Jimmy Rollins prop

[bigboydan]

heres an interesting prop i found at wagerweb.

5-9 games might be worth a shot at +600

Jimmy Rollins Hit Safely?


0 - 4 Games -300

5 - 9 Games +600

10 - 14 Games +1500

15 - 19 Games +2500

20 Or More Games +5000

[onlooker]

5-9 looks like some good value at +600. I think the pressure of the start of the season will hurt his chances to do 10+.

[bigboydan]

i'm thinking the media won't hound rollins as much so early in the season. if anything does it, it'll be the new season starting if anythng due to the rust factor.

[bigboydan]

heres the updated odds on this one at wagerweb. seems like there was some big movers on this event.

Jimmy Rollins Hit Safely?

0 - 4 Games -400

5 - 9 Games +500

10 - 14 Games +1500

15 - 19 Games +1500

20 Or More Games +2500

[onlooker]

Man looks like people took the higher games, because they moved big time. I still like the 5-9 games even at the new +500. Still good value there.

[RickySteve]

Man looks like people took the higher games, because they moved big time. I still like the 5-9 games even at the new +500. Still good value there.

What is your reasoning behind this?

In order for this to be +EV, you need to assume that he has a >73% chance of getting a hit in any given game. Looking at the Poisson distribution for Rollins' career and '05 hits/game stats, I don't think you can make this assumption.

[Willie Bee]

Of the games he started, Rollins failed to get a hit in 39 of them (a little less than 25% of his starts). In addition to the 36-game streak he ended the year with, Rollins had two streaks of 6-games, and one each that were 8-games, 9-games and 10-games long.

Working against him coming out of chute #1 is the fact he'll face the Cardinals, Dodgers and Braves in his first nine games. The good news is the six games to start the year against St. Louis and LA are at home in Philly which is a decent park for hitters.

Pitchers he could be facing in those first nine games...(Rollins stats in parentheses).

St. Louis
C.Carpenter (.286, 4 Ks, 14 AB)
M.Mulder (.500, 0 Ks, 8 AB)
J.Suppan (.250, 0 Ks, 12 AB)
J.Isringhausen (.500, 0 Ks, 2 AB)
B.Looper (.227, 6 Ks, 22 AB)

Los Angeles
B.Tomko (.400, 0 Ks, 10 AB)
D.Lowe (.250, 0 Ks, 8 AB)
B.Penny (.216, 5 Ks, 37 AB)
D.Baez (.667, 0 Ks, 3 AB)
E.Gagne (.167, 2 Ks, 6 AB)

Atlanta
T.Hudson (.200, 0 Ks, 15 AB)
H.Ramirez (.476, 0 Ks, 21 AB)
J.Thomson (.276, 5 Ks, 29 AB)
J.Sosa (.250, 0 Ks, 12 AB)
C.Reitsma (.300, 2 Ks, 10 AB)

[Ganchrow]

In order for this to be +EV, you need to assume that he has a >73% chance of getting a hit in any given game. Looking at the Poisson distribution for Rollins' career and '05 hits/game stats, I don't think you can make this assumption.

For the +500 bet to an even money prop or better prop, it would need to occur with probability >= 16.67%.

To estimate the actual probability looking purely at the math and ignoring the matchups, we'd have to make a couple of assumptions about his BA next year and how expect ABs per game. So to that end:

1. Assume that Rollins's BA of .290 from last year continues to hold this year.
2. Assume that Rollins averages 4.25 AB per game.

So what's the probability that Rollins will get at least onen hit in any given game?
= 1-(1-.290)^4.25
≈ 76.7%

So what's the probability that Rollins will get a hit in all of the first 5 games of the season but NOT in the 6th?
≈ 76.7%^5 * (1-76.7%)
≈ 6.2%

And generalizing, the first i games but not the (i+1)th?
≈ 76.7%^i * (1-76.7%)

So the probability of Rollins hitting safely in the first 5-9 games and then not hitting safely in the following game would be:
≈ 76.7%^5 * (1-76.7%) +
76.7%^6 * (1-76.7%) +
76.7%^7 * (1-76.7%) +
76.7%^8 * (1-76.7%) +
76.7%^9 * (1-76.7%)
≈ 19.5%

which would imply that insofar as the two assumptions above are correct (ands there's definitely reason to believe that they're not completely accurate) +500 is an excellent bet yielding an expected return of 16.9%.

Of course if we could come up with better estimates of Rollins's BA and AB's against likely pitchers and teams we'd be able to more readily judge the merits of this bet.

[RickySteve]

For the +500 bet to an even money prop or better prop, it would need to occur with probability >= 16.67%.

To estimate the actual probability looking purely at the math and ignoring the matchups, we'd have to make a couple of assumptions about his BA next year and how expect ABs per game. So to that end:

1. Assume that Rollins's BA of .290 from last year continues to hold this year.
2. Assume that Rollins averages 4.25 AB per game.

So what's the probability that Rollins will get at least onen hit in any given game?
= 1-(1-.290)^4.25
≈ 76.7%

So what's the probability that Rollins will get a hit in all of the first 5 games of the season but NOT in the 6th?
≈ 76.7%^5 * (1-76.7%)
≈ 6.2%

And generalizing, the first i games but not the (i+1)th?
≈ 76.7%^i * (1-76.7%)

So the probability of Rollins hitting safely in the first 5-9 games and then not hitting safely in the following game would be:
≈ 76.7%^5 * (1-76.7%) +
76.7%^6 * (1-76.7%) +
76.7%^7 * (1-76.7%) +
76.7%^8 * (1-76.7%) +
76.7%^9 * (1-76.7%)
≈ 19.5%

which would imply that insofar as the two assumptions above are correct (ands there's definitely reason to believe that they're not completely accurate) +500 is an excellent bet yielding an expected return of 16.9%.

Of course if we could come up with better estimates of Rollins's BA and AB's against likely pitchers and teams we'd be able to more readily judge the merits of this bet.

Thanks for the 7th grade math lesson.

Your logic is flawed when you give him credit for having a fixed 4.25 AB per game. Because this is an exponent, deviations from from the mean will skew your estimates. When he gets 5 AB, the probability of him getting a hit is 82.0%, a +5.3% increase. But if he deviates the same amount in the other direction to 3.5 AB his chances of getting a hit are only 69.8%, a -6.9% difference. In other words, the games he gets fewer than average ABs hurts his chances more than the times he gets more helps him. A Poisson model is a more accurate estimate for this situation, and it gives an expected hit total >0 in 71.1% of games.

It's also a little shaky to just accept his '05 numbers as his fundamental values, since they were all career highs. On the other hand, he's entering his peak season at age 27. It's difficult to choose which factor might weigh more heavily, and it probably washes.

The bottom line is in order for the bet to be +EV you have to assume Rollins has >73% of getting a hit in any given game. I don't think this is true, but if you do, then fire away on that +500.

[Ganchrow]

The bottom line is in order for the bet to be +EV you have to assume Rollins has >73% of getting a hit in any given game. I don't think this is true, but if you do, then fire away on that +500.

I would argue that the Poisson distribution would tend to overestimate a player's chances of going hitless for any given game.

Remember that Poisson represents the limit of the binomial distribution as number of trials approaches inifinity. It's best used do describe events which could occur continuously, or at least almost continuously. The canonical example is a the number of typing errors made by a per page by a good typist. Now a good typist isn't liable to make many errors per page but nevertheless has many opportunities to do so.

Now this is not the case with hits per game.

A player is only likely to have a very limited number of plate appearances each one of which is relatively likely to produce a hit. As such, Poisson will overestimate the chances of getting a large number of hits per game and underestimate the chances of getting a small number of hits.

On another note, just as you correctly point out that when using the binomial distribution, deviations from the mean in number of at bats per game will tend to make estimates of per game hit likelihood using that mean too high, your criticism applies just as strongly to Poisson. Recall from your 7th frade math class that Poisson requires that the likelihood of the occurance of the event in question be proportional to the length of the interval over which it might occur. In this context it's just another way of saying that ABs per game would need to be constant for Poisson to hold using average hits per game.

So although you do bring up a valid criticism of the binomial distribution, you're not getting around it just by inappropriately using the Poisson distribution.

I think the way to handle this is to go exactly the way that I did. While I suppose I could have explicitly stated my methodology, I had left it out in the name of simplicity and reading ease. Anyway though, what I originally did was first come up with an a snapshot of AB distribution from the historical record. (For this I chose to use Rollins's ABs/game from games he started during the 2005 season, reprinted below.) I then looked at expected hits under each AB scenario using a BA of .290. I then took the dot product of hit likelihoods and scenario frequencies. This gave me my 76.7% figure from which I then backed out my 4.25 ABs per game statistic. (This is quite a bit lower that his actual ABs per game in 2005 of 4.34. Had we used the 4.34 figure we have seen a hit likelihood of 77.38%. That number would have been too high. Now I'm just curious -- at any point did you ask yourself why I didn't use that historically accurate 4.34 number? Or in your apparent zeal to prove me wrong did you simply overlook that fact?)

ABs	Freq	Hit Likelihood
2	0.6%	49.6%
3	8.3%	64.2%
4	50.6%	74.6%
5	37.2%	82.0%
6	3.2%	87.2%

Anyway, it probaly also makes sense to point out that in 2005 Rollins hit successfully in 74.36% of the games he started.

[bigboydan]

Jimmy Rollins stretched his hitting streak to 38 games Wednesday with a double in the first inning of Philadelphia's game against St. Louis.

[bigboydan]

it sure doesn't look good for him extending his streak today.

[bigboydan]

rollins streak ended today. did anyone win any money from this prop ?