Found on Twitter this afternoon:
Just made a bet with a co-worker that Utley won’t get an extra base hit in his first game back.Thoughts?#gophils #gotigers
— Logical Betting (@LogicalBetting) June 26, 2012
A picosecond after reading that I thought “sure, that’s a great bet.” Then I realized that it was not the first at-bat in his first game back, but the entire game. Also, terms were not specified.
But supposing it was even money, I was still pretty sure this was a good bet for our Tweep.
Now off to the spreadsheet to check.
| Chase Utley Career to June 26, 2012 | |
|---|---|
| Stat | Number |
| Plate Appearances: | 4,778 |
| Doubles: | 258 |
| Triples: | 34 |
| Home Runs: | 188 |
| XBH: | 480 |
| XBH Rate | 10% |
| Non-XBH Rate | 90% |
Using that as a basis, the chance of going 4 plate appearances without an XBH are (0.9)4 = .655, or 65.5%.
The chance of going 5 plate appearances without an XBH are (0.9)5 = .588 or 58.8%. Still in favor of the “no” on the prop bet.
If Utley somehow gets to the plate 6 times the chance of going without an extra base hit is still 53%. And six plate appearances is not likely, even if Utley were not just making a return from injury.
In case you want to make that prop bet (Will he have 6 PA in the game), you can offer long odds on it. Rollins has only had 6 or more PA in 4 games out of 75 this year. Ian Kinsler has the most games in MLB this year with 6 or more PA, with 8 in 72 games played. Offer 8 to 1 on that and collect some ducats.
Utley read this. Got mad. Killed first available pitch.