can occur are on the downside. This creates a false perception of inconsistency, and the talking heads on TV and radio will talk about the inconsistency endlessly, but in fact the consistency, measured by the standard deviation about a mean, remains the same.
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