After John Thompson said goodbye to Patrick Ewing and before he said hello to Alonzo Mourning, he had a void at the center position. In light of the quality of the aforementioned players, it was a huge void. In 1987, Thompson brought seven-footer Ben Gillery to Georgetown from the junior college ranks. Gillery, in a word, was a "project" and he never quite panned out. What I remember about him was that he would start a game, be pulled at the first stoppage, and never return. I marveled at box scores where he was listed as a starter, played 2 minutes, and the rest of his line was filled with zeroes. It was like his only purpose was to win the jump ball.

In truth, my memory can’t be too accurate, since according to Jazzy J’s site, Gillery averaged about eight minutes a game during his career. So the two-minute games must have been rare. Nonetheless, I want to test how important a Ben Gillery as I remembered him would be. How important is it to win the opening tip?

Actually, what I really want to know is this: how important is it to have one more possession that your opponent? When computing possession statistics, by convention it’s assumed that each team has an equal number of possessions. But in reality, this doesn’t have to be true. Because teams alternate possessions, if one team starts and ends a half with the ball, they can have one more possession than the opponent in each half. This happens in roughly 50% of all games. Winning the opening tip doesn’t guarantee you an extra possession for the game, but it certainly increases your chances.

To demonstrate how much of an advantage this is, I’ll use the Pythagorean formula. As regular readers have figured out by now, I think this formula can be used to solve any of college basketball’s great mysteries. And here’s another example.

Let’s say teams A and B both average a point per possession. In a 70 possession game, you’d expect each team to score 70 points (totally ignoring defense). So A’s expected winning percentage against B would be…

70^10 / ( 70^10 + 70^10 ) = .500

We didn’t need to work through this formula to know that Team A has a 50% chance to beat a team equal to it. But what if Team A gets an extra possession? They would be expected to score 71 points in their 71 possessions. Their expected winning percentage in this scenario would be…

71^10 / ( 71^10 + 70^10 ) = .535

So the Gillery effect results in an increased chance of winning of 3.5% in this case. As I said before, winning the tip does not guarantee an extra possession. But in the long haul, teams winning the tip will average about a half a possession more than their opponent. (Actually, for reasons I won’t get into it’s probably slightly less than that.) Since losing the tip results in a loss of a half possession, it’s accurate to say that the tip itself is worth a possession.

Naturally, in a game with fewer possessions, the tip is more valuable. Here’s a list of the increased chance of winning in games with various tempos.

        Incr. in
Poss      Win%
 85       2.9 
 80       3.1 
 75       3.3 
 70       3.5 
 65       3.8 
 60       4.1 
 55       4.5 
 50       4.9 

So in those methodical Horizon League games, the tip means more than in the relatively frenetic ACC games.

But this is the best case scenario. As teams become more unequal, the extra possession means less. If All-American Team is playing Intramural Scrubs, it doesn’t matters who gets the extra possession, All-American Team will win all of the time.

For a more realistic example, let’s use teams that average 1.1 and 0.9 points per possession. With each team getting 70 possessions, Team A wins 88.1% of the time…

77^10 / ( 77^10 + 63^10 ) = .881

Give Team A an extra possession and that figure improves to 89.6…

78.1^10 / (78.1^10 + 63^10 ) = .896

That’s a difference of only 1.5%, compared to 3.5% for the game between equal teams.

This is more than we really needed to know on the impact a seldom used Georgetown center had on the game over 15 years ago. Nonetheless, this exercise illustrates that the jump ball is more than a ceremonial start to the game.